CN114503019A - Quantum mechanics framework for OAM interaction with matter and applications in solid state, bioscience and quantum computing - Google Patents

Abstract

One method includes first generating a plane wave beam. At least one orbital angular momentum is applied to the plane wave beam to generate a sum OAM beam. Transitions of electrons between quantized states within the semiconductor material are controlled in response to at least one orbital angular momentum applied to the plane wave beam. An OAM beam is emitted at the semiconductor material to induce transitions of electrons between quantized states within the semiconductor material.

Description

A quantum mechanical framework for OAM-matter interactions and applications in solid-state, bioscience, and quantum computing

CROSS-REFERENCE TO RELATED APPLICATIONS

This application calls for a document entitled "QUANTUM MECHANICAL FRAMEWORK FORINTERACTION OF OAM WITH MATTER AND APPLICATIONS IN SOLID", entitled "QUANTUM MECHANICAL FRAMEWORK FORINTERACTION OF OAM WITH MATTER AND APPLICATIONS IN SOLID", filed on October 22, 2019 STATES, BIOSCIENCESAND QUANTUM COMPUTING)" (Attorney Docket No. NXGN60-34719) of US Patent Application No. 16/660246 priority and/or interest. This application also claims priority to U.S. Provisional Application No. 62/902146 (Attorney Docket No. NXGN60-32718), entitled OAM BEAM INTERACTIONS WITHMATTER FOR APPLICATIONS TO SOLID STATES, BIOSCIENCES AND QUANTUM COMPUTING, filed on September 18, 2019 and/or or interest, the specification of which is incorporated herein by reference in its entirety.

technical field

The present invention relates to controlling the motion of particles within a material, and more particularly, to controlling the motion of particles using the orbital angular momentum of photons applied to a beam of light.

Background technique

In photonic devices, light energy is used to excite electrons to higher energy levels and generate electrical energy or current in response to the light energy. The ability to control electronic states in materials such as semiconductors, biological materials, and quantum computers has many advantages over these materials. Currently, the available technology suffers from many flaws. Accordingly, certain means for increasing the ability to control electronic states within various types of materials would provide many improvements in the use and operation of these materials.

SUMMARY OF THE INVENTION

As disclosed and described herein, the present invention includes, in one aspect thereof, a method involving first generating a plane wave beam. At least one orbital angular momentum is applied to the plane wave beam to generate an OAM beam. Transitions of electrons within the semiconductor material between quantized states are controlled in response to at least one orbital angular momentum applied to the plane wave beam. The OAM beam is transmitted at the semiconductor material to induce transitions of electrons within the semiconductor material between quantized states.

Description of drawings

For a more complete understanding, reference is now made to the following description taken in conjunction with the accompanying drawings, in which:

Figure 1A shows a general view of various components of a general-purpose quantum computer system using OAM Quantum Dieter with DLP;

Figure 1B shows a block diagram of a general-purpose quantum computer system using OAM Quantum Dieter with DLP;

Figure 2 shows the use of spin polarization for quantum gate input;

Figure 3 shows the use of OAM for quantum gate input;

Figure 4 shows various types of quantum logic circuits;

Figure 5 shows a single-bit revolving gate;

Figure 6 shows a two-bit controlled NOT gate; and

Figure 7 shows a quantum Dieter network.

8 illustrates various techniques for increasing spectral efficiency within a transmitted signal;

9 illustrates particular techniques for increasing spectral efficiency within a transmitted signal;

Figure 10 shows a general overview of the manner in which communication bandwidth is provided between various communication protocol interfaces;

11 is a functional block diagram of a system for generating orbital angular momentum within a communication system;

Figure 12 is a functional block diagram of the orbital angular momentum signal processing block in Figure 6;

13 is a functional block diagram illustrating the manner in which orbital angular momentum is removed from a received signal comprising multiple data streams;

Figure 14 shows a single wavelength with two quantum spin polarizations providing an infinite number of signals with various orbital angular momentums associated therewith;

Figure 15A shows an object with spin angular momentum;

Figure 15B shows an object with orbital angular momentum;

Figure 15C shows a circularly polarized beam carrying spin angular momentum;

Figure 15D shows the phase structure of a beam carrying orbital angular momentum;

Figure 16A shows a plane wave with only a change in spin angular momentum;

Figure 16B shows a signal with spin and orbital angular momentum applied;

Figures 17A-17C show various signals applied with different orbital angular momentum;

Figure 17D shows the propagation of Poynting vectors for various eigenmodes;

Figure 17E shows a spiral phase plate;

Figure 18 shows a system for free-space spatial multiplexing using the orthogonality of the HG modality;

Figure 19 shows various ways for converting a Gaussian beam to an OAM beam;

Figure 20 shows a manner for generating a beam comprising orthogonal functions;

Figures 21A-21H show holograms that can be used to modulate light beams;

22A is a block diagram of a digital micromirror device;

Figure 22B shows the way the micromirror interacts with the light source;

Figure 23 shows the mechanical structure of the micromirror;

24 is a block diagram of the functional components of a micromirror;

Figure 25 shows a flowchart of a process for changing the position of a micromirror;

Figure 26 shows the intensity of a phase interferometer used to measure the intensity and phase of the generated beam;

Figure 27A illustrates the manner in which switching between different OAM modes can be achieved in real time;

Figure 27B illustrates the manner in which a transmitter processes multiple data channels passing through a cylindrical lens to a focusing lens;

Figure 28 shows the window transmission curve for Corning 7056;

Figures 29-33 are enlarged views of the visible and UV AR coating window transmittance of Corning 7056;

Figure 34 shows a circuit for generating an OAM twisted beam using a hologram within a microelectromechanical device;

Figure 35 illustrates multiplexing using multiple single holograms;

Figure 36 shows various simplified binaries for applying OAM level holograms;

Figure 37A shows the combined use of OAM and polarization processing;

Figure 37B shows a basic quantum module;

Figure 38 shows an example of a quantum gate;

Figure 39 shows a quantum Dieter gate implemented using OAM degrees of freedom;

Figure 40 shows an OAM-based quantum Dieter teleportation module;

Figure 41 shows the syndrome calculator module;

42 shows syndromes for identifying quantum errors based on syndrome measurements;

Figure 43 shows a block diagram of a quantum computer;

Figure 44 shows an E/O modulator;

Figure 45 shows a generalized CNOT gate;

Figure 46 shows the operation of a CNOT gate on a quantum register consisting of two qubits;

Figure 47 shows a block diagram of an OAM processing system utilizing quantum key distribution;

Figure 48 shows a basic quantum key distribution system;

Figure 49 shows the manner in which two separate states are combined into a single conjugate pair within a quantum key distribution;

Figure 50 illustrates one way in which 0 and 1 bits can be sent using different bases within a quantum key distribution system;

Figure 51 is a flowchart illustrating a process by which a transmitter sends a quantum key;

Figure 52 illustrates the manner in which a receiver can receive and determine a shared quantum key;

Figure 53 shows in more detail the manner in which a transmitter and receiver can determine a shared quantum key;

54 is a flowchart illustrating a process for determining whether to keep or relinquish a determined key;

Figure 55 shows a functional block diagram of a transmitter and receiver utilizing a free-space quantum key distribution system;

Figure 56 shows a network cloud-based quantum key distribution system;

Figure 57 shows a high-speed single-photon detector in communication with multiple users;

Figure 58 shows a node quantum key distribution network;

Figure 59 shows the beam;

Figure 60 shows a plane wavefront;

Figure 61 shows a helical wavefront;

Figure 62 shows the generation of electron-hole pairs using a Light Harvesting Complex (LHC);

Figure 63 shows the generation of electron-hole pairs using an Organic Photovoltaic Cell (OPV);

Figure 64 shows the effect of spin and dispersion on electron-hole recombination;

Figure 65 shows the effect of an OAM twisted beam on electron-hole recombination;

Figure 66 shows a functional block diagram of one approach for improved suppression of electron-hole recombination in photonic circuits;

Figure 67 shows the way electrons move between different states within an organic photovoltaic cell;

68 is a flow chart illustrating a process for controlling electron-hole recombination using orbital angular momentum applied to a beam;

Figure 69 shows a flowchart of a process for applying OAM to electrons using a beam;

Figure 70 shows a block diagram of a system for performing the operations shown in Figure 69;

Figure 71 illustrates the manner in which various energy bands of a semiconductor can be excited by photoexcitation;

Figure 72 illustrates the use of orbital angular momentum in photons to impart orbital angular momentum to electrons, resulting in current and magnetic fields;

Figure 73 shows a flowchart of a process for determining the total current/magnetic field provided by a set of electrons;

Figure 74 shows a flow chart for determining the effect of the mean field and collision terms of twisted light;

Figure 75 shows a flow diagram for determining beam interactions of a volume system using a solid imagined as a cylinder;

Figure 76 shows electrons within an ionic lattice within a solid;

Figure 77 shows a manner for encoding information by twisting a state function (wave function);

Figure 78 shows an example of weaving anyons;

Figure 79 shows the braiding of any sub-stent;

Figure 80 shows another example of weaving;

Figure 81 shows the interaction between OAM light and graphene;

Figure 82 shows a graphene lattice in a honeycomb structure; and

Figure 83 shows the means for making corrections to gene sequences using CRISPR-CAS9 technology using OAM beams.

Detailed ways

Referring now to the drawings, wherein like reference numerals are used throughout to refer to like elements throughout, various views of the quantum mechanical framework for the interaction of OAM with applications in solid state, biological science, and quantum computing are illustrated and described and embodiments, and other possible embodiments are described. The drawings are not necessarily to scale, and in some instances, the drawings have been exaggerated and/or simplified in places for illustrative purposes only. Based on the following examples of possible embodiments, those of ordinary skill in the art will appreciate many possible applications and variations.

Referring now to FIG. 1A , there is shown a general view of various components that facilitate the use of a general-purpose quantum computer system using OAM quantum dits (qudits) with DLP. The present invention uses a method for both quantum communication and quantum computing applications 100 to work simultaneously using OAM Quantum Dieter to achieve Quantum-Dieter Gate 102 and Quantum with Integrated Photonics (ie DLP) 106 Dieter Quantum Key Distribution (QKD) 104. The OAM signal is generated using DLP 106 and allowed to propagate through fiber 108 using OAM propagation. OAM-propagated signals are used within a quantum-Dieter gate 102 and a quantum-Dieter QKD 104 may be utilized to perform quantum computation, communication, and encryption 100 . A quantum diet contains a quantum unit of information that can take any of d states, where d is a variable.

Referring now to FIG. 1B , a block diagram of a general-purpose quantum computer system using OAM Quantum Dieter with DLP is shown. Input data stream 120 is provided to OAM 122 to apply OAM values to data 120 . OAM processing enables photons to carry any number of bits per photon. As described below, the OAM processed data bits are applied to photons using DLP techniques of DLP processing 123 . The signal from the DLP process 123 is provided to a quantum Dieter 124 . Quantum Dieter gates 124 may include generalized X gates, generalized Z gates, and generalized CNOT gates, which are quantum Dieter versions of existing quantum bit (qubit) gates. Quantum Dieter 124 may also include modules, such as fault-tolerant quantum computing modules, QKD modules, and the like. These modules can provide quantum error correction (ie, non-binary syndrome modules); entanglement-assisted QKD (ie, generalized Bell states, etc.). The basic quantum Dieter 124 will include a QFT (Quantum Fourier Transform). Therefore, an F gate on a quantum ditter has the same effect as a Hadamard gate on a qubit, |0> is mapped to 1/sqrt(2){|0>+|1>}, |1> is mapped to 1/sqrt(2){|0>-|1>}. The signal emitted from the quantum Dieter gate 124 may then be used, for example, in a quantum key distribution (QKD) process 126 . Existing QKDs with high-speed communication and computation are very slow. By using the system described herein, both security and throughput can be increased while further increasing the computational and processing power of the system.

The photon angular momentum of photons can be used to carry spin angular momentum (Spin Angular Momentum, SAM) and orbital angular momentum (Orbital Angular Momentum, OAM) to transmit multiple data bits. SAM is polarization dependent, whereas OAM is related to the azimuthal phase dependence of the complex electric field. Assuming that the OAM eigenstates are mutually orthogonal, each single photon can transmit a large number of bits. This is explained in more detail with respect to FIGS. 2 and 3 . FIG. 2 shows how polarization spins 202 are applied to data bit values 204 to generate qubit values 206 . Because each data bit value 204 may only have positive or negative spin polarization applied to it, only one pair of qubit states is available for each data value. However, as shown in FIG. 3 , if an OAM value 302 is applied to each data bit value 304 , a greater number of quantum Ditt values 306 may be obtained for each data bit value 304 . The number of quantum Ditt values may range from 1 to N, where N is the maximum number of distinct OAM states applied to the data value 304 . The manner for applying the OAM value 302 to the data bit value 304 may use the DLP process 123 described more fully below.

Returning now to FIG. 1, OAM propagation in optical fiber 108 may be used to transmit the OAM processed signal. The ability to generate/analyze states with different photon angular momentums imposed on them by using holographic methods allows quantum states to be realized in multidimensional Hilbert space. Because the OAM state provides an infinite ground state, whereas the SAM state is only 2-D, the OAM state can also be used to increase the security of quantum key distribution (QKD) applications 104 and increase the computational power of quantum computing applications 100 . The goal of this system is to build deterministic universal quantum quantum Dieter gates 102 based on angular momentum, i.e., generalized X quantum gates, generalized Z quantum gates, and generalized CNOT quantum gates, as well as different quantum modules of importance for various applications, Includes fault-tolerant quantum computing, teleportation, QKD, and quantum error correction. For example, basic quantum modules for quantum teleportation applications include generalized Bell state generation modules and QFT modules. The basic module for entanglement-assisted QKD is the generalized Bell state generation module or the Weyl operator module. The approach is to implement all these modules in integrated optics using a multidimensional quantum ditter on DLP.

In quantum computing, a quantum bit, or qubit, is the fundamental unit of quantum information, and includes a quantum version of a classical binary bit that is physically implemented using two-state devices. Qubits are two-state quantum mechanical systems, one of the simplest quantum systems that exhibit quantum mechanical properties. Examples include: the spin of an electron, where the two energy levels can be thought of as spin-up and spin-down; or the polarization of a single photon, where the two states can be thought of as vertical and horizontal polarization. In classical systems, bits must be in one state or the other. However, quantum mechanics allows qubits to be in a coherent superposition of two states/energy levels at the same time, a property of quantum mechanics and thus the basis of quantum computing.

>保持状态|0>和|1>的相干叠加：In quantum computing, the concept of "qubit" has been introduced as the counterpart to the classical concept of "bit" in conventional computers. The two qubit states labeled |0> and |1> correspond to classical bits 0 and 1, respectively. Arbitrary Qubit State|

>Keep the coherent superposition of states |0> and |1>:

>以概率|a|²塌陷为|0>状态，抑或以概率|b|²塌陷为|1>状态，且满足|a|²+|b|²＝1。where a and b are complex numbers called probability magnitudes. That is, the qubit state|

> collapse into the |0> state with probability |a| ² , or collapse into |1> state with probability |b| ² , and satisfy |a| ² +|b| ² =1.

>被描述为Qubit State|

> is described as

This is called a Bloch spherical representation. To give a minimal representation of an elementary quantum logic gate, it is rewritten as a function with a complex-valued representation by corresponding the probability magnitudes a and b as the real and imaginary parts of the function, respectively. A quantum state with a complex-valued representation is described as

f(θ)=e ^iθ =cosθ+i sinθ,

In quantum computing, especially the quantum circuit model of computing, quantum logic gates (or simply quantum gates) are basic quantum circuits that work on a small number of qubits. They are the building blocks of quantum circuits, just like the classical logic gates used in traditional digital circuits.

quantum gate

In quantum computing, especially the quantum circuit model of computing, quantum logic gates (or simply quantum gates) are basic quantum circuits that work on a small number of qubits. They are the building blocks of quantum circuits, just like the classical logic gates used in traditional digital circuits.

Unlike many classical logic gates, quantum logic gates are reversible. However, classical computations can be performed using only reversible gates. For example, a reversible Toffoli gate can implement all Boolean functions, usually at the expense of having to use auxiliary bits. Tofley gates have direct quantum equivalents, showing that quantum circuits can perform all the operations performed by classical circuits.

Quantum logic gates are represented by unitary matrices. The most common quantum gates operate on a space of one or two qubits, just as common classical logic gates operate on one or two bits. As a matrix, a quantum gate can be described by a unitary matrix of size 2 ⁿ × 2 ⁿ , where n is the number of qubits the gate acts on. The variable that the gate acts on, the quantum state, is a vector of ²ⁿ complex dimensions, where n is again the number of qubits of the variable. Basis vectors are possible outcomes if measured, and quantum states are linear combinations of these outcomes.

Referring now to FIG. 4 , in a quantum logic circuit, the elementary quantum gates 3802 are a single-bit rotating gate 404 and a two-bit controlled NOT gate 406 . Any quantum logic circuit can be constructed by the combination of these two gates. As shown in FIG. 5 , a single-bit spin gate 404 takes a quantum state as its input 502 and outputs a spin state in the complex plane at its output 504 . The gate can be described as f(θ ₁ +θ ₂ )=f(θ ₁ )·f(θ ₂ ).

As shown in FIG. 6, a two-bit controlled NOT gate 602 takes as its input 602 two quantum states and gives two outputs: one of the input states 604 and the XOR result 606 of the two inputs. To describe this operation, one needs to represent the inversion and non-inversion of the quantum state, so a controlled input parameter is introduced

The output state of neuron k denoted as x _k is given as:

Similar formulations for quantum diets and corresponding neural network methods are also available.

In recent years, scientists have developed quantum neural computing, in which quantum computing algorithms are used to improve the efficiency of neural computing systems. In information processing systems, both quantum states and quantum computing operators are important to achieve parallelism and plasticity, respectively. Complex-valued representations of these quantum concepts allow neural computing systems to advance in their ability to learn and expand the possibilities for their practical applications. The aforementioned application of nonlinear modeling and prediction to AI can be implemented according to two specific proposals. One is to use a qubit neural network model based on two-dimensional qubits, and the other is to extend qubits to multi-dimensional qubits and further study their characteristics, such as the effects of quantum superposition and probabilistic interpretation in a way that applies quantum computing to neural networks .

One of the applications of quantum networks is the prediction of time series from dynamical systems, especially from chaotic systems, through its various applications. There have been several attempts to use real-valued neural networks for prediction, but no attempt has been made to use a complex-valued quantum Dieter-based neural network for nonlinear attractor reconstruction, where learning iterations, learning success rates, and prediction errors can be examined. Thus, as shown in FIG. 7 , a quantum Dieter-based network 702 can enable nonlinear modeling and prediction of AI 704 , which generates nonlinear attractor reconstructions 706 from time series data 708 .

The process enables the development of quantum neural computing, where algorithms from quantum computing are used to improve the efficiency of neural computing systems, and these algorithms can be combined with attractors for predicting future behavior. The attractor method is entirely classical rather than quantum mechanical. For example, a simple process of delayed embedding occurs multiple times in parallel when delaying embedding to reconstruct attractors, so quantum computing can be used to parallelize the process of performing delayed embedding in real time. The first implementation is to use a two-dimensional qubit-based neural network model of qubits to construct attractors and provide predictions of future behavior as described in this paper, and the second implementation is to extend qubits to multiple dimensions for the same purpose Quantum Diet, and further study their characteristics, such as the effects of quantum superposition and probabilistic interpretation in the way quantum computing is applied to neural networks.

OAM generation

Applying orbital angular momentum to the photons provided as inputs to the quantum gate enables a larger amount of data to be provided to each individual photon. The use of OAM enables each photon to carry any number of bits. Achieving higher data portability may be one of the main interests of the computing community. This has led to studies using different physical properties of light waves for communication and data transmission, including amplitude, phase, wavelength and polarization. Orthogonal modes in spatial locations are also under investigation and appear to be useful as well. Generally these research efforts can be grouped into two categories: 1) encoding and decoding more bits on a single optical pulse; a typical example is the use of advanced modulation formats, which encode information about amplitude, phase and polarization state, and 2) Multiplexing and demultiplexing techniques that allow parallel propagation of multiple independent data channels, each with different optical properties (e.g. wavelength, polarization, and space, corresponding to Wavelength-Division Multiplexing, WDM), Polarization-Division Multiplexing (PDM), and Space Division Multiplexing (SDM)). One way to achieve higher data capacity is through the use of OAM communications and computing, which is the process of applying orbital angular momentum to communications/quantum computing signals to prevent interference between signals and provide increased bandwidth, as in As described in US Patent Application No. 14/864,511, entitled "Application of Orbital Angular Momentum to Optical Fiber, FSO, and Radio Frequency (RF)," which is incorporated herein by reference in its entirety.

The recognition of the existing applications of orbital angular momentum (OAM) in communications and quantum computing has made it an interesting research topic. It is well known that photons can carry spin angular momentum and orbital angular momentum. In contrast to spin angular momentum (eg, circularly polarized light) discriminated in the direction of the electric field, OAM is typically carried by a beam with a helical phase wavefront. Owing to the helical phase structure, OAM-carrying beams typically have annular intensity distributions with a phase singularity at the center of the beam. Importantly, depending on the discrete twist velocities of the helical phase, it is possible to quantify that OAM beams are distinct states that are fully distinguishable when propagating on-axis. This property allows OAM beams to potentially be used in either of the above two categories to help improve the performance of free-space or fiber-optic communication or quantum computing systems. Specifically, OAM states can be used as different dimensions to encode bits on a single pulse (or single photon), or to create additional data carriers in SDM systems.

There are several potential benefits to using OAM for communications and quantum computing, and some new types of specially designed fibers allow for less mode coupling and crosstalk when propagating in the fiber. Furthermore, OAM beams with different states share a ring-shaped beam profile that indicates the rotational insensitivity for receiving the beam. Since the differentiation of OAM beams does not depend on wavelength or polarization, OAM multiplexing can be used in addition to WDM and PDM techniques, which can provide potentially improved system performance.

Referring now to the drawings, and more particularly to FIG. 8, two ways of increasing the spectral efficiency of a communication system or quantum computing system are shown. Generally, there are basically two ways to improve the spectral efficiency 802 of a communication system or quantum computing system. This improvement can be achieved by signal processing techniques 804 in the modulation scheme, or by using multiple access techniques. Additionally, spectral efficiency can be improved by creating new eigenchannels 806 within electromagnetic propagation. The two technologies are completely independent of each other, and innovations in one category can be added to innovations in the other. Therefore, this combination of technologies introduces further innovations.

Spectral efficiency 802 is a key driver of business models for communication systems or quantum computing systems. Spectral efficiency is defined in bits/sec/hz, and the higher the spectral efficiency, the better the business model. This is because spectral efficiency can translate to a larger number of users, higher throughput, higher quality, or some of each of the foregoing within a communication system or quantum computing system.

Regarding techniques using signal processing techniques or multiple access techniques. These technologies include innovations such as TDMA, FDMA, CDMA, EVDO, GSM, WCDMA, HSPA, and the latest OFDM technology used in 4G WIMAX and LTE. Almost all of these techniques use a decades-old modulation technique based on sinusoidal eigenfunctions known as QAM modulation. In a second category of techniques involving the creation of new eigenchannels 806, innovations include diversity techniques (including spatial and polarization diversity) and Multiple Input/Multiple Output (MIMO), where uncorrelated The radio path creates independent eigenchannels and electromagnetic wave propagation.

Referring now to Figure 9, the present system configuration introduces two techniques that are completely independent of each other, one from the category of signal processing techniques 804 and one from the category of creating new eigenchannels 806. Their combination provides a unique way to disrupt the access portion of an end-to-end communication system or quantum computing system, from twisted pair and cable to fiber optics, to free space optics, to use in cellular, backhaul and satellite RF, to RF satellite, to RF broadcast, to RF point-to-point, to RF point-to-multipoint, to RF point-to-point (backhaul), to RF point-to-point (fronthaul to provide cloudification and virtualization for RAN and cloud HetNet higher throughput CPRI interface), to Internet of Things (IOT), to Wi-Fi, to Bluetooth, to personal device cable replacement, to hybrid RF and FSO systems, to radar, to electromagnetic tags and to all type of wireless access. The first technique involves the use of new signal processing techniques that use new quadrature signals to upgrade QAM modulation using non-sinusoidal functions. This is called Quantum Level Overlay (QLO) 902. The second technique involves applying a new electromagnetic wavefront using a property of electromagnetic waves or photons known as Orbital Angular Momentum (QAM) 104 . In the combination of quantum level layer stacking technique 902 and orbital angular momentum application 904, the application of each uniquely provides an order of magnitude higher spectral efficiency 906 within a communication system or quantum computing system.

Regarding the quantum level superposition technique 209, new eigenfunctions are introduced which, when superimposed (overlapping each other within one symbol), significantly improve the spectral efficiency of the system. The quantum horizontal layer superposition technique 902 borrows special quadrature signals that reduce the time-bandwidth product from quantum mechanics, thereby improving the spectral efficiency of the channel. Each quadrature signal is superimposed as an independent channel within the symbol. These independent channels differentiate this technique from existing modulation techniques.

Regarding the application of orbital angular momentum 904, the technique introduces a twisted electromagnetic wave or beam with a helical wavefront carrying orbital angular momentum (OAM). The different OAMs carrying the waves/beams can be mutually orthogonal to each other in the spatial domain, allowing the waves/beams to be efficiently multiplexed and demultiplexed within the link. OAM beams are of interest in communications or quantum computing due to their potential ability to specifically multiplex multiple independent data-carrying channels.

Regarding the combination of quantum horizontal layer stacking technique 902 and orbital angular momentum application 904, this combination is unique in that OAM multiplexing techniques are compatible with other electromagnetic techniques such as wavelength and polarization division multiplexing. This indicates the possibility of further improving system performance. The combined application of these technologies in high-capacity data transmission disrupts the access portion of end-to-end communication systems or quantum computing systems, from twisted pair and cable to fiber optics, to free space optics, to cellular/backhaul and satellite RF used, to RF satellite, to RF broadcast, to RF point-to-point, to RF point-to-multipoint, to RF point-to-point (backhaul), to RF point-to-point (fronthaul to provide cloudification and virtualization for RAN and cloud HetNet enhanced higher throughput CPRI interfaces), to the Internet of Things (IOT), to Wi-Fi, to Bluetooth, to personal device cable replacement, to hybrid RF and FSO systems, to radar, to electromagnetic tags and to All types of wireless access.

Each of these techniques can be applied independently of each other, but the combination offers a unique opportunity to improve not only spectral efficiency but also spectral efficiency without sacrificing distance or signal-to-noise ratio.

Using the Shannon capacity equation, it is possible to determine if there is an increase in spectral efficiency. This mathematically translates to more bandwidth. Because bandwidth has value, spectral efficiency gains can easily be converted into financial benefits to estimate the commercial impact of using higher spectral efficiencies. Furthermore, when using sophisticated Forward Error Correction (FEC) techniques, the net effect is higher quality at the expense of some bandwidth. However, if higher spectral efficiency (or more virtual bandwidth) can be achieved, some of the gained bandwidth can be allowed to be sacrificed due to FEC, so higher spectral efficiency can also translate to higher quality.

System vendors are interested in improving spectral efficiency. However, the problem with this improvement is cost. Each technology at different layers of the protocol has a different price tag associated with it. Technologies implemented at the physical layer have the greatest impact, as other technologies can be superimposed on top of the underlying technologies and thus further improve spectral efficiency. The price tag of some technologies can be significant when other associated costs are considered. For example, multiple-input multiple-output (MIMO) techniques use additional antennas to create additional paths, where each RF path can be treated as an independent channel, and thus improve aggregate spectral efficiency. In a MIMO scenario, the operator has other associated soft costs of dealing with structural issues such as antenna installation. Not only do these techniques have huge costs, but they have huge timing issues, as structural activities take time and there are significant delays in achieving greater spectral efficiency, which also translate into financial losses.

The quantum level layer superposition technique 902 has the ability to create independent channels within the symbols. This would have huge cost and time benefits compared to other techniques. Furthermore, the quantum level layer stacking technique 902 is a physical layer technique, which means that there are other techniques at higher layers of the protocol that can all sit on top of the QLO technique 902, and thus improve spectral efficiency even further. The QLO technique 902 uses the standard QAM modulation used in OFDM-based multiple access technologies such as WIMAX or LTE. QLO technique 902 essentially enhances QAM modulation at the transceiver by injecting new signals into the baseband I&Q components and adding them up before QAM modulation, as will be described more fully below. At the receiver, the inverse process is used to separate the superimposed signals, and the net effect is pulse shaping, which enables better spectral localization than standard QAM or even root raised cosine. The effect of this technique is to have significantly higher spectral efficiency.

Referring now more specifically to FIG. 10 , there is shown the use of a combination of multi-level superposition modulation 1004 and application of orbital angular momentum 1006 to increase the number of communication channels or the amount of data transmitted, thereby providing improved communication within various interfaces 1002 A general overview of how bandwidth and/or data transfer bandwidth.

The various interfaces 1002 may include various links, such as RF communications, wired communications (such as cable or twisted pair connections), or optical communications utilizing optical wavelengths (such as fiber optic communications or free space optics). Various types of RF communications can include a combination of RF microwave or RF satellite communications, and real-time multiplexing between RF and free-space optical signals.

By combining the multi-layer superposition modulation technique 1004 with the orbital angular momentum (OAM) technique 1006, higher throughput can be achieved on various types of links 1002. The use of multi-level superposition modulation alone without OAM can improve the spectral efficiency of the communication link 1002, whether wired, optical, or wireless. However, with OAM, the increase in spectral efficiency is more significant.

The multi-level superposition modulation technique 1004 provides new degrees of freedom beyond the conventional 2 degrees of freedom, where time T and frequency F are independent variables in a two-dimensional symbol space that defines orthogonal axes in the information graph. This includes a more general approach than modeling the signal as a fixed frequency domain or fixed time domain. Previous modeling methods using fixed time or fixed frequency were considered to be more restrictive cases in the general method using multi-level superposition modulation 1004 . Within the multi-level superposition modulation technique 304, signals can be differentiated in two-dimensional space rather than along a single axis. Thus, the information carrying capacity of a communication channel can be determined by multiple signals occupying different time and frequency coordinates and can be distinguished in a notational two-dimensional space.

In the symbol two-dimensional space, the minimization of the time-bandwidth product, i.e. the area occupied by the signal in this space, enables denser packing within the allocated channel, and therefore more signal and/or data use, with more High obtained information carrying capacity. Given a frequency channel increment (Δf), a given signal transmitted through it in a minimum time Δt will have an envelope described by some temporal bandwidth minimization signal. The time-bandwidth product of these signals takes the form:

ΔtΔf=1/2(2n+1)

where n is an integer in the range 0 to infinity, representing the order of the signal.

These signals form an orthogonal set of infinite elements, each of which has a finite amount of energy. They are finite in both the time and frequency domains and can be detected from a mixture of other signals and noise by correlation, eg by matched filtering. Unlike other wavelets, these quadrature signals have similar time and frequency patterns.

The orbital angular momentum process 306 provides a twist to the wavefront of the electromagnetic field carrying the data stream, which may enable transmission of multiple data streams at the same frequency, wavelength, or other signal support mechanism. Similarly, other quadrature signals may be applied to different data streams to enable transmission of multiple data streams on the same frequency, wavelength, or other signal support mechanism. This would increase bandwidth on a communication link by allowing a single frequency or wavelength to support multiple intrinsic channels, each individual channel having a different orthogonal and independent orbital angular momentum than its associated channel.

Referring now more specifically to FIG. 11, there is shown a functional block diagram of a system for generating an orbital angular momentum "twist" within a communication system or quantum computing system, such as that shown in relation to FIG. A combination of data streams for transmission on the same wavelength or frequency. A plurality of data streams 1102 are provided to the transport processing circuit 1100 . Each data flow 1102 includes, for example, an end-to-end link connection that carries a voice call or a packet connection that transports non-circuit-switched encapsulated data over the data connection. Multiple data streams 1102 are processed by modulation/demodulation circuitry 1104. Modulation/demodulation circuitry 1104 modulates the received data stream 1102 onto wavelength or frequency channels using a multi-level superposition modulation technique, as will be described more fully below. Communication links may include fiber optic links, free space optical links, RF microwave links, RF satellite links, wireline links (untwisted), and the like.

The modulated data stream is provided to an orbital angular momentum (OAM) signal processing block 1106 . The orbital angular momentum signal processing block 1106 applies orbital angular momentum to the signal in one embodiment. In other embodiments, the processing block 1106 may apply any orthogonal function to the signal being transmitted. These orthogonal functions may be spatial Bessel functions, Laguerre-Gaussian functions, Hermite-Gaussian functions or any other orthogonal functions. Each modulated data stream from modulation/demodulation 1104 is provided with a different orbital angular momentum by orbital angular momentum electromagnetic block 1106 such that each modulated data stream has a unique and different orbital angular momentum associated with it. Each modulated signal with an associated orbital angular momentum is provided to an optical transmitter 1108, which transmits each modulated data stream with a unique orbital angular momentum at the same wavelength. Each wavelength has a selected number of bandwidth time slots B, and can have its data transfer capability increased by a factor of degrees of orbital angular momentum 1 provided from the OAM electromagnetic block 1106 . An optical transmitter 1108 that transmits a signal at a single wavelength can transmit group B information. Optical transmitter 1108 and OAM electromagnetic block 1106 may transmit 1×B sets of information according to the configurations described herein.

In the receive mode, the optical transmitter 1108 will have a wavelength that includes multiple signals transmitting therein and having different orbital angular momentums embedded therein. Optical transmitter 1108 forwards these signals to OAM signal processing block 1106 , which separates each signal having a different orbital angular momentum and provides the separated signal to demodulation circuit 1104 . The demodulation process extracts the data stream 1102 from the modulated signal and places it at the receiving end using a multi-layer additive demodulation technique.

Referring now to FIG. 12, a more detailed functional description of the OAM signal processing block 1106 is provided. Each input data stream is provided to OAM circuit 1202 . Each OAM circuit 1202 provides a different orbital angular momentum to the received data stream. Different orbital angular momentums are achieved by applying different currents to generate the signal being transmitted to generate a specific orbital angular momentum associated with it. The orbital angular momentum provided by each OAM circuit 1202 is unique to the data stream provided to it. An infinite number of orbital angular momentum can be applied to different input data streams or photons using many different currents. Each individually generated data stream is provided to a signal combiner 704 which combines the signals onto wavelengths for transmission from transmitter 706 . Combiner 1204 performs spatial mode division multiplexing to place all signals on the same carrier signal in the spatial domain.

Referring now to FIG. 13, the manner in which the OAM processing circuit 1106 may separate a received signal into multiple data streams is shown. Receiver 1302 receives the combined OAM signal on a single wavelength and provides this information to demultiplexer 1304. Signal separator 1304 separates each signal with a different orbital angular momentum from the received wavelength and provides the separated signal to OAM de-twist circuit 1306 . OAM de-twist circuit 1306 removes the associated OAM twist from each correlated signal and provides the received modulated data stream for further processing. Signal separator 1304 separates each received signal from which orbital angular momentum has been removed into a separate received signal. The individual received signals are provided to receiver 1302 for demodulation using, for example, multi-stage superposition demodulation, as described more fully below.

Figure 14 is shown in a way where a single wavelength or frequency with two quantum spin polarizations can provide an infinite number of twists with various orbital angular momentums associated therewith. The l-axis represents the various quantified orbital angular momentum states that can be applied to a particular signal at a selected frequency or wavelength. The notation omega (ω) denotes the various frequencies of the signal that can impart different orbital angular momentum. Top grid 1402 represents potentially usable signals for left-hand signal polarization, while bottom grid 1404 is for potentially usable signals with right-hand polarization.

By applying different orbital angular momentum states to a signal at a particular frequency or wavelength, a potentially infinite number of states can be provided at the frequency or wavelength. Thus, states at frequency Δω or wavelength 1406 in left-hand polarization plane 1402 and right-hand polarization plane 1404 can provide an infinite number of signals at different orbital angular momentum states Δl. Blocks 1408 and 1410 represent particular signals having orbital angular momentum Δl at frequencies Δω or wavelengths in right-hand polarization plane 1404 and left-hand polarization plane 1410, respectively. Different signals can also be transmitted by changing to different orbital angular momentum within the same frequency Δω or wavelength 1406 . Each angular momentum state corresponds to a different determined current level for transmission from the optical transmitter. By estimating the equivalent current for generating a specific orbital angular momentum in the optical domain, and applying this current for the transmission of the signal, the transmission of the signal can be achieved in the desired state of orbital angular momentum.

Thus, the diagram of Figure 15 shows two possible angular momentums, spin angular momentum and orbital angular momentum. The spin form manifests within the polarization of macroscopic electromagnetism, and has only left-hand and right-hand polarization due to the up and down spin directions. However, orbital angular momentum indicates an infinite number of states that are quantized. There are more than two paths, and in theory the level of orbital angular momentum through the quantization could be infinite.

的相位项有关，其中θ是角坐标，并且

是指示缠绕螺旋的数量的整数(即，沿着围绕光束轴的圆的2π相移的数量)。

可以是正整数、负整数或零，分别对应于顺时针、逆时针相位螺旋或没有螺旋的高斯光束。It is well known that the concept of linear momentum is often associated with objects moving in a straight line. If the object has rotational motion, such as spin (ie, spin angular momentum (SAM) 1502) or rotation about axis 1506 (ie, OAM 1504) (as shown in Figures 15A and 15B, respectively), the object may also carry angular momentum. The light beam can also have rotational motion as it propagates. In the paraxial approximation, if the electric field rotates along the beam axis 1506 (ie, circularly polarized light 1505), the beam carries the SAM 1502, and if the wave vector spirals around the beam axis 1506, the beam carries the OAM 1504, resulting in a helical phase A wavefront 1508, as shown in Figures 15C and 15D. In its analytical expression, the helical phase wavefront 1508 is generally related to the

is related to the phase term of , where θ is the angular coordinate, and

is an integer indicating the number of winding spirals (ie, the number of 2π phase shifts along a circle around the beam axis).

Can be a positive integer, a negative integer, or zero, corresponding to a Gaussian beam with a clockwise, counterclockwise phase helix, or no helix, respectively.

和p表示，其中

具有与一般OAM光束相同的含义，并且p指强度分布中的径向节点。LG光束的数学表达式在空间域中形成正交且完整的基。相反，由于没有径向定义，一般的OAM光束实际上包括一组LG光束(每个光束具有相同的

指数但不同的p指数)。术语“OAM光束”指的是所有的螺旋相控光束，并且用于与LG光束区分开。Two important concepts related to OAM include: (1) OAM and polarization: As mentioned above, an OAM beam appears as a beam with a helical phase wavefront and thus a twisted wave vector, while the polarization state can only be connected to the SAM 1502 . If the beam is left circularly polarized or right circularly polarized, the beam carries ±h/2π (h is Planck's constant) SAM 1502 per photon, while if the beam is linearly polarized, the beam carries no SAM 1502. Although in some cases the SAM 1502 and OAM 1504 of light can be coupled to each other, they can be clearly distinguished for paraxial beams. Therefore, under the paraxial assumption, OAM1504 and polarization can be considered as two independent properties of light. 2) OAM beams and Laguerre-Gaussian beams: In general, an OAM-carrying beam can refer to any helical phased beam, regardless of its radial distribution (although sometimes OAM can also be carried by a non-spiral-phased beam) . The LG beam is a special subset of all OAM-carrying beams because the analytical expression for the LG beam is an eigensolution of the paraxial form of the wave equation in cylindrical coordinates. For LG beams, both the azimuthal and radial wavefront distributions are well-defined and are defined by two exponents

and p denotes, where

Has the same meaning as a general OAM beam, and p refers to a radial node in the intensity distribution. The mathematical expression of the LG beam forms an orthogonal and complete basis in the spatial domain. In contrast, since there is no radial definition, a general OAM beam actually consists of a set of LG beams (each with the same

index but a different p-index). The term "OAM beam" refers to all helical phased beams and is used to distinguish them from LG beams.

Using the orbital angular momentum state of the transmitted energy signal, physical information can be embedded within the radiation transmitted by the signal. The Maxwell-Heaviside equation can be expressed as:

是del算符，E是电场强度，B是磁通密度。使用这些方程，可以从麦克斯韦的原始方程导出23个对称/守恒量。然而，只有十个众所周知的守恒量，并且这些中只有一些是商业上使用的。历史上，如果麦克斯韦方程保持在其原始的四元数形式，将更容易看到对称/守恒量，但当他们被海维赛德修改为他们目前的矢量形式时，变得在麦克斯韦方程中更难以看到这样的固有对称性。in

is the del operator, E is the electric field strength, and B is the magnetic flux density. Using these equations, 23 symmetric/conserved quantities can be derived from Maxwell's original equations. However, there are only ten well-known conserved quantities, and only some of these are used commercially. Historically, it would have been easier to see symmetric/conserved quantities if Maxwell's equations were kept in their original quaternion form, but when they were modified by Heaviside to their current vector form, became more in Maxwell's equations It is difficult to see such inherent symmetry.

Maxwell's linear theory has U(1) symmetry with Abelian commutation relations. They can be extended to higher symmetry group SU(2) forms with non-Abelian commutation relations that resolve global (spatially nonlocal) properties. The Wu-Yang and Harmuth interpretation of Maxwell's theory hints at the existence of magnetic monopoles and magnetic charges. In the classical realm, these theoretical structures are pseudoparticles or instantons. The interpretation of Maxwell's work actually proceeds in a large way from Maxwell's original intention. In Maxwell's original formulation, Faraday's electronic states (Aμ fields) were centered, making them compatible with Yang-Mills theory (before Heaviside). Mathematically dynamic entities called solitons can be classical or quantum, linear or nonlinear, and describe EM waves. However, the soliton has the form of SU(2) symmetry. In order for the classically interpreted theory of classical Maxwell's U(1) symmetry to describe such entities, the theory must be extended to the SU(2) form.

In addition to dozens of physical phenomena (which cannot be explained by traditional Maxwell's theory), the recently formulated Harmuth Ansatz also addresses the incompleteness of Maxwell's theory. Harmuth's modified Maxwell equation can be used to calculate the EM signal velocity, provided the magnetic field current density and magnetic charge are added, which is consistent with the Young-Mills equation. Therefore, with the correct geometry and topology, the Aμ potential always has physical meaning.

Conserved quantities and electromagnetic fields can be expressed in terms of the conservation of system energy and the conservation of system linear momentum. Time symmetry, the conservation of system energy, can be expressed using Poynting's theorem according to the following equation:

哈密尔顿算符(总能量)

Hamiltonian (total energy)

能量守恒

Conservation of energy

Spatial symmetry, that is, the conservation of the linear momentum of the system representing the electromagnetic Doppler shift, can be expressed by the following equation:

线性动量

Linear Momentum

线性动量守恒

Conservation of Linear Momentum

The conservation of energy at the system center is represented by the following equation:

Similarly, the conservation of the angular momentum of the system causing the azimuthal Doppler shift is expressed by the following equation:

角动量守恒

Conservation of Angular Momentum

For a radiation beam in free space, the EM field angular momentum ^Je can be divided into two parts:

For each singular Fourier mode in the real-valued representation:

The first part is the EM spin angular momentum S ^em , whose classical manifestation is wave polarization. The second part is the EM orbital angular momentum ^Lem , which is classically represented as a wave spiral. In general, the EM linear momentum ^Pem and the EM angular momentum ^Jem = ^Lem + ^Sem are radiated all the way to the far field.

By using Poynting's theorem, the optical vorticity of a signal can be determined from the light velocity equation:

连续性方程

Continuity Equation

where S is the Poynting vector

U is the energy density

where E and H include the electric and magnetic fields, respectively, and ε and _μ0 are the dielectric constant and permeability of the medium, respectively. The optical vorticity V can then be determined from the curling of the optical velocity according to the following equation:

Referring now to Figures 16A and 16B, the manner of the signal and its associated Poynting vector in the case of a plane wave is shown. In the plane wave case shown generally at 1602, the transmitted signal can take one of three configurations. When the electric field vectors are in the same direction, a linear signal is provided, as shown generally at 1604 . Within circular polarization 1606, the electric field vector rotates by the same magnitude. Within elliptical polarization 1608, the electric field vector rotates, but with different magnitudes. The Poynting vector remains in a constant direction for the signal configuration of Figure 16A and is always perpendicular to the electric and magnetic fields. Referring now to Figure 16B, when a unique orbital angular momentum is applied to a signal as described above, the Poynting vector S1610 will spiral around the direction of propagation of the signal. The helix can be altered to enable the transmission of signals on the same frequencies as described herein.

Figures 17A to 17C show the difference in signals with different helicity (ie, orbital angular momentum). Each of the spiral Poynting vectors associated with signals 1702, 1704, and 1706 provides a different shape of the signal. Signal 1702 has +1 orbital angular momentum, signal 1704 has +3 orbital angular momentum, and signal 1706 has -4 orbital angular momentum. Each signal has a different angular momentum and associated Poynting vector, enabling the signal to be distinguished from other signals within the same frequency. This allows different types of information to be sent on the same frequency because the signals are individually detectable and do not interfere with each other (eigenchannels).

Figure 17D shows the propagation of Poynting vectors for various eigenmodes. Each ring 1720 represents a different eigenmode or twist representing a different orbital angular momentum within the same frequency. Each of these rings 1720 represents a different orthogonal channel. Each eigendie has a Poynting vector 1722 associated with it.

Topological charges can be multiplexed to frequencies for linear or circular polarization. In the case of linear polarization, topological charges will be multiplexed across vertical and horizontal polarizations. In the case of circular polarization, the topological charges will be multiplexed on left-hand circular polarization and right-hand circular polarization. Topological charge is another name for the helicity index "I" or the amount of twist or OAM applied to a signal. Furthermore, the use of the orthogonal functions discussed above can also be multiplexed together onto the same signal in order to transmit multiple information streams. The helicity index can be positive or negative. In wireless communications, different topological charge/orthogonal functions can be created and multiplexed and demultiplexed together to separate topological charge/orthogonal functions. Signals with different orthogonal functions are spatially combined on the same signal, but do not interfere with each other because they are orthogonal to each other.

Topological charges l can be generated using a Spiral Phase Plate (SPP), as shown in Figure 17E, using appropriate materials with specific refractive indices and shop capabilities or phase masks, holograms made from new materials, or A new technique was used to create an RF form of Spatial Light Modulator (SLM) that twists the RF wave (as opposed to the beam) by adjusting the voltage across the device to obtain a topologically charged RF wave twist. A helical phase plate can transform an RF plane wave (l=0) into a twisted RF wave with a specific helicity (ie, l=+1).

Crosstalk and multipath interference can be corrected using RF Multiple Input Multiple Output (MIMO). Most channel impairments can be detected using control or pilot channels and corrected using algorithmic techniques (closed loop control systems).

While applying orbital angular momentum to various signals allows the signals to be orthogonal to each other and used on the same signal-carrying medium, other orthogonal functions/signals can be applied to data streams to create orthogonal signals on the same signal medium carrier .

Minimizing the time-bandwidth product (ie, the area occupied by the signal in this space) within the symbol two-dimensional space enables denser packing and thus more signals to be used within the allocated channel, with Higher resulting information carrying capacity. Given a frequency channel delta (Δf), a given signal transmitted through it for the shortest time Δt will have an envelope described by some temporal bandwidth minimization signal. The time-bandwidth product of these signals is of the form:

ΔtΔf=1/2(2n+1)

where n is an integer ranging from 0 to infinity, indicating the order of the signal.

These signals form a set of orthogonal infinite elements, each of which has finite energy. They are finite in both the time and frequency domains, and can be detected from a mixture of other signals and noise by correlation (for example, by matched filtering). Unlike other wavelets, these quadrature signals have similar time and frequency patterns. These types of quadrature signals reduce the time-bandwidth product, thereby increasing the spectral efficiency of the channel.

The Hermitian-Gaussian polynomial is an example of a classical sequence of orthogonal polynomials, which are the eigenstates of quantum harmonic oscillators. Signals based on Hermitian-Gaussian polynomials have the minimum time-bandwidth product property described above and can be used in embodiments of the system. However, it should be understood that other signals, such as orthogonal polynomials such as Jacobi polynomials, Gegenbauer polynomials, Legendre polynomials, Chebyshev polynomials, may also be used ) polynomial, and Laguerre-Gaussian polynomial, etc. Q-functions are another class of functions that can be used as the basis for MLO signals.

In addition to performing the temporal bandwidth minimization described above, the plurality of data streams may also be processed to provide minimization of the spatial momentum product in the spatial modulation. in this case:

Processing the data stream in this way produces a spatial wavefront. This process produces wavefronts that are also orthogonal to each other like the OAM twist functions, but these wavefronts include different types of orthogonal functions in the spatial domain rather than the time domain.

The above solutions are applicable to twisted pair, coaxial cable, optical fiber, RF satellite, RF broadcast, RF point-to-point, RF point-to-multipoint, RF point-to-point (backhaul), RF point-to-point (fronthaul is cloudification and cloudification of RAN and cloud HetNet). Virtualization provides higher throughput CPRI interfaces), Free-Space Optics (FSO), Internet of Things (IOT), WiFi, Bluetooth as a cable replacement for personal devices, RF and FSO hybrid systems, radar, Magnetic tags and all types of wireless access. The method and system are compatible with many current and future multiple access systems, including EV-DO, UMB, WIMAX, WCDMA (with or without), Multimedia Broadcast Multicast Service (MBMS)/Multiple Input Multiple output (MIMO), HSPA evolution and LTE.

Hermitian Gaussian beam

Hermitian Gaussian beams can also be used to transmit orthogonal data streams. In a scalar field approximation (for example, ignoring the vector character of electromagnetic fields), any electric field amplitude distribution can be represented as a superposition of plane waves, namely:

This representation is also known as the angular spectrum of the plane wave or the plane wave expansion of the electromagnetic field. Here, A(k _x , _ky ) is the amplitude of the plane wave. The representation is chosen in such a way that the net energy flux connected to the electromagnetic field is towards the propagation axis z. Each plane wave is connected to an energy flow with direction k. Practical lasers generate spatially coherent electromagnetic fields that have limited lateral extension and propagate in a moderately extended manner. This means that the wave amplitude only varies slowly along the propagation axis (z-axis) compared to the wavelength and finite width of the beam. Therefore, assuming that the magnitude function A(k _x , _ky ) decreases fast enough with increasing values of (k _x , _ky ), a paraxial approximation can be applied.

Two main characteristics of the total energy flux can be considered: divergence (spread of plane wave amplitude in wave vector space), defined as:

And the lateral spatial extension (the extension of the field strength perpendicular to the z direction) is defined as:

We now consider the fundamental mode of a beam as an electromagnetic field with both minimal divergence and minimal lateral extension, ie as a field that minimizes the product of divergence and extension. Due to symmetry, this leads to finding a magnitude function that minimizes the product:

Therefore, finding the field with minimum divergence and minimum lateral extension can lead directly to a fundamental Gaussian beam. This means that a Gaussian beam is the mode with minimal uncertainty, i.e. the product of its magnitude in real space and wave vector space is the theoretical minimum given by Heisenberg's uncertainty principle of quantum mechanics . Therefore, the Gaussian mode has less dispersion than any other light field of the same size, and its diffraction sets a lower threshold for diffraction of real light beams.

Hermitian-Gaussian beams are structurally stable laser modes with rectangular symmetry along the propagation axis. In order to derive such a pattern, the easiest way is to include an additional form of modulation:

The new field mode happens to be the differential derivative of the fundamental Gaussian mode _E0 .

Observing the explicit form E ₀ shows that the differentiation in the last equation leads to an expression of the form:

with some constants p and α. Now using the definition of Hermitian polynomials,

Then the field amplitude becomes

in

ρ ² =x ² +y ²

and the Rayleigh length z _R

and beam diameter

In cylindrical coordinates, the field takes the form:

是拉盖尔(Laguerre)函数。in

is the Laguerre function.

Mode Division Multiplexing (MDM) of multiple orthogonal beams increases system capacity and spectral efficiency in optical communication systems. For free space systems, multiple beams, each in a different orthogonal mode, can be transmitted by a single transmitter and receiver aperture pair. Furthermore, the modal orthogonality of the different beams enables efficient multiplexing at the transmitter and efficient demultiplexing at the receiver.

There are different optical modal basis sets that exhibit orthogonality. For example, in free space optical systems and RF transmission systems, multiple orthogonal beams can be multiplexed using orbital angular momentum (OAM) beams of Laguerre Gaussian (LG) mode or Laguerre Gaussian light mode. However, there are other modality groups that can also be used for multiplexing without OAM. The Hermitian Gaussian (HG) mode is one such mode group. The intensity of the HG _m,n beam is given by:

where H _m (*) and H _n (*) are Hermitian polynomials of order m and order n. The value w ₀ is the waist at distance Z=0. The spatial orthogonality of HG modes with the same beam waist w0 depends on the orthogonality of the Hermitian polynomials in the _x or y direction.

Referring now to FIG. 18, a system for free space spatial multiplexing in free space using the orthogonality of the HG modality group is shown. Laser 1802 is provided to beam splitter 1804. Beam splitter 1804 splits the beam into a plurality of beams, each beam being provided to modulator 1806 for modulation with data stream 1808 . The modulated beam is provided to a collimator 1810, which provides the collimated beam to a spatial light modulator 1812. A spatial light modulator (SLM) 1812 may be used to transform the input plane wave into HG modes of different orders, each mode carrying a separate data channel. These HG patterns are spatially multiplexed using multiplexer 1814 and transmitted coaxially on free space link 1816 . At receiver 1818, several factors may affect the demultiplexing of these HG modes, such as receiver aperture size, receiver lateral displacement, and receiver angular error. These factors affect the performance of the data channel, such as signal-to-noise ratio and crosstalk.

Regarding the properties of a diverging HG _m,0 beam (m=0-6), a wavelength of 1550 nm is assumed, and the transmit power of each mode is 0 dBm. Higher-order HG modes have been shown to have larger beam sizes. For smaller aperture sizes, less power is received for higher order HG modes due to divergence.

Since the orthogonality of the HG modes depends on the light field distribution in the x and y directions, a finite receiver aperture can cut off the beam. Truncation will destroy the orthogonality and cost crosstalk of the HG channel. When the aperture is small, there is higher crosstalk to other modes. When a finite receiver is used, if an HG mode with an even (odd) order is transmitted, it only causes crosstalk with other HG modes with an even (odd) number. This is explained by the fact that the orthogonality of odd and even HG modal groups is preserved when the beam is systematically truncated.

In addition, misalignment of the receiver can lead to crosstalk. In one example, lateral displacement can be induced when the receiver is not aligned with the beam axis. In another example, angular errors may be introduced when the receiver is on-axis but there is an angle between the receiver orientation and the beam propagation axis. As the lateral displacement increases, the less power is received from the transmit power mode, the more power leaks into other modes. For modes with a larger mode index separation from the transmit mode, there is less crosstalk.

Mode conversion method

的OAM光束，板的厚度轮廓应加工成

其中n是介质的折射率。使用SPP 1902的限制在于每个OAM态需要不同的特定板。作为替代，可重新配置的衍射光学元件，例如，像素化的空间光调制器(SLM)1904或数字式微反射镜器件，可被编程为在给定波长处用作任意选择的折射元件。如上所述，如在1904处所示，螺旋相位轮廓

将线性偏振高斯激光束转换为OAM模式，其波前类似于

折叠旋塞1906。重要的是，通过简单地更新加载在SLM 1904上的全息图，可以容易地改变所生成的OAM光束。为了在空间上将相位调制光束与来自SLM的零阶非相位调制反射分离，将线性相位斜坡加到螺旋相位码(即，“叉”形相位图案1908)上，以产生空间上不同的一阶衍射OAM光束，携带期望的电荷。还应当注意，上述方法仅通过方位指数控制产生OAM光束。为了产生纯LG_(l,p)模式，必须共同控制波前的相位和强度。这可以使用具有更复杂相位全息图的仅相位SLM来实现。Referring now to Figure 19, of all the external cavity approaches, perhaps the simplest is to pass a Gaussian beam through a coaxially placed Spiral Phase Plate (SPP) 1902. SPP 1902 is an optical element with a helical surface, as shown in Figure 17E. In order to generate the state as

The OAM beam, the thickness profile of the plate should be machined to

where n is the refractive index of the medium. The limitation of using SPP 1902 is that each OAM state requires a different specific board. Alternatively, a reconfigurable diffractive optical element, such as a pixelated spatial light modulator (SLM) 1904 or a digital micromirror device, can be programmed to act as an arbitrarily selected refractive element at a given wavelength. As described above, as shown at 1904, the helical phase profile

Convert a linearly polarized Gaussian laser beam to OAM mode with a wavefront similar to

Folding stopcock 1906. Importantly, the generated OAM beam can be easily changed by simply updating the hologram loaded on the SLM 1904. To spatially separate the phase-modulated beam from the zero-order non-phase-modulated reflections from the SLM, a linear phase ramp is applied to the helical phase code (ie, "fork"-shaped phase pattern 1908) to produce spatially distinct first-order Diffracted the OAM beam, carrying the desired charge. It should also be noted that the above method produces OAM beams only with azimuthal index control. To generate pure LG_(l,p) modes, the phase and intensity of the wavefront must be jointly controlled. This can be achieved using phase-only SLMs with more complex phase holograms.

Generate OAM with DLP

The OAM signal used within a quantum computer as described above can be generated using a Digital Light Processor (DLP). The DLP includes a digital light processor, which is a display device based on optical microelectromechanical technology using digital micromirror devices, which are "Systems and Methods for Applying Histogram Constraints to Light Beams," the technique disclosed in US Patent Application No. 14/864,511, which is incorporated herein by reference in its entirety. Referring now to FIG. 20, there is shown another way of generating a beam 2002 that includes orthogonal functions, such as OAM, Hermitian Gaussian, Laguerre Gaussian, etc., to interpret the information in the beam coding. The laser beam generator 2004 produces a light beam 2006 that includes a plane wave provided to a MicroElectroMechanical system (MEM) device 2008 . Examples of the MEM device 2008 include a Digital Light Processing (DLP) projector or a Digital Micro-mirror Device (DMD) capable of producing light beams with various characteristics. The MEM device 2008 can generate Hermitian Gaussian, Laguerre Gaussian (LG), and Vortex OAM modes that are programmed in response to inputs to the MEM device 2008 . MEM device 2008 has mode selection logic 2010 that enables selection of Laguerre Gaussian, Hermitian Gaussian, and Vortex OAM modes (or other orthogonal function modes) to process input beam 2006. The MEM device 2008 also enables switching between different modes at a very high rate of several thousand times per second, which is not possible using spatial light modulators (SLMs). Switching between modes is controlled via mode switching logic 2012 . This fast switching enables the generation of OAM, HG or LG modes for communication and these forms of quantum key distribution (QKD) and quantum computers for quantum information processing. The orthogonal nature of the Laguerre-Gaussian (LG) and OAM and Hermitian Gaussian (HG) beams combined with the high-speed switching of the MEM makes the device useful for achieving higher data capacities. This can be achieved using holograms, which are programmed into the memory of the DLP, which programs micromirrors to selected positions, and these mirrors can be used to twist the beam with the programmed information.

This enables binary gratings (holograms) that can be switched between on demand using external digital signals at very high speeds. Using eg DLP techniques, switching between different modes (different binary gratings) can be achieved at very high rates of several thousand times per second, which cannot be achieved using spatial light modulators (SLMs). This allows dynamic control of the helicity provided to the beam for the new modulation and/or multiple access technique to encode information.

DLP allows high resolution and precision from microns to millimeters, enabling the utilization of frequencies from infrared to ultraviolet. The use of DLP for MDM (Mode Division Multiplexing) minimizes color, distance, movement and environmental sensitivity and is therefore ideal for building integrated optics. Most SLMs are limited by frame refresh rates of about 60 Hz, which makes the high-speed, wide operating spectral bandwidth of digital micromirror devices (DMDs) useful in a variety of applications. The DMD design inherently minimizes temperature sensitivity for reliable 3-D wave construction.

The vast majority of commercially available SLM devices are limited to frame rates around 60Hz, which greatly limits the speed of operation of any system based on this technology. DMDs are amplitude-only spatial light modulators. The DMD's high speed, wide operating spectral bandwidth and high power threshold make this device a useful tool for a variety of applications. Variants of DMD are commercially available at a fraction of the cost of phase-only SLMs. Intensity shaping of the spatial mode can be achieved by rapidly turning the micromirrors on and off. However, the patterns created in this process can be temporally unstable and have the desired intensity distribution only when averaged by a slow detector.

Phase and amplitude information can be encoded by modulating the position and width of binary amplitude gratings implemented within the hologram, such as those shown in Figures 21A-21H. By implementing such a hologram to control the DMD, HG mode, LG mode, OAM vortex mode or any angular (ANG) mode can be created by appropriately programming the DMD with the hologram. In addition, switching between the generated patterns can be performed at very high speed.

This approach can be implemented by considering a one-dimensional binary magnitude grating. The transfer function of this raster can be written as:

in

This function can be depicted as a pulse train with period x ₀ . Parameters "k" and "w" are unitless quantities that set the position and width of each pulse, and are equal to constant values for a uniform grating. The values of these parameters can be changed locally to achieve phase and amplitude modulation of the light field. The transmittance function τ(x) is a periodic function and can be extended to a Fourier series.

In the case where k(x) and w(x) are functions of x and the binary grating is illuminated by a monochromatic plane wave. The first order diffracted light can be written as:

Thus, w(x) is related to the amplitude of the diffracted light, while k(x) sets its phase. Therefore, the phase and amplitude of the diffracted light can be controlled by setting the parameters k(x) and w(x). In communication theory, these methods are sometimes referred to as Pulse Position Modulation (PPM) and Pulse Width Modulation (PWM). The above equations are good approximations for the slowly varying k(x) and w(x) functions.

The above analysis deals with the one-dimensional case. Two-dimensional gratings can be generated by thresholding a rapidly changing modulated carrier, such as:

Here, sgn(x,y) is the sign function. This can be checked in the limits where w(x,y) and k(x,y). For general complex scalar fields, the corresponding w(x,y) and k(x,y) functions can be found:

According to relationship

2-D binary amplitude holograms can be designed to generate LG modes. A grating hologram designed for the vortex mode will have a fairly uniform width across the aperture, while for the case of the LG mode, the grating gradually disappears when the amplitude becomes negligibly small.

Digital Micromirror Devices (DMDs) are amplitude-only spatial light modulators. The device includes an array of micromirrors that can be controlled in a binary fashion by setting the deflection angle of the individual mirrors to +12° or -12°. Referring now to FIG. 22A, a general block diagram of DMD 2202 is shown. DMD 2202 includes a plurality of micromirrors 2208 arranged in an XxY array. The array may comprise a 1024x768 array of aluminum micromirrors, such as the 1024x768 array of aluminum micromirrors implemented in a DLP 5500 DMD array. However, it will be appreciated that other array sizes and DMD devices may be used. Each micromirror 2208 includes a combination of optomechanical and electromechanical elements. Each micromirror 2208 includes a pixel of the DMD 2202 . Micromirror 2208 is an electromechanical element with two stable micromirror states of +12° and -12°. The micromirrors have a pitch of 10.8 microns and are designed for light with wavelengths from 420nm to 700nm. The state of the micromirror 2208 is determined by the geometry and electrostatic properties of the pixels during operation. The two positions of the micromirror 2208 determine the direction in which the light beam impinging on the mirror is deflected. In particular, DMD 2202 is a spatial light modulator. By convention, the positive (+) state is tilted toward the illumination and is referred to as the "on" state. Similarly, the negative (-) state deviates from the illumination slope and is referred to as the "off" state.

Figure 22B shows how the micromirror 2208 would interact with a light source 2230, such as a laser. The light source 2230 illuminates a beam of light at an angle of -24°, which illuminates the micro-mirror 2208. When the mirror is in the "off" state 2232 at an angle of -12°, the off state energy 2234 is reflected at an angle of 48°. When mirror 2208 is in flat state 2236 of 0°, flat state energy 2238 is reflected at an angle of 24°. Finally, when the mirror is in the "on" state 2240 of +12°, the on state energy 2242 is reflected at 0° through the projection lens 2234 of the DMD.

Referring now to FIG. 23, a view of the mechanical structure of the micromirror 2208 is shown. Micromirror 2208 includes mirror 2302 attached to torsional hinge 2304 along mirror diagonal 2306. The underside of micromirror 2302 is in electrical contact with the rest of the circuit through spring tip 2308. A pair of electrodes 2310 are used to hold the micromirror 2302 in one of two operating positions (+12° and -12°).

Referring now also to FIG. 24, a block diagram of the functional components of the micromirror 2208 is shown. Below each micromirror 2208 is a memory cell 2402 consisting of dual CMOS memory elements 2404. The states of the two memory elements 2404 are not independent, but are always complementary. If one CMOS memory element 2404 is at a logic "1" level, the other CMOS element is at a logic "0" level, and vice versa. The state of the memory cell 2402 of the micromirror 2208 plays a role in the mechanical position of the mirror 2208. However, the loading information within the memory unit 2402 does not automatically change the mechanical state of the micro-mirror 2208.

While the state of dual CMOS memory element 2404 plays a role in determining the state of micromirror 2208, the state of memory element 2304 is not the only determining factor. Once the micromirror 2208 has landed, changing the state of the memory cell 2402 will not cause the micromirror 2208 to flip to another state. Therefore, the memory state and the micromirror state are not directly linked together. In order for the state of CMOS memory element 2404 to be transferred to the mechanical position of micromirror 2208, micromirror 3108 must receive a "mirror clock pulse" signal. The mirror clock pulse signal temporarily releases the micromirror 3108 and repositions the mirror based on the state of the mirror memory element 2304. Thus, the information related to the mirror position can be pre-loaded into the memory element 2404, and the mechanical position of the mirror 2302 of each mirror within the MEM device 2202 changes simultaneously in response to the mirror clock pulse signal. One way in which information within memory cell 2402 can be programmed is through the use of holograms, such as those described herein for defining the position of each of micromirrors 2208 with MEM device 2202.

When the DMD 2202 is "powered up" or "powered down," there are prescribed actions necessary to ensure proper orientation of the micromirrors 2208. These operations position the micromirrors 2208 during power up and release them during power down. The process for changing the position of the micromirror 2208 is shown in more detail in the flowchart of FIG. 25 . Initially, at step 2502, the memory state within memory unit 2402 is set. Once the memory state is set within memory cell 2402, a mirrored clock pulse signal may be applied at step 2504. Micromirror 3108 will have an established specification of the time before and after the mirror clock pulse that can load data into memory cell 2402. Then, at step 2506, application of the mirror clock pulse signal sets the mirrors to their new state established by the memory. The process is completed at step 2508 and the mirror 2302 position is fixed and new data can be loaded into the memory unit 2402.

Referring now to FIG. 26, an intensity and phase interferometer used to measure the intensity and phase of the generated beam is shown. Spatial patterns can be generated by loading computer-generated Matlab holograms 2602, such as those described above and shown in Figures 31A-31H, onto DMD memory. The hologram 2602 used to generate the pattern can be created by modulating the grating function with 20 micromirrors per cycle. Hologram 2602 is provided to DMD 2604. Imaging system 2606 in conjunction with aperture 2608 separates the first order diffracted light into separate modes. The imaging system includes a laser 2610 that provides light through a pair of lenses 2612, 2614. Lens 2612 expands the beam to lens 2614 which collimates the beam. Beam splitter 2616 splits the beam towards lens 2618 and mirror 2621. Lens 2618 focuses the beam through lens 2620, which collimates the beam through filter 2622. The filtered beam is reflected by mirror 2624 through second beam splitter 2626. Beam splitter 2626 splits the beam towards lens 2628 and charge coupled device camera 2630. A Charge Couples Device (CCD) camera 2630 measures the intensity distribution of the generated light beam. The plane wave beam provided to lens 2628 is focused on aperture 2608 to interfere with the twisted beam from the DMD. The twisted beam from DMD 2604 is also focused on aperture 2608. The beam from DMD 2604 is provided through lens 2632, which is also focused on aperture 2608. The phase of the generated mode is determined by the number of helices in the mode and is caused by interfering the twisted beam with the plane wave beam. Also, whether the phase is positive or negative can be determined by whether the spiral is clockwise (positive) or counterclockwise (negative). A Mach-Zehnder interferometer can be used to verify the phase pattern of the created beam. The collimated plane wave provided from lens 2628 interferes with the mode created by the beam from DMD 2604 passing through lens 2632. This produces an interference pattern (spiral pattern) at aperture 2608. The patterns generated from the DMD can then be multiplexed together using a memory-based static fork on the DLP.

Therefore, it is possible to use binary holograms to coherently control the phase and amplitude of the beam. The low number of pixels per period of the binary grating leads to quantization errors in encoding phase and intensity. The total number of grating periods in the incident beam on the DMD 2604 sets an upper limit on the spatial bandwidth of the generated patterns. Therefore, in order to generate high quality patterns, a large number of micromirrors are preferred. This can be achieved by using a newer generation of DMDs. Another set of patterns required for OAM-based quantum key distribution is the Angular (ANG) pattern group.

Referring now to FIG. 27A, there is shown how switching between different OAM modes can be achieved in real time. Laser 2702 generates a collimated beam to DMD 2708 through lenses 2704 and 2706. DMD 2708 provides a light beam focused by lens 2710 onto aperture 2712. The output from aperture 2712 is provided to lens 2714, which collimates the beam onto mirror 2716. The collimated beam is provided to an OAM sorter 2718, which separates the signal into various OAM modes 2720 that are detected by a computer 2722.

Referring now to FIG. 27B , the manner in which the transmitter 2750 processes a plurality of data channels 2752 that pass through the cylindrical lens 2754 to the focusing lens 2756 is shown more generally. Lens 2756 focuses the beam on OAM sorter 2758. The collimated beam passes through the OAM sorter 2758 for multiplexing the OAM beams together for transmission to the receiver 2764 as a multiplexed OAM beam 2764. The multiplexed OAM beam 2760 passes through a second OAM splitter 2762 at receiver 2764 to demultiplex the beam into separate OAM channels. The received OAM channels 2768 pass through a lens 2766 to focus these separate OAM beam channels 2768.

Using a DMD for generating OAM patterns provides the ability to switch between different patterns at very high speeds. This involves a much smaller number of optical elements than conventional techniques, as the OAM patterns are generated using a series of separate forked holograms, multiplexed using beam splitters. Therefore, dynamic switching between vortex OAM modes with different quantum numbers can be achieved. Computer-generated holograms for these modes must be loaded onto the memory of the DMD 2708, and switching is accomplished using a clock signal. An input pattern can be mapped to a series of discrete points using a pattern sorter. The intensity corresponding to each pattern can then be measured at the location corresponding to each pattern using a high bandwidth PIN detector. DMD devices can be obtained at a fraction of the cost of phase spatial light modulators.

The DMD efficiency observed in a particular application depends on application-specific design variables such as illumination wavelength, illumination angle, projection aperture size, overfill of the DMD micromirror array, and the like. The overall optical efficiency of each DMD can generally be estimated as the product of window transmission, diffraction efficiency, micromirror surface reflectivity, and array fill factor. The first three factors depend on the wavelength of the illumination source.

DLP technology uses two types of materials for DMD mirrors. The mirror material for all DMDs except Type A is Corning Eagle XG, which uses Corning 7056 for Type A DMDs. Both mirror types have an Anti-Reflectivity (AR) thin film coating on the top and bottom of the glazing material. AR coating reduces reflection and improves transmission efficiency. DMD mirrors are designed for three transmission areas. These ranges include the ultraviolet light region from 300 nm to 400 nm, the visible light region from 400 nm to 700 nm, and the Near Infrared Light (NIR) region from 700 nm to 2500 nm. The coating used depends on the application. The UV window has a special AR coating designed to be more transmissive for UV wavelengths, a visible coating for visible DMDs, and a NIR coating for NIR DMDs.

The measurement data presented in the following sections reflect typical one-pass transmittance through top and bottom AR-coated mirror surfaces with random polarization. Unless otherwise stated, an angle of incidence (AOI) of 0° was measured normal to the window surface. As the number of window passes increases, the efficiency will decrease.

Figure 28 shows the Corning 7056 window projection curve. The window transmission response curve in this figure is for the Taipei MDM in its specified illumination wavelength region. Figure 28 shows the UV window transmittance measured normal to the window surface and the visible window transmittance at orientations of 0° and 30°. Figures 29-33 are enlarged views of typical visible and UV AR coating window transmittances in their regions of maximum transmission. As shown in Figure 32, the visible Corning Eagle XG window transmission data is for the DMD of the DLP 5500, DLP 1700, DLP 3000, and DLP 3000. The typical transmittance observed in these DMDs is about 97% in the broadband visible region. The NIR Corning Eagle XG window transmission data of Figure 33 is for the DLP 3000NIR DMD. Typical transmittance observed in NIR DMDs in the broadband NIR region is around 96% for most regions, dropping to 90% as it approaches 2500 nm.

Referring now to FIG. 34, a configuration of a generation circuit for generating an OAM twisted beam using a hologram within a microelectromechanical device is shown. Laser 3402 generates a light beam with a wavelength of approximately 543 nm. The beam is focused by telescope 3404 and lens 3406 onto a mirror/system of mirrors 3408. The beam is reflected from mirror 3408 into DMD 3410. The DMD 3410 programs into its memory one or more forked holograms 3412 that generate a desired OAM twisted beam 3413 with a beam encoded into the beam detected by the CCD 3414 Any required information for OAM mode. The hologram 3412 is loaded into the memory of the DMD 3410 and displayed as a static image. In the case of a 1024x768 DMD array, the image must include a 1024x768 image. The control software of the DMD 3410 converts the holograms to .bmp files. Holograms can be displayed individually or together as multiple holograms to multiplex specific OAM modes onto a single beam. The manner in which the hologram 3412 is generated within the DMD 3410 can be implemented in a number of ways that provide qualitative differences between the generated OAM beams 3413. Phase and amplitude information can be encoded into the beam by modulating the position and width of a binary amplitude grating used as a hologram. By implementing this hologram on a DMD, the creation of HG modes, LG modes, OAM vortex modes, or any angular mode can be achieved. Furthermore, by performing the switching of the generated patterns at very high speeds, information can be encoded within dynamically changing helicity to provide novel helicity modulations. Spatial patterns can be generated by loading computer-generated holograms onto the DMD. These holograms can be created by modulating the grating function with 20 micromirrors per period.

Rather than just generating an OAM beam 3413 having only a single OAM value included therein, multiple OAM values may be multiplexed into the OAM beam in various ways as described below. Using multiple OAM values allows different information to be incorporated into the beam. Programmable structured light provided by DLP allows customized and adaptable patterns to be projected. These patterns can be programmed into the DLP's memory and used to impart different information through the beam. Furthermore, if the patterns are dynamically timed, a modulation scheme can be created in which information is encoded in the helicity of the structured beam.

Referring now to FIG. 35, instead of just having the laser beam 3502 impinge on a single hologram, multiple holograms 3504 can be generated by the DMD 3410. FIG. 35 shows an implementation in which a 4x3 array of holograms 3504 is generated by DMD 3410. Hologram 3504 is square, and each edge of the hologram is aligned with the edge of an adjacent hologram to create a 4x3 array. By shining a light beam 3502 onto an array of holograms 3504, the OAM values provided by each of the holograms 3504 are multiplexed together. Several configurations of holograms 3504 can be used to provide different qualities of the OAM beam 3413 and associated patterns generated by passing the beam through the array of holograms 3504.

Figure 36 shows various reduced binary fork holograms that can be used to apply different OAM levels to light. Figure 36 shows a hologram for applying 100 cycles of OAM light from 1=1 to 1=10.

Referring now to FIG. 37, there is shown how the combined use of OAM processing and polarization processing can be used to augment data using any particular signal combination using a DLP system. The various data (Data 1, Data 3, Data 5, Data 7) 3702 have different OAM levels (OAM1, OAM2, OAM3, OAM4) 3704 and different X and Y polarizations 3706. This enables the signals to be multiplexed together into a polarization multiplexed OAM signal 3708. The polarization multiplexed OAM signal 3708 is demultiplexed by removing the X and Y polarizations 3706 and the OAM to reconstruct the data signal 3702.

给出。而轨道角动量(OAM)与复电场的方位角相位相关。具有方位角相位依赖性的每个光子是

的形式并且携带

的OAM。因此，对于每个光子，我们可以关联在计算基态|I,σ>上定义的光子角动量。因为OAM本征态是相互正交的，所以每个单光子可以传输任意数量的比特。通过使用全息方法生成/分析具有不同光子角动量的状态的可能性允许在多维希尔伯特空间中实现量子态。因为OAM态提供无限的基态，而SAM态仅是二维的，所以OAM还可用于同时增加QKD的安全性并提高量子计算应用的计算能力。我们介绍以下基于光子角动量的确定性量子量子迪特门和模块。Spin angular momentum (SAM) is polarization dependent and (for circular polarization) is given by

given. The orbital angular momentum (OAM) is related to the azimuthal phase of the complex electric field. Each photon with azimuthal phase dependence is

form and carry

OAM. Therefore, for each photon, we can associate the photon angular momentum defined on the computed ground state |I,σ>. Because the OAM eigenstates are mutually orthogonal, each single photon can transmit any number of bits. The possibility to generate/analyze states with different photon angular momentum by using holographic methods allows the realization of quantum states in multidimensional Hilbert space. Because OAM states provide infinite ground states, whereas SAM states are only two-dimensional, OAM can also be used to simultaneously increase the security of QKD and improve the computational power of quantum computing applications. We introduce the following deterministic quantum quantum Dieter gates and modules based on photon angular momentum.

Quantum Dieter

Referring now to FIG. 37B , a basic quantum module 302 for quantum teleportation applications includes a generalized Bell state generation module 304 and a QFT module 306 . The basic module of entanglement-assisted QKD is the generalized Bell state generation module 304 or the Weil operator module 312 . Universal quantum quantum Dieter gate based on photon angular momentum, namely generalized X quantum Dieter door, generalized Z quantum Dieter door, generalized CNOT quantum Dieter door. A universal quantum gate set is any set of gates to which any possible operation on a quantum computer can be reduced, i.e., any other unit operation can be represented as a finite sequence of gates from this set. This is technically impossible because the number of possible quantum gates is uncountable, while the number of finite sequences from finite sets is countable. To solve this problem, we only require that any quantum operation can be approximated by a sequence of gates from this finite set. Furthermore, for units over a constant number of qubits, the Solovay-Kitaev theorem guarantees that this can be done efficiently.

Different important quantum modules 302 are introduced for different applications, including (fault-tolerant) quantum computing, teleportation, QKD, and quantum error correction. Quantum quantum Dieter modules include Generalized Bell State Generation Module 304, QFT Module 306, Non-Binary Syndrome Calculator Module 308, Generalized Universal Quantum Dieter Gate 310, Weil Operator Module 312, and Generalized Controlled Phase Determination Using Optical Devices Sexual quantum Dieter gate 314, which is a key advantage over probabilistic SAM-based CNOT gates. Furthermore, by describing such gates and modules, we introduce their corresponding integrated optical implementations on DLP. We also introduce several entanglement assistance protocols by using the generalized Bell state generation module. The approach is to implement all these modules in integrated optics using a multidimensional quantum ditter on DLP.

Universal Quantum Dieter Gate and Quantum Module Based on Photonic OAM

An arbitrary photon angular momentum state |ψ> can be expressed as a linear superposition of |I,σ>-basic right vectors as follows:

where the |I,σ>-basic right vectors are mutually orthogonal, that is

<m,σ|n,σ′>=δ _mn δ _σσ ′; m,n,∈{-L-,…,-1,0,1,…,L _± };σ,σ′∈{-1 ,1}

中。右矢被定义为希尔伯特空间中的向量，特别是表示量子机械系统的状态。注意，在最一般的情况下，具有负OAM索引的状态的数量，表示为L，不需要与具有正OAM索引的OAM态的数量相同。描述光子状态的光子角动量概念不同于定义为

的光子的总角动量。Therefore, the right vector of photon angular momentum exists in D=2(L _- +L ₊ +1) dimension Hilbert space

middle. A right vector is defined as a vector in Hilbert space, specifically representing the state of a quantum mechanical system. Note that in the most general case, the number of states with negative OAM indices, denoted L, need not be the same as the number of OAM states with positive OAM indices. The concept of photon angular momentum, which describes the photon state, is different from that defined as

The total angular momentum of the photon.

As an illustration, in the total angular momentum-sign of j=4, we cannot distinguish between |I=5,σ=−1> and |I=3,σ=1> photon angular momentum states. Therefore, the use of the |I=σ> notation is more common. The SAM (circularly polarized) state can be expressed in the computational basis {{|H>, [V>|H>-horizontal photon, [V>-vertical photon) as follows:

The SAM operator is represented as:

Obviously, the right circle (|+1>) state and the left circle (|-1>) state are the eigenright vectors of this operator, because:

S|+1>=|+1>,S|-1>=-|-1>

The OAM states (|+1>) and (|-1>) generated using, for example, the procedure described previously can be represented in the reduced two-dimensional subspace as follows, respectively:

Referring now to FIG. 38, there is shown generated in response to input qubits |x> applied to the inputs of quantum gates 3802a, 3802b, 3802c and 3802d and input qubits |x> and |y> applied to the inputs of gate 3802e Several examples of the output quantum gate 3802. The outputs of various quantum gates 3802 may be provided depending on the type of processing implemented within the quantum gate. While the examples below are insane for qubit gates with spin angular momentum based inputs and outputs, by applying the OAM processing described in this paper to the inputs and outputs, the gates can function as gates that can operate on a larger number of input states. qubit gates to operate.

In the representation shown in Figure 38, since the mode of l=0 has no OAM value, it can be represented as:

|0>[0 0] ^T

In this particular case, the photon angular momentum state is only reduced to the SAM state. By assuming that the OAM-right vector is aligned with the propagation direction (z-axis), the OAM operator can be expressed as:

It is directly verified that the states |l> and |-l> are eigenright vectors of the OAM operator L _z :

L _z |±I>=(±I)|±I>

The spin operator S and the SAM operator L _z satisfy the following properties:

where I ₂ is the identity operator. The photon angular momentum operator can now be defined as

表示张量积。对应的本征值方程由下式给出：where the operator

represents the tensor product. The corresponding eigenvalue equation is given by:

J|±l,±1>=(±l)(±1)|±l,|±1>

For convenience, we can use a single index of photon angular momentum, and the computational basis associated with the photon angular momentum state is denoted as {|0>,|1>,...,|D-1>}, D=2(L _- +L ₊ ).

的基右矢的叠加。By appropriately choosing L- _and L ₊ to ensure that the dimension D is equal to some power of two, then the dimension D can be expressed as D=q= ^2p , where p≥1 is a prime number. If the addition operation is performed over the Galois field GF(2 ^p ) instead of "per mod D", the set of gates that can be used to perform arbitrary operations on quantum Diets can be defined as shown in Figure 38 Show. The F gate corresponds to a Quantum Fourier Transform (QFT) gate. Its effect on the right vector |0> is that all have the same probability magnitude

The superposition of the base right vector of .

Therefore, the F-gate on the quantum ditter has the same effect as the Hadamard gate on the qubit. The functions of the generalized X gate and the generalized Z gate can be described as follows:

X(a)|x>=|x>=|x+a>, Z(b)|x>=ω ^tr(bx) |x>; x,a,b∈GF(q)

where x, a, b, ∈ GF(q), tr(.) represent the tracking operation from GF(q) to GF(p), and ω is the p-th unit root, that is, ω=exp(j2π/p) . By omitting SAM as a degree of freedom, since it represents a fragile source of quantum information, the corresponding space becomes (L ₋ +L ₊ )-dimensional (D=L ₋ +L ₊ ).

By choosing (L-+L+) as the prime number P, the corresponding addition operation represents "mod P addition", in other words a right circular shift. A left circular shift can be defined as:

X(a)|x>=|x-a>

这种形式中对应的广义Hadamard门是F门，因为：At the same time, the tracking operation becomes simple, and the action of the generalized Z-gate becomes

The corresponding generalized Hadamard gate in this form is an F gate because:

Therefore, all these single-quantum Dieter gates can be realized by using the OAM as the degree of freedom. A particularly suitable technique is based on spatial modes in few-mode fibers. As shown in Figure 39, the basic building blocks for this purpose are an OAM multiplexer 3902, an OAM demultiplexer 3904, the few-mode fiber itself, and a series of electro-optic modulators 3906. Since few-mode fibers are not compatible with integrated optics, the gates based on single-quantum Dieter OAM can be modified as described below.

By using the basic quantum Dieter gate shown in Figure 38, a more complex quantum module as shown in Figure 40 can be realized. An OAM-based quantum teleportation module 4002 is shown in FIG. 40 . Module 4002 includes an OAM-based quantum quantum Dieter teleportation module 4004 , which includes a generalized Bell state generator module 4006 . The generalized Bell state generator module 4006 includes a generalized F gate 4008 and a generalized X gate 4010. Input 4012 is applied to generalized F gate 4008 and input 4014 is provided to generalized X gate 4010. The output of generalized F-gate 4008 is also provided as a second input to generalized X-gate 4010 . In addition to including the generalized Bell state generator module 4006, the OAM-based quantum quantum Dieter teleportation module 4004 provides outputs from each F-gate 4008 to the generalized Xnot gate 4012 and from the generalized Xnot gate 4010 to the Xnot gate 4014 . A second input is provided from input 4016 to generalized Xnot gate 4012 . Input 4016 is also provided to generalized F-gate 4018. Xnot gate 4012 also provides input to measurement circuit 4024 for performing measurements on the output of the gate. The output of generalized F-gate 4018 is provided as input to measurement circuit 4020 and as input to generalized Z-gate 4022, which also has an input from Xnot gate 4014 therein. The output of the generalized Z-gate 4022 provides the output 4026 of the OAM waste quantum quantum diet teleportation module 4002. |B ₀₀ > can be used to represent the following simplest generalized Belki right vector:

Another example as shown in FIG. 41 illustrates the syndrome calculator module 4102. The syndrome calculator module 4102 is important in fault-tolerant computing and quantum error correction. The syndrome calculator module 4102 includes |x>input 4104 and |y>input 4106. |y> input 4106 is provided to generalized F-gate 4108. The output of the generalized F-gate 4108 is provided to an inverse G-function gate 4110, the output of which is connected to an adder circuit 4112, which adds the output of the |x> input AND the output of the gate 4110. Adder circuit 4112 also receives input from |x> input 4104 and its output is connected to generalized G-gate 4114. The output of the generalized G-gate is connected to the input of the generalized F-gate 4116. The output of generalized F-gate 4116 is connected to the input of inverse G-function gate 4118, whose output is connected to adder circuit 4120, which adds the output of the |x> input to the output of gate 4118. Adder circuit 4120 is also connected to |x> input 4104. The output of the adder circuit 4120 is connected to the input of a generalized G-gate 4122, the output of which is provided as an output node 4124. |x> The output of input 4104 is also provided as output 4126.

In both applications, syndromes may be determined according to the scheme shown by block 4202 shown in Figure 42 to identify quantum errors based on syndrome measurements. The |0> input 4204 is provided to the input of the generalized F-gate 4206. The output of generalized F-gate 4206 is provided to the input of another generalized F-gate 4208 to the input of syndrome calculator module 4210 , which provides a pair of outputs to another functional module 4212 . Function module 4212 also receives |Xn> input 4214. The output of generalized F-gate 4208 is provided to measurement circuit 4214.

In the syndrome decoding module 4202, the syndrome calculator module 4210S(b _i ,a _i ) corresponds to the quantum check of the non-binary quantum error correction code of the ith generator g _i =[a _i |b _i ] matrix:

In the above formula, the parameter a _i is used to represent the action of the X( _ai ) quantum Dieter gate on the _i -th quantum Dieter position, and the use of bi is used to represent the Z(bi ) quantum Dieter gate on the _ith quantum The role of the Dieter position. Any error belongs to the multiplicative Pauli group (error group) on the quantum Dieter G _N = {ω ^c X(a)Z(b)|a,b∈GF(q) ^N }. By denoting the error operator as e=(c|d), corresponding to E= ^ωc X(c)Z(d), the syndrome can be calculated as S(E)=S(c,d)=eA ^T .

The quantum circuit of Figure 42 will provide non-zero measurements if the detectable errors are not equivalent to multiples of _gi . A correctable quantum Dieter error is a qK-dimensional subspace that maps the code space to a qN-dimensional Hilbert space. Since there are NK generators, or equivalent syndrome positions, there are q ^NK distinct cosets. All quantum Dieter errors belonging to the same coset have the same syndrome. By choosing the most probable quantum Dieter error, usually the lowest weight error, for the coset representative, quantum Dieter errors can be uniquely identified and error correcting actions performed accordingly. Alternatively, maximum likelihood decoding can be used. However, the decoding complexity will be significantly higher.

表示的量子态到达单量子迪特门的输入。现在参考图43，示出了根据本公开实现的量子计算机的框图。量子计算机4300接收输入数据4302并响应于此提供输出数据4304。量子计算机利用多个部件来提供该处理功能。量子计算机4300包括量子门4306与量子模块4308的组合，用于执行处理功能。量子门4306和量子模块4308的结构性质如本文所述。在量子计算机4300内传输的信号可以使用轨道角动量处理130和自旋角动量处理4302的组合。轨道角动量处理4310和自旋角动量处理4312的特定性质如本文所述。利用DLP或其它光处理系统4314辅助信号的OAM处理，如下文所述。The implementation of OAM-based single-quantum Ditt gates and generalized CNOT gates will now be described more fully. OAM-based single-quantum Dieter gates can be implemented in integrated optics with the aid of computer-generated holograms implemented using DLP as described above. Depend on

The represented quantum state arrives at the input of the single-quantum Dieter gate. Referring now to FIG. 43, shown is a block diagram of a quantum computer implemented in accordance with the present disclosure. Quantum computer 4300 receives input data 4302 and provides output data 4304 in response thereto. Quantum computers utilize multiple components to provide this processing capability. Quantum computer 4300 includes a combination of quantum gates 4306 and quantum modules 4308 for performing processing functions. The structural properties of quantum gate 4306 and quantum module 4308 are as described herein. Signals transmitted within quantum computer 4300 may use a combination of orbital angular momentum processing 130 and spin angular momentum processing 4302. Specific properties of orbital angular momentum processing 4310 and spin angular momentum processing 4312 are described herein. OAM processing of the signal is facilitated using a DLP or other optical processing system 4314, as described below.

作为图示，通过将E/O调制器3606实现为引入衰减D^-1/2的衰减器与在第m分支中引入相移-(2π/p)nm的相位调制器3906的级联来获得F门。通过对应的相位调制器在第m分支中引入相移(2π/p)bm来获得广义Z(b)门。通过在第m个分支中使用CGH(计算机生成的全息图)以引入exp(jaφ)形式的方位角相移来获得广义X(a)门。As previously shown in Figure 39, in the OAM demultiplexer 3904, the basis right vector is split by a set of electro-optic modulators 3606 (E/O MOD) prior to processing. The desired phase shift and/or amplitude change is introduced by the electro-optic modulator 3606 to perform the desired single quantum Ditt operation. The basis right vector is compounded into a single quantum ditter in the OAM multiplexer 3902 to obtain the output quantum state

As an illustration, obtained by implementing the E/O modulator 3606 as a cascade of an attenuator introducing an attenuation D ^-1/2 and a phase modulator 3906 introducing a phase shift -(2π/p)nm in the mth branch F gate. A generalized Z(b) gate is obtained by introducing a phase shift (2π/p)bm in the mth branch by a corresponding phase modulator. A generalized X(a) gate is obtained by using a CGH (computer-generated hologram) in the mth branch to introduce an azimuthal phase shift of the form exp(jaφ).

Referring now to FIG. 44, by implementing E/O modulator 3906 as a cascade of amplitude modulator 4402 and phase modulator 4404 or a single I/Q modulator, by appropriately adjusting the amplitude and phase changes in each branch to simply initialize to an arbitrary state. For example, a superposition of all basis right vectors with the same probability magnitude is obtained by simply introducing an amplitude change D- ^1/2 in each branch, while setting the phase shift to zero.

Referring now to FIG. 45, a generalized CNOT gate 4502 (in which polarization qubits 4404 are used as control qubits and OAM quantum ditters 4406 are used as target qubits) is a quantum gate that is an essential component in quantum computer architecture. Generalized CNOT gates can be used to entangle or disentangle EPR states. Any quantum circuit can be simulated to arbitrary precision using a combination of CNOT and single quantum Dieter rotations. Here, we focus on implementations in which both the control 4404 quantum ditter and the target 4406 quantum ditter are OAM states. The holographic interaction between the OAM state | _IC and the OAM state | _IT can be described by the following Hamiltonian:

H=gJ _C J _T

Referring now to Figure 46, the operation of a CNOT gate on a quantum register consisting of two qubits is shown. The CNOT gate flips the second qubit (target qubit) 4406 if and only if the first qubit (control qubit) 4404 is |1>.

The corresponding time evolution operator is given by:

U(t)=exp[-jtgJ _C J _T ]=exp[-jtgI _C I _T I ₄ ]

By choosing gt=2π/(L _- +L ₊ ), the following unary operator is obtained:

This is clearly the generalized controlled Z operator. The generalized CNOT operator can be obtained by transforming the generalized controlled Z operator as follows:

Because such OAM interactions do not require the use of nonlinear crystals or highly nonlinear fibers, OAM states represent interesting quantum Dieter representations for quantum computing, quantum teleportation, and QKD applications. Arbitrary quantum computations are possible by using the described OAM gates, assuming that generalized X gates, generalized Z gates, and generalized CNOT gates represent a set of universal quantum gates. It has been shown that the quantum Dieter set of the following gates including generalized X, generalized Z, and generalized CNOT or generalized controlled phase is universal.

Bell state

Generalized Bell states |B ₀₀ > can also be generated. Generate arbitrary generalized Bell states in the following way. By applying the same gates as in the figure, but now on the right vectors |n> and |m>, we obtain:

By now applying the generalized CNOT gate, the desired generalized Bell state |B _mn > is obtained:

Another way to generate |B _mn > is to start with |B ₀₀ > and apply a Wilman on the second quantum Dieter in the entangled pair, which is defined as

Welmen can be easily implemented by moving from the dth branch to the (d+m)mod D branch and introducing a phase shift -2πdk/D in this branch.

All elements required to formulate entanglement assistance protocols based on OAM are now available. Multidimensional QKD is described more fully below. The proposed quantum Dieter gates and modules can be used to implement important quantum algorithms more efficiently. For example, the basic building block of the Grover's search algorithm that performs searches of entries in an unstructured database is the Grover Quantum Dieter operator, which can be expressed as:

where F is the QFT quantum Dieter gate and O is the Oracle operator, defined as:

O|x>=(-1) ^f(x) |x>; x=(x ₁ x ₂ …x _N ), x _i ∈ GF(q)

where f(x) is the search function, which generates 1 when the search item is found, and 0 otherwise. Shor's decomposition and Simon's algorithms are also easy to generalize.

The main problem associated with OAM-based gates is the imperfect generation of OAM patterns (especially using DLP). Currently existing CGHs still exhibit measurable OAM crosstalk. On the other hand, OAM is a very stable degree of freedom that does not change much unless the OAM mode propagates over the atmospheric turbulent channel. Furthermore, the OAM state is maintained after kilometer-scale propagation in a properly designed fiber. Noise affects OAM-carrying photons in the same way that it affects the polarization state of photons. Noise is more relevant in photon number-based optical quantum computing than in OAM-based quantum computing.

Quantum Key Distribution

As mentioned above, one way of using OAM-based quantum computing involves the use in processes such as quantum key distribution (QKD). In the current QKD system, the system is very slow. By implementing the above quantum gate computing system using OAM, the system can increase the security and throughput communication while increasing the computing and processing power of the system. The QKD operation will be implemented in a quantum module implementing the process described above. Referring now to FIG. 47, a further improvement of the system utilizing orbital angular momentum processing, Laguerre Gaussian processing, Hermitian Gaussian processing, or processing using any orthogonal function is shown. In the illustration of FIG. 47 , transmitter 4702 and receiver 4704 are interconnected by optical link 4706. Optical links 4706 may include fiber optic links or free space optical links. The transmitter receives data stream 4708 processed via orbital angular momentum processing circuit 4710. As described above, the orbital angular momentum processing circuit 4710 provides orbital angular momentum twist on separate channels to the various signals. In some embodiments, the orbital angular momentum processing circuit may further provide multi-layer superposition modulation to the signal channel to further increase the system bandwidth.

The OAM processed signal is provided to quantum key distribution processing circuit 4712. Quantum key distribution processing circuit 4712 utilizes the principles of quantum key distribution, described more fully below, to enable encryption of signals transmitted over optical link 4706 to receiver 4704. The received signal is processed within receiver 4704 using quantum key distribution processing circuit 4714. The quantum key distribution processing circuit 4714 decrypts the received signal using quantum key distribution processing, which is described more fully below. The decrypted signal is provided to orbital angular momentum processing circuit 4716, which removes any orbital angular momentum twist from the signal to generate a plurality of output signals 4718. As previously mentioned, the orbital angular momentum processing circuit 4716 may also demodulate the signal using the multi-layer superposition modulation included within the received signal.

Orbital angular momentum combined with optical polarization is utilized in the circuit of Figure 47 to encode information in a rotationally invariant photon state to ensure complete independence of communications from local reference frames from transmit unit 4702 and receive unit 4704, There are many ways to implement quantum key distribution (QKD), a protocol that exploits the properties of quantum mechanics to guarantee unconditional security in cryptographic communications with error rate performance that is fully compatible with real-world application environments.

Encrypted communication requires the exchange of keys in a protected manner. This key exchange is usually done through a trusted authority. Quantum key distribution is an alternative solution to the key establishment problem. In contrast to e.g. public key cryptography, key distribution is proven to be unconditionally secure, i.e. secure even against any future attack, regardless of computing power or any other resources that may be used. Quantum key distribution security relies on the laws of quantum mechanics, and more specifically on the fact that it is impossible to obtain information about non-orthogonal quantum states without disturbing these states. This feature can be used to establish a random key between the transmitter and receiver and guarantee that the key is completely secret from any online third party eavesdropping.

In parallel with the "full quantum proof" described above, the security of QKD systems has been placed on a stable information-theoretic basis, thanks to the work done within the framework of information-theoretic cryptography on secret key agreements and its extensions. Referring now to FIG. 48, within a basic QKD system, a QKD link 4802 is a point-to-point connection between a transmitter 4804 and a receiver 4806 that wish to share a secret key. QKD link 4802 consists of a combination of quantum channel 4808 and classical channel 4810. Transmitter 4804 generates a random stream of classical bits and encodes it into a non-orthogonal sequence of states for light transmitted over quantum channel 4808. Upon receiving these quantum states, the receiver 4806 performs some appropriate measurements, causing the receiver to share some classical data on the classical link 4810 associated with the transmitter bit stream. Classical channel 4810 is used to test these correlations.

If the correlation is high enough, this statistic means that no significant eavesdropping has occurred on the quantum channel 4808, and therefore with a very high probability, a preferably secure symmetric key can be obtained from the one shared by the transmitter 4804 and receiver 4806 extracted from the relevant data. In the opposite case, the key generation process must be aborted and started again. Quantum key distribution is a symmetric key distribution technique. For authentication purposes, quantum key distribution requires the transmitter 4804 and receiver 4806 to pre-share a short key whose length is only logarithmically scaled on the length of the secret key generated by the OKD session.

Regional-scale quantum key distribution has been demonstrated in many countries. However, free-space optical links are required for long-distance communication (including the important case of satellite-based links) between areas not suitable for fiber optic installations or mobile terminals. The present method exploits the spatial lateral modes of the beam, in particular the spatial lateral modes of the OAM degrees of freedom, in order to obtain a significant technical advantage, namely the insensitivity of the communication to the relative alignment of the user's reference frame. This advantage may be very relevant to upgrading quantum key distribution implementations from regional scales to countries or continents, or links across hostile ground, or even envisioning quantum key distribution on a global scale by utilizing orbital terminals on satellite networks.

的光子表征。“l”的潜在无限值开放了利用OAM来增加通信系统的容量的可能性(尽管以也增加了信道横截面尺寸为代价)，以及基于OAM复用的太比特经典数据传输可以在自由空间和光纤中展示。这种特征也可以在量子域中利用，例如扩展每个光子的量子比特数量，或者实现新的功能，例如量子比特的旋转不变性。OAM eigenmodes are characterized by twisted wavefronts consisting of helices wound with "l", where "l" is an integer, and, by carrying spin angles other than those associated with polarization, which are more common In addition to momentum (SAM) there is (orbital) angular momentum

photon characterization. The potentially infinite value of "l" opens up the possibility of utilizing OAM to increase the capacity of communication systems (albeit at the expense of also increasing the channel cross-sectional size), and that OAM multiplexing-based terabit classical data transmission can be performed in free space and Displayed in fiber optics. This feature can also be exploited in the quantum domain, for example to expand the number of qubits per photon, or to enable new functions such as the rotational invariance of qubits.

In free-space QKD, two users (Alice and Bob) must establish a shared reference frame (SRF) in order to communicate with good fidelity. Indeed lack of SRF is equivalent to an unknown relative rotation, which introduces noise into the quantum channel, disrupting communication. When the information is encoded in the photon polarization, such a frame of reference can be defined by the orientation of Alice and Bob's "horizontal" linear polarization direction. Alignment of these directions requires additional resources and can impose severe obstacles in long-range free-space QKD/or when misalignment varies over time. As pointed out, we can solve this problem by using rotation-invariant states, which completely remove the need to build an SRF. This state is obtained as a specific combination of OAM and polarization modes (hybrid states) for which the transformation caused by misalignment in polarization is precisely balanced by the effect of the same misalignment in spatial mode. These states exhibit global symmetry under the rotation of the beam around its axis, and can be visualized as spatially varying polarization states, generalizing the well-known azimuthal and radial vector beams, and forming a two-dimensional Hilbert space. Furthermore, this rotation-invariant mixing space can also be considered as a decoherence-free subspace of the Hilbert space of the four-dimensional OAM polarization product, which is insensitive to the noise associated with random rotations.

Mixed states can be created by a specific spatially varying birefringent plate with a topological charge "q" (called a "q-plate") at its center. In particular, a polarized Gaussian beam (with zero OAM) passing through a q-plate with q=1/2 will undergo the following transformation:

的SAM的本征态)，|0>_O表示具有零OAM的横向高斯模式，OAM的|L>_O_和|R>_O本征状态的|l|＝1且具有本征值

)。出现在方程右手侧的状态是旋转不变状态。与此相反的操作可以通过具有相同q的第二q板来实现。在实践中，q板作为偏振空间和混合电路之间的接口进行操作，以通用(量子比特不变)方式将量子比特从一个空间转换到另一个空间，反之亦然。这又意味着我们的QKD实现协议中的信息的初始编码和最终解码可以方便地在偏振空间中执行，而传输在旋转不变混合空间中完成。|L> _{π_} and |R> _π denote the left and right circular polarization states (with eigenvalues

SAM of eigenstates), |0> _O denotes a transverse Gaussian mode with zero OAM, |L> _{O_ and |R>O eigenstates} of OAM |l|=1 and have eigenvalues

). The states that appear on the right-hand side of the equation are rotationally invariant states. The opposite operation can be achieved by a second q-plate with the same q. In practice, q-plates operate as an interface between polarization space and hybrid circuits, converting qubits from one space to another and vice versa in a universal (qubit-invariant) manner. This in turn means that the initial encoding and final decoding of information in our QKD implementation protocol can be conveniently performed in polarization space, while transmission is done in rotation-invariant mixing space.

OAM is a conserved quantity for light propagation in vacuum, which is obviously important for communication applications. However, OAM is also highly sensitive to atmospheric turbulence, a feature that limits its potential use in many practical situations unless new techniques are developed to address such issues.

Quantum cryptography describes the use of quantum mechanical effects, particularly quantum communication and quantum computing, to perform cryptographic tasks or to break cryptographic systems. Known examples of quantum cryptography are the use of quantum communication to securely exchange keys (quantum key distribution) and the hypothetical use of quantum computers that allow breaking various popular public key encryption and signature schemes (eg, RSA).

The beauty of quantum cryptography is that it allows for a variety of cryptographic tasks that have proven impossible to accomplish using only classical (ie, non-quantum) communication. For example, quantum mechanics guarantees that measuring quantum data interferes with that data; this can be used to detect eavesdropping in quantum key distribution.

Quantum Key Distribution (QKD) uses quantum mechanics to guarantee secure communications. It enables both parties to generate a shared random encryption key known only to them, which can then be used to encrypt and decrypt messages.

An important and unique property of quantum distributions is the ability of two communicating users to detect the presence of knowledge of any third party trying to obtain a key. This comes from a fundamental aspect of quantum mechanics: The process of measuring a quantum system usually disturbs the system. A third party trying to eavesdrop on the key would have to measure the key in some way, introducing a detectable anomaly. By using quantum overlap, or quantum entanglement, and sending information in a quantum state, a communication system that detects eavesdropping can be achieved. If the eavesdropping level is below a certain threshold, a secure key can be generated (ie, the eavesdropper has no information about it), otherwise no secure key is possible and the communication is aborted.

The security of quantum key distribution relies on the foundations of quantum mechanics, as opposed to traditional key distribution protocols that rely on the computational difficulty of certain mathematical functions, and cannot provide any indication of eavesdropping or guarantees of key security.

Quantum key distribution is only used to reduce and distribute keys, not to transmit any message data. This key can then be used with any encryption algorithm of choice to encrypt (and decrypt) messages transmitted over standard communication channels. The algorithm most often associated with QKD is the one-time pad, as it is proven secure when used with an encrypted random key.

Quantum communication involves encoding information in quantum states, or qubits, as opposed to traditional communication, which uses bits. Typically, photons are used for these quantum states and thus can be applied in quantum computing systems. Quantum key distribution exploits certain properties of these quantum states to ensure their security. There are several methods for quantum key distribution, but they can be divided into two main categories, depending on the properties they exploit. The first of these features is the preparation and measurement protocol. Contrary to classical physics, the act of measuring is an integral part of quantum mechanics. Generally speaking, measuring an unknown quantum state changes the state in some way. This is called quantum uncertainty, and fundamental results such as Heisenberg's uncertainty principle, the information distribution theorem, and the non-cloning theorem. This can be exploited in order to detect any eavesdropping on communications (which necessarily involve measurements) and, more importantly, to calculate the amount of information that has been intercepted. Thus, by detecting changes in the signal, the amount of wiretapping or information that has been intercepted can be determined by the recipient.

The second category involves the use of entanglement-based protocols. The quantum states of two or more separate objects can be linked together in such a way that they must be described by the combined quantum state, rather than as separate objects. This is called entanglement, and means that, for example, performing a measurement on one object affects another. If an entangled pair of objects is shared between two parties, any interception of either object alters the entire system, revealing the existence of third parties (and the amount of information they have acquired). Thus, undesired receipt of information can be determined by changes in the entangled pair of objects shared between parties when intercepted by an unauthorized third party.

An example of a quantum key distribution (QKD) protocol is the BB84 protocol. The BB84 protocol was originally described using the photon polarization state to transmit information. However, any two pairs of conjugated states can be used for this protocol, and a fiber-based implementation described as BB84 can use phase-encoded states. A transmitter (traditionally called Alice) and a receiver (traditionally called Bob) are connected by a quantum communication channel that allows the emission of quantum states. In the case of photons, this channel is usually an optical fiber, or simply free space, as previously described with respect to FIG. 47 . Furthermore, the transmitter and receiver communicate via a common classical channel, eg using broadcast radio or the Internet. None of these channels need to be secure. The protocol is designed to assume that an eavesdropper (called Eve) can interfere with the transmitter and receiver in any way.

Referring now to Figure 49, the security of the protocol comes from encoding information in a non-orthogonal state. Quantum uncertainty means that these states generally cannot be measured without disturbing the original state. BB84 uses two pairs of states 4902, each conjugated to the other to form a conjugated pair 4904. The two states 4902 within the pair 4904 are orthogonal to each other. Orthogonal state pairs are called bases. Typical polarization state pairs used are vertical (0 degrees) and horizontal (90 degrees) straight-line bases, diagonal bases of 45 and 135 degrees, or left-handed and/or right-handed circular bases. Any two of these groups are conjugated to each other, so any two can be used in the protocol. In the example of Figure 50, a linear basis is used at 5002 and 5004, and a diagonal basis is used at 5006 and 5008, respectively.

The first step in the BB84 protocol is quantum transmission. Referring now to FIG. 51, there is shown a flow chart describing the process in which the transmitter creates random bits (0 or 1) at step 5102, and at 5104 randomly selects one of the two bases, rectilinear or diagonal, to Send random bits. The transmitter prepares the photon polarization state at step 5106 according to the bit value and the selected basis. For example, 0 is encoded as the vertical polarization state in the linear basis (+) and a1 is encoded as the 135 degree state in the diagonal basis (X). The transmitter at step 5108 transmits a single proton to the receiver in the specified state using the quantum channel. The process repeats from the random bit stage of step 5102, with the transmitter recording the state, basis and time of each photon sent over the optical link.

According to quantum mechanics, there is no possible measurement to distinguish between the four different polarization states 5002 to 5008 of Figure 50, since they are not all orthogonal. The only possible measurements are between any two orthogonal states (and orthogonal bases). Thus, for example, measuring on a straight line base gives horizontal or vertical results. If the photo is created horizontal or vertical (as a line eigenstate), this measures the correct state, but if it is created as 45 degrees or 135 degrees (diagonal eigenstates), the line measurement instead randomly returns horizontal or vertical. Furthermore, after this measurement, the protons are polarized in the measured state (horizontal or vertical), where all information about their original polarization is lost.

Referring now to Figure 52, since the receiver does not know the basis in which the photons are encoded, the receiver can only choose a random basis, measured in a straight line or diagonally. In step 5202, the transmitter does this for each received photon, and in step 5204, the time measurement base used and the measurement results are recorded. At step 5206, it is determined whether additional protons are present, and if so, control returns to step 5202. Once inquiry step 5206 determines that the receiver has measured all protons, the transceiver communicates with the transmitter at step 5208 over a common communication channel. The transmitter broadcasts the basis of each photon transmitted at step 5210 and the receiver broadcasts the basis of each photon measured at step 5212. At step 5216, each of the transmitter and receiver discards the photon measurement, where the receiver uses a different basis at step 5214, which averages half, at step 5216 leaving half of the bits as the shared key. This process is shown more fully in FIG. 53 .

The transmitter transmits random bits 01101001. For each of these bits, the transmitter selects a transmit base of straight, straight, diagonal, straight, diagonal, diagonal, diagonal, and straight. Thus, the polarization indicated in line 5202 is provided based on the selected associated random bits and random transmit bases associated with the signal. Upon receiving a photon, the receiver selects a random measurement basis as shown by line 5304. The photon polarization measurements from these bases will then be shown as line 5306. A public discussion of the transmitted basis and the measurement basis is discussed at 5308, and the encryption key is determined to be 0101 at 5310 based on the matching basis for the emitted photons 1, 3, 6, and 8.

Referring now to FIG. 54, shown is a process for determining whether to keep or relinquish a confirmed key based on errors detected within the determined bit string. To check for the presence of eavesdropping, the transmitter and receiver compare at step 5402 some subset of their remaining bit strings. If a third party obtains any information about the polarization of the photon, this can introduce errors in the receiver's measurements. If there are more than P bits different in challenge step 5404, the key is discarded in step 5406, and the transmitter and receiver may try again using different quantum channels, since the security of the key cannot be guaranteed. P is chosen such that if the number of bits known to the eavesdropper is less than this value, privacy amplification can be used to reduce the eavesdropper's knowledge of the key to an arbitrarily small amount by reducing the length of the key. If query step 5404 determines that the number of bits is not greater than P, then at step 5408 the key may be used.

The E91 protocol includes another quantum key-partitioning scheme using entangled proton pairs. This protocol can also be used for entangled proton pairs processed using orbital angular momentum processing, Laguerre-Gaussian processing, Emmelt-Gaussian processing, or any orthogonal function using Q bits. An entangled pair may be created by a transmitter, receiver, or some other source separate from both the transmitter and receiver including the eavesdropper. The photons are distributed so that the transmitter and receiver each end up with one photon in each pair. The scheme relies on two properties of entanglement. First, the entangled states are perfectly correlated, in the sense that if both the transmitter and receiver measure whether their particles both have vertical or horizontal polarization, they always get the same answer with 100% probability. The same is true if they both measure the complementary (orthogonal) polarization of any other pair. However, specific outcomes are not completely random. It is impossible for the transmitter to predict whether the transmitter and therefore the receiver will obtain vertical or horizontal polarization. Second, any attempt to eavesdrop on a third party destroys these correlations in a way that the transmitter and receiver can detect. The original Ekert protocol (E91) includes three possible states and tests for Bell's inequality violations to detect eavesdropping.

Currently, the highest current bit rate systems using quantum key distribution demonstrate secure key exchange of 1 megabit per second over 20 kilometers of fiber and 10 kilobits per second over 100 kilometers of fiber.

The longest distance to prove quantum key distribution using fiber optics is 148 kilometers. This distance is long enough for almost all spans found in today's fiber optic networks. The distance recorded for free-space quantum key distribution with BB84 enhanced by the decoy state is 134 km.

而X基状态对应于

发射机5502使用四个不同的偏振衰减激光器5508通过量子比特生成器5510产生量子比特。来自量子比特生成器4550的光子通过单模光纤5512被传送到望远镜5514。通过q＝1/2的q板5516将偏振状态|H>、|V>、|R>、|L>变换为旋转不变混合状态。然后可以将光子传输到接收站5504，其中第二q板变换5518将信号变换回由接收机参考框架5504限定的原始偏振状态|H>、|V>、|R>、|L>。然后可以通过偏光器5520和单光子检测器5522分析量子点。来自偏光器5520和光电检测器5522的信息然后可以被提供给接收机控制器5524，使得可以通过仅仅保留与由通信确定的发射机和接收机侧的相同基对应的比特来获得移位的密钥，其中所述通信在发射机5502和接收机5504中的收发器5526、5528之间的经典信道上进行。Referring now to FIG. 55, there is shown a functional block diagram of a transmitter 5502 and a receiver 5504 that can implement the alignment of free-space quantum key distribution. The system can execute the BB84 protocol with decoy state. Controller 5506 enables bits to be encoded in two mutually unbiased basis Z={|0>,|1>} and X={|+>,|->}, where |0> and |1> are spanning quantum Two orthogonal states of the bit space, |±>=1/√2 (|0>±|1>). Transmitter controller 5506 randomly selects between Z and X bases to transmit classical bits 0 and 1. In hybrid coding, the Z basis corresponds to

while the X-based state corresponds to

Transmitter 5502 generates qubits through qubit generator 5510 using four different polarization attenuated lasers 5508. Photons from qubit generator 4550 are transmitted to telescope 5514 through single mode fiber 5512. The polarization states |H>, |V>, |R>, |L> are transformed into rotation-invariant hybrid states by the q-plate 5516 with q=½. The photons may then be transmitted to the receiving station 5504, where a second q-plate transform 5518 transforms the signal back to the original polarization states |H>, |V>, |R>, |L> defined by the receiver reference frame 5504. The quantum dots can then be analyzed by polarizer 5520 and single photon detector 5522. The information from the polarizer 5520 and photodetector 5522 can then be provided to the receiver controller 5524 so that the shifted encryption can be obtained by retaining only the bits corresponding to the same base on the transmitter and receiver sides as determined by the communication. key, where the communication takes place on a classical channel between transceivers 5526, 5528 in transmitter 5502 and receiver 5504.

Referring now to FIG. 56, a network cloud based quantum key distribution system is shown that includes a central server 6202 and various attached nodes 5604 in hub and spoke configurations. The trend in networks presents new security issues that are challenging to meet conventional cryptography due to limited computational resources or the difficulty of providing proper key management. In principle, quantum cryptography, with its forward security and lightweight computing power, can meet these challenges, as long as it can evolve from current point-to-point architectures to forms compatible with multimodal network architectures. Trusted quantum key distribution networks for peer-to-peer link-based networks lack scalability, require dedicated optical fibers, are expensive, and are not suitable for mass production because they provide only one of the cryptographic functions, the encryption required for secure communication key assignment. Therefore, they have limited practical interest.

A new scalable approach such as that shown in Figure 56 provides quantum information assurance, which is a network-based quantum communication that can address new cybersecurity challenges. In this approach, BB84-type quantum communication between each of the N client nodes 5604 and the central server 5602 at the physical layer supports a quantum key management layer, which in turn enables the communication between approximately N2 client pairs. Secure communication functions at the application layer (confidentiality, authentication and non-repudiation). This network-based communication "hub and spoke" topology can be implemented in a network setting and allows for a layered trust architecture that allows the server 5602 to act as a server for quantum authentication key establishment Trusted Authority in Cryptographic Protocols. This avoids the problem of poor scalability in previous approaches that required a pre-existing trust relationship between each pair of nodes. By making a server 5602, a single multiplexed QC (quantum communication) receiver and client node 5604 QC transmitter, the network can simplify the complexity of multiple network nodes. In this way, the network-based quantum key distribution architecture is scalable both in terms of quantum physical resources and trust. One can time multiplex server 5602 with three transmitters 5604 on single mode fiber, which can be accommodated using a combination of time and wavelength multiplexing and orbital angular momentum multiplexed with wavelength division multiplexing Larger number of clients to support higher clients.

Referring now to Figures 57 and 58, various components of a multi-user orbital angular momentum based quantum key distribution multiple access network are shown. Figure 57 shows a high-speed single-photon detector 5702 located at a network node, which can be shared among multiple users 5704 using conventional network architectures, thereby significantly reducing the hardware requirements for each user added to the network. In one embodiment, the single photon detector 5702 can be shared by up to 64 users. This shared-receiver architecture removes one of the main barriers limiting the widespread application of quantum key distribution. This embodiment presents a feasible method for implementing a resource-efficient multi-user quantum key distribution network.

Referring now also to FIG. 58, in a node quantum key distribution network, multiple trusted repeaters 5802 are connected via point-to-point links 5804 between nodes 5806. The repeaters are connected by a point-to-point link 5804 between the quantum transmitter and the quantum receiver. These point-to-point links 5804 can be implemented using long fiber lengths and can even utilize ground-to-satellite quantum key distribution communications. While point-to-point connections 5804 are suitable for forming backbone quantum core networks, they are less suitable for providing the last mile services required to provide multiple users with access to quantum key distribution infrastructure. Reconfigurable optical networks based on optical switches or wavelength division multiplexing can enable more flexible network structures, however, they also require the installation of a full quantum key distribution system for each user, which is very expensive for many applications.

The quantum key signal used in quantum key distribution only needs to travel in one direction along the fiber to establish a secure key between the transmitter and receiver. The transmitter is located at the network node 5806 for single-photon quantum key distribution and the receiver at the customer premises is therefore suitable for passive multi-user network approaches. However, this downstream implementation has two major drawbacks. First, each user in the network requires a single photon detector, which is often expensive and difficult to operate. Additionally, it is not possible to address the user deterministically. Therefore, all detectors must operate at the same speed as the transmitter in order not to miss photons, which means that most of the detector bandwidth is unused.

Most systems associated with downstream implementations can be overcome. The most valuable resource should be shared by all users and should be operated at full capacity. An upstream quantum access network can be constructed where transmitters are placed at end user locations and common receivers are placed at network nodes. In this way, operation with up to 64 users is feasible, which can be done with a 1x64 passive optical splitter for multi-user quantum key distribution.

The above QKD solution can be applied to twisted pair, coaxial cable, optical fiber, RF satellite, RF broadcast, RF point-to-point, RF point-to-multipoint, RF point-to-point (backhaul), RF point-to-point (fronthaul to provide for RAN and cloudification) HetNet's cloudified and virtualized higher throughput CPRI interface), free space optics, Internet of Things (IOT), WiFi, Bluetooth, as a cable replacement for personal devices, hybrid systems of RF and FSO devices, radar, electromagnetic tags and All types of wireless access. The method and system are compatible with many current and future multiple access systems, including EV-DO, UMB, WIMAX, WCDMA (with or without), Multimedia Broadcast Multicast Service (MBMS)/Multiple Input Multiple Output (MIMO), HSPA Evolution and LTE. These techniques would be useful for combating denial of service attacks by routing communications over alternate links in the event of an outage, as a technique against Trojan horse attacks (which do not require physical access to endpoints), and as a countermeasure Techniques for pseudo-state attacks, phase remapping attacks, and time-shift attacks.

Therefore, using various configurations of the above-described orbital angular momentum processing, multilayer superposition modulation, and quantum key distribution within various types of communication networks (more specifically, fiber optic networks and free-space optical communication networks), system bandwidth and Multiple benefits and improvements in capacity.

和沿垂直于波前的光束轴5906指向的

的线性动量。独立于频率，光束5904内的每一个光子5902具有

的与光束传播方向平行或反平行的自旋角动量5908。所有光子5902自旋的对准产生圆偏振光束。除了圆偏振外，还可以处理光束以携带不依赖于圆偏振并且因此与光子自旋无关的轨道角动量5910。Referring now to the drawings, and more particularly to FIG. 59, one embodiment of a light beam for use with the system is shown. Beam 5904 consists of photon stream 5902 within beam 5904. Each photon has energy

and pointing along the beam axis 5906 perpendicular to the wavefront

linear momentum. Independent of frequency, each photon 5902 within beam 5904 has

of spin angular momentum 5908 parallel or antiparallel to the beam propagation direction. The alignment of all photon 5902 spins produces a circularly polarized beam. In addition to circular polarization, the beam can also be processed to carry orbital angular momentum 5910 that is independent of circular polarization and therefore independent of the photon spin.

Referring now to Figures 60 and 61, a planar wavefront and a helical wavefront are shown. Typically, a laser beam with a plane wavefront 6002 is characterized by Hermitian-Gaussian modes. These modes have rectangular symmetry and are described by two mode indices m 6004 and n 6006 . There are m nodes in the x direction and n nodes in the y direction. The combined mode in the x and y directions together is labeled HG _mn 6008. In contrast, as shown in FIG. 61 , the beam with a helical wavefront 6102 is best characterized by the Laguerre-Gaussian mode described by the index I 6103 , the number of staggered spirals 6104 and p, the number of radial nodes 6106 . The Laguerre-Gaussian mode is labeled LG _mn 610. For l≠0, the phase singularity on beam 6004 results in an on-axis intensity of 0. When a beam 6004 with a helical wavefront is also circularly polarized, the angular momentum has an orbital component and a spin component, and the total angular momentum of the beam is per photon

Existing techniques for improving electron hole recombination vary according to the particular type of device used. For example, as shown in Figure 62, within a biological Light Harvesting Complex (LHC), a light beam 6202 is applied to the LHC such that photon absorption 6204 produces molecular excited states. These molecular excited states contain excitons 6206 that are collected into reaction centers 6208 where they are dissociated into electrons 6210 and holes 6212. Electrons 6210 and holes 6212 are further separated by a series of cascaded charge transfer steps.

As shown in Figure 63, an organic photovoltaic cell (OPV) receives beam 6302 and uses light absorption 6304 to generate excitons 6306, which are applied to a single donor-acceptor formed in a demixed mixture of donor and acceptor semiconductors Primary heterojunction 6308 to generate electrons 6310 and holes 6312. The most efficient OPV systems include nanoscale (less than 5 nm in symbol) domains of pure fullerene acceptors and fullerene domains intimately mixed with polymer donors. These length scales are smaller than the Coulomb Capture Radius (CCR) in organic semiconductors (kT=e ² 4πε ₀ εr), which is restricted at room temperature due to the low dielectric constant of the material (approximately 3-4). Estimated to be up to 16nm. Therefore, in contrast to LHC, electrons and holes diffused through OPVs may meet each other before they reach the electrodes. This is similar to standard inorganic solar cells, where Bimolecular Electron-Hole Recombination (BR) determines solar cell performance. In addition to applying these techniques to OPV systems, the described techniques can be used to control electronics in solid-state semiconductor materials, quantum computing systems, and biological systems, as described below.

The electron-hole encounter rate that produces a Coulomb bound state is given by R=γn(p), where n(p) is the electron (hole) population density, and γ is given by γ=q<μ>/ε The Langevin recombination constant, where q equals the charge, <μ> equals the effective electron/hole mobility, and ε equals the permittivity. This model successfully describes the main operating mechanism of OLEDs, in which charges injected through the electrodes trap each other to form strongly bound excitons.

In empirically optimized OPVs, the recombination rate is suppressed by up to three orders of magnitude compared to the Langevin rate, allowing up to 80% external quantum efficiency. The recombination of bound states formed by electron/hole collisions is mediated not only by energetics, but also by spin and delocalization to allow free charge reformation from these bound states, thereby inhibiting recombination. This is illustrated in more detail in Figure 64, which shows that a beam including spin properties 6406 can be applied to a photonic device 6408 ( or other device/system). The results show that the photonic device 6408 (or other device/system) will have improved recombination rate suppression due to spin and delocalization properties.

Referring now also to FIG. 65, similar suppression of recombination between electrons and holes can be achieved using twisted photons carrying orbital angular momentum. The beam 6502 has orbital angular momentum imparted to it by, for example, a passive hologram, SLM (spatial light modulator), phase plate, or the like. The resulting twisted beam 6506 can then generate new quantum states that, when applied to the photonic device 6508 (or other device/system) providing a further improved recombination rate, slow the recombination rate.

A new design for an artificial light-conversion system uses circuits such as phase-mask holograms to apply orbital angular momentum (OAM) to optical signals and enables electron holes by avoiding triplet formation while improving fluorescence efficiency Compound inhibition. By placing the OAM circuit within the path of the photon, the orbital angular momentum generated by the photon can be transferred to the electron and the resulting new quantum state in which the suppression of electron-hole recombination is supported. This suppression is due to changes in the total angular momentum of electrons (spin and orbital) using a device that uses a variety of methods (either passively using holograms or actively using other methods) to twist protons with defined topological charges. The amount of applied orbital angular momentum results in a specific topological charge that can control the rate of recombination. Thus, by controlling the amount of OAM applied, the rate of inhibition of recombination can be controlled.

Thus, referring now to FIG. 66, a functional block diagram of one approach for improving the suppression of electron-hole recombination in photonic circuits is shown. Light beam 6602 passes through OAM device 6604 to produce OAM twisted light beam 6606. OAM device 6604 may include passive holograms, spatial light modules (SLMs), spatial plates, amplitude masks, phase masks, or any other device capable of applying orbital angular momentum to a beam of light. The amount of OAM twist applied to the beam can be controlled via the OAM control circuit 6605. The OAM control circuit 6605 can control the level of OAM twist based on the desired level of electron-hole recombination within the photonic device. The OAM twisted beam 6606 is applied to some type of photonic circuit 6608 that, in response to the OAM beam 6606, excites electrons to higher states that will resolve to the ground state. Photonic circuits may include optical LEDs, organic photovoltaic cells, biological light harvesting complexes, organic semiconductors, PN junctions, semiconductors, solid state devices, solar cells, or any other device affected by light. Additional components such as semiconductors, quantum circuits and biological materials can also apply OAM to their electrons from the OAM beam.

Reference is now made to Figure 67, which illustrates the manner in which electrons move from different states between various quantum states within an organic photovoltaic cell or other semiconductor, quantum circuit, or biological material. Transitions between excited state species are shown at 6702, while the recombination channel is shown at 6704. State S ₁ 6706 and state T ₁ 6708 are the lowest singlet excitons 6706 and triplet excitons 6708 , respectively. CT is the charge transfer state. At 6712, the photoexcitation goes from the ground state S ₀ 6710 to the singlet excitation S ₁ 6706. The singlet exciton S ₁ 6706 ionizes at the heterojunction, resulting in the formation of ^{a 1} CT state, which at 6714 separates into free charges (FC) 6702, 6704 with high efficiency. , biomolecular recombination of electrons and holes results in the formation of a ¹ CT state at 6716 and a ³ CT state at 6718 in a 1:3 ratio as dictated by spin statistics. ¹ CT can slowly recombine to the ground state as shown at 6720. The recombination of the ³ CT state to the ground state S ₀ 6710 is spin forbidden, but the relaxation of the T ₁ state 6708 at 6722 is energetically favorable. The triplet excitons ³ CT once formed can return to the ground state via the effective triplet charge annihilation channel at 6724. Under favorable conditions, the time required for the CT state to reorganize to a free charge at 6718 is less _than the time required to relax to T1 at 6722. Therefore, the CT state is recycled back to free charge, leading to the inhibition of recombination.

To probe the dynamics of these bound states, we can first consider the initial dissociation of the photogenerated singlet excitons S ₁ 6706 at the DA interface. The first step in this process is charge transfer through the DA interface, which may lead to long-range charge separation or the formation of bound interface charge transfer (CT) states. This bound charge pair then decays to the ground state S ₀ 6710 via Geminate Recombination (GR). It is important to note that spins must be taken into account when considering CT states, as they can have singlet ( ^1CT ) or triplet ( ^3CT ) spin features that are nearly energetically degenerate. Separation of light-generated singlet excitons results in the formation of only ¹ CT state 6704 due to spin conservation. In contrast, the recombination of spin-independent charges leads to the formation of ¹ CT and ³ CT states at a ratio of 1:3 based on spin statistics. The ¹ CT state can dissociate or recombine to the ground state by luminescent or non-radioactive decay that is slow for this intermolecular DA process. For the ³ CT state, the decay to the ground state is spin forbidden, so both the radiative and nonradiative processes are very slow. However, if the energy of the lowest molecular triplet exciton (T ₁ ) is lower than the ³ CT energy, then the ³ CT can relax to T ₁ .

The recombination model in the importance of spin statistics is well established in OLEDs where the formation of non-luminescent triplet excitons is the dominant loss mechanism. Efforts to overcome this problem have focused on the use of metal-organic complexes to induce spin-orbit coupling and, more recently, on the use _of low exchange energy materials that can facilitate the crossover _of internal systems from T1 to S1.

Thin films using Transient Absorption (TA) spectroscopy have been used in the past. In this technique, a pump pulse produces photoexcitation within the membrane. Later, broadband probe pulses are used to interrogate the system. Although TA has been widely used to study the photophysics of OPV blends, previous measurements have been individually limited by three factors. The first limitation has insufficient time range, typically a maximum 2ns delay between pump and probe. The second limitation has a limited spectral range and lack of broadband probes, which hinder the observation of dynamic interactions between excitations. Finally, the sensitivity is insufficient, which requires the use of high-throughput pump pulses to generate large signals.

These problems have recently been addressed using wide time (up to 1 ms) and spectral windows (up to 1500 nm) and high sensitivity (better than 5×10 ⁻⁶ ). This time window is created by using an electrically delayed pump pulse and allows the study of long-lived charges and triplet excitons. In conjugated polymers, local geometric relaxation (polaron formation) around the charge induces a rearrangement of energy levels, bringing states into the semiconductor gap and producing strong optical transitions 700nm–1500nm. The absorption bands of singlet and triplet excitons are also found to lie in the near IR, thus forming the broadband spectral window necessary to track the evolution of excited state species. The high sensitivity of the experiment is necessary because it allows probing the dynamics of the system when the excitation density is similar to solar illumination conditions (10 ¹⁶ -10 ¹⁷ excitations/cm ³ ). At higher excitation densities, bimolecular exciton-exciton and exciton-charge annihilation processes can dominate, creating artifacts that make this measurement an unreliable indicator of device operation. One can further combine these measurements with advanced numerical techniques that allow resolving spectral signatures of overlapping excited state signatures and tracking their dynamics.

The overlapping of excited state spectra makes it difficult to analyze their dynamics. To overcome this problem, Genetic Algorithm (GA) can be used, which allows us to extract individual spectra and dynamics from the dataset. In this approach, linear combinations of two or more spectra and associated dynamics can be taken and "evolved" until they best fit the experimental data.

The extracted kinetics can demonstrate that the triplet state can grow as the charge decays. It can be considered that the dominant decay channel for triplet states is triplet charge annihilation due to the presence of high charge density, and the time evolution of the system is modeled using the Langevin equation given below:

in:

p: charge concentration;

_NT : triplet concentration;

a: is the fraction of decay charges that form triplet states;

β: is the rate constant for triplet charge annihilation.

We now turn to the question of the time it takes to relax from ³ CT to T ₁ , is the process 6722 shown in Figure 67 with an associated timescale τ ₄ fast, and if not, is there a decay for ³ CT competitive process. As before, the CT energy is higher _than T1, making the relaxation from ^3CT to T1 _{energetically} favorable. However, for the more efficient 1:3 blend, triplet formation at room temperature is not possible. But at low temperature (<240K), the formation of bimolecular triplet states can be observed in this blend. This suggests that there is _a thermal activation process that competes with relaxation to T1. We consider the process to be the dissociation of ³ CT back to free charge. Thus, at high temperature (>240K), the dissociation of ³ CT back to free charge, process 6718 shown in Figure 67 with an associated timescale τ ₃ , outperforms the relaxation of ³ CT to T ₁ , That is, τ ₄ is greater than τ ₃ . Therefore, one of the two channels used for compounding is suppressed (the other signal is compounded by ¹ CT), allowing high EQE. At lower temperatures, this dissociation process is suppressed such that τ ₄ <τ ₃ , resulting in the accumulation of triplet excitons.

Referring now to Figure 68, there is shown a flow chart describing one way of suppressing electron-hole conversion within a photonic device by applying orbital angular momentum to the beam. First at step 6810, a desired OAM level for application to the beam is selected. The selected OAM level will provide the desired inhibition of the electron-hole recombination rate. At step 6812, an OAM generating device is placed in the path between the light beam and the photonic device. At step 6814 the beam is allowed to pass through the OAM generating device and an OAM twist is applied to the beam. Then, at step 6816, the twisted beam interacts with the photonic device to generate energy such that electron-hole recombination within the photonic device is affected by the OAM twisted beam.

Interaction of OAM beams with other matter

As mentioned above, OAM-infused light beams can also interact with other types of matter such as semiconductors, quantum circuits, and biological materials. Light can carry spin angular momentum and orbital angular momentum. Multiple patents describing applications of OAM in several fields including communications, spectroscopy, radar, and quantum informatics, such as filed on October 13, 2015 (Attorney Case No. NXGN60-32777) entitled " U.S. Patent No. 14/882085 for Applications of Orbital Angular Momentum to Optical Fibers, FSOs, and RF; and methods"; filed July 11, 2019 (Attorney docket NXGN60-34555) entitled "Universal Quantum Computers, Communications, QKD Security and Using OAM Quantum Die with DLP" "Special Quantum Networks", US Patent Application No. 16/509,301, the entire contents of which are incorporated herein by reference. However, these techniques can be used to extend the application of OAM to solid-state systems, including potential techniques to improve the efficiency of solar cells, display units, and other applications.

As mentioned above, quantum technologies use individual atoms, molecules and photons to build new kinds of devices. Quantum objects are not restricted to the binary rules of traditional computing, but can be in two or more logical states at the same time. Therefore, it is possible to construct higher-radix quantum systems. When a group of objects collectively occupy two or more states at a time, they are said to be entangled. Photons interact very weakly with their environment, so entangled states of photons hold considerable promise for applications ranging from imaging and precise measurements to communications and computing.

Quantum entanglement is the physical phenomenon that occurs when pairs or groups of particles are created, interact, or share spatial proximity such that, even when the particles are separated by large distances, they cannot be determined independently of the states of other particles. Describe the quantum state of each particle.

Entangled systems are defined as systems whose quantum states cannot be considered as the product of the states of their local components; that is, they are not individual particles, but inseparable wholes. In entanglement, one component cannot be fully described without considering the other components. The state of a combined system can always be represented as a sum or superposition of the products of the states of the local components; if the sum necessarily has more than one term, the combined system is entangled. Quantum systems can become entangled through various types of interactions. For some of the ways in which entanglement can be achieved for experimental purposes. Entanglement is broken when entangled particles are unraveled through interaction with the environment (eg, when measurements are taken).

As an example of entanglement, a subatomic particle decays into an entangled pair of other particles. Decay events obey various conservation laws, and as a result, measurements from one daughter particle must be highly correlated with measurements from another daughter particle (so that total momentum, angular momentum, energy, etc. remain roughly the same before and after the process). For example, a spin-zero particle can decay into a pair of spin-1/2 particles. Since the total spin before and after this decay must be zero (conservation of angular momentum), whenever a first particle is measured to spin up on some axis, when another particle on the same axis is measured, it is always found to be Spin down. (This is called the spin anticorrelation case; if the prior probabilities used to measure each spin are equal, the pair is said to be in a singlet state.)

In every quantum information processing scheme, information bits must be stored in the states of a set of physical objects, and there must be physical means to influence the interactions between these qubits (as described above for higher basis systems). qubit or quantum ditter). However, when individual photons are used to store and process information, the problem manifests as photons interacting very weakly or not at all, so it seems unlikely that they will be used directly for quantum information processing.

A scheme has been constructed for efficient quantum interactions between photons that does not require the photons to physically interact. When a set of photons is in an entangled state, measurements of one or more states of these photons cause the states of the remaining photons to collapse. This state collapse can be viewed as an efficient interaction between the remaining photons. This collapse can be used to allow photons to interact and entangle. The nature of the interaction depends on the measurement of each observed photon. The appearance of some predetermined result of the measurement indicates an efficient interaction of the remaining photons.

This approach can be used to implement quantum logic gates in a scheme known as linear optical quantum computing. Substantial progress has been made in linear optical quantum computing, such as the design and demonstration of teleportation gates and controlled NOT (C-NOT) logic gates, and the preparation of entangled states of two photons. But serious challenges remain.

When using photons as qubits to encode information, each photon must be created to be in one of two different quantum states or a superposition of these two states. If photons occupy more states in an uncontrolled manner, the scheme used to achieve interactions between photons will fail. The quantum states of photons are characterized by their spectrum, pulse shape, arrival time, shear wave vector, and position. All these variables must be precisely controlled to ensure that only two distinct quantum states exist and perform.

Since photons do not interact well, a technique is described that provides a way to interact photons with various types of quantum matter and control quantum transitions in semiconductor materials to build quantum gates for quantum computing Methods. To extend the capability beyond 2-state qubits, OAM-infused twisted beams can be used to create higher-radix systems that can represent quantum ditter (rather than qubits) using the techniques described above.

First, a theoretical framework for transitions between quantum states of a material (i.e. optical transitions with optical frequencies above the band gap) such that generation of free carriers rather than excitons is constructed by using an associated control circuit Control of the OAM level within the applied beam. There is a transfer of angular momentum between the light and the photoexcited electrons, resulting in a net current. Magnetic fields can also be induced by these photocurrents. This is shown in more detail in FIGS. 69 and 70 . Figure 69 shows the process in which beam generation is performed at 6902 to provide beam 6903 to beam generation process 6904. The OAM generation process 6904 applies orbital angular momentum to the plane wave light in the manner described above to provide an OAM processed beam 6905. An OAM-treated beam 6905 is applied to the physical substance to cause at 6906 OAM excitation of electrons within the substance. The OAM-treated beam 6905 with OAM within the photons of the transmitted light group delivers the OAM to the electrons of the matter at a process 6906 that generates an electric current and a magnetic field.

The structure for carrying out this process is shown in more detail in FIG. 70 . Beam generator 1002 generates beam 6903. Beam 6903 comprises a plane wave beam as described above and is applied to OAM generator 7004 such that orbital angular momentum can be applied to the plane wave beam which imparts OAM values to the photons of beam 6903. The beam 6905 generated by the OAM is provided to some type of beam transmitter 7006 which emits the beam 6905 to or at a particular physical device/system 7008. Physical devices/systems 7008 may include various types of semiconductor materials, quantum computer components, biological materials, and solid state materials.

中，通过光激发7110使得价带7104与导带7106之间的跃迁成为可能。在晶体半导体中，价带7104和导带7106中的电子占据布洛赫态。这种简化的两带模型可以具有半导体的主要特征，并且是真实体系统的良好模型。框架描述了由扭转光诱导的体半导体的两带模型中的带间跃迁，并且在下文中进一步描述。必须评估对导带状态(具有光子能量>带隙能量的情况)的相干光激发。在这种情况下，激子的产生可以忽略，并且可以考虑通过光激发从价带7104转移到导带7106的自由载流子。该过程通过首先构造完整的半经典哈密顿算符来执行，在该半经典哈密顿算符中，量子力学算符用于电子，而经典变量用于由两个项(裸电子能和相互作用哈密顿量)组成的光场。Referring now to FIG. 71 , a semiconductor 7102 is a solid at zero temperature having a highest occupied (valence) energy band 7104 and a lowest empty (conduction) energy band 7106 separated by a band gap E _g 7108 . In this regard, they are closer to insulators than metals. However, in a typical semiconductor

, the transition between the valence band 7104 and the conduction band 7106 is made possible by photoexcitation 7110. In crystalline semiconductors, electrons in the valence band 7104 and conduction band 7106 occupy Bloch states. This simplified two-band model can have the main characteristics of semiconductors and is a good model for real bulk systems. The framework describes the interband transitions in the two-band model of bulk semiconductors induced by twisted light and is described further below. Coherent optical excitation of conduction band states (those with photon energy > bandgap energy) must be evaluated. In this case, the generation of excitons is negligible and free carriers transferred from the valence band 7104 to the conduction band 7106 by photoexcitation can be considered. The process is performed by first constructing a complete semi-classical Hamiltonian in which quantum mechanical operators are used for electrons and classical variables are used for two terms (bare electron energy and interaction The light field composed of the Hamiltonian).

To understand the effect of twisted beams on the ground state of a semiconductor, we look at the positive part of the interacting Hamiltonian. The action of this interacting Hamiltonian on the full ground state of the N-electron semiconductor provides an eigenvector whose expected value of the orbital angular momentum is equal to

Referring now to FIG. 72 , the net transfer of orbital angular momentum from photons 7202 to photo-excited electrons 7204 induces a current 7206 and associated magnetic field 7208 . Both of them can be detected, but of course the magnetic field 7208 is detected. These detectable photoexcitation phenomena can also lead to optoelectronic applications.

Referring now to FIG. 73, a flowchart of a process for determining the total current/magnetic field provided by a set of electrons is shown. By calculating the total number of electrons excited by the field at step 7302 and then determining the current/magnetic field for a single electron at step 7304, an estimate of the total current/magnetic field produced by all electrons can be obtained. Finally, at step 7306 the single electron current/magnetic field is multiplied by the number of photoexcited electrons. Start with a single particle framework that does not account for electron-electron Coulomb interactions. This assumption is acceptable because the main correction introduced by the Coulomb interaction will be the renormalization of the single-particle energy. Due to the low excitation (small density of photogenerated electrons and holes), this mean field effect will be small and it does not affect the model of the framework. In addition to the mean-field approximation, Coulomb interactions introduce complex and potentially interesting scattering effects.

The excitation process produces a superposition of conduction band states with well-defined angular momentum. This superposition state is related to the current density as the source of the magnetic field. Note that the single-particle theory has the disadvantage of not taking into account the Pauli repulsion in the photoexcitation of many electrons, and it dispenses with electron-electron interaction effects. Therefore, a more complete theoretical treatment of the interband excitation of solid twisted light is required.

The complete framework should include the generalized semiconductor Bloch equations for twisted light OAM from the bulk and coherent Heisenberg equations of motion of photoexcited electrons. This framework is valid for pulsed or continuous wave twisted beams and takes into account the non-uniform distribution of the beam and the transfer of momentum from the light to electrons in a plane perpendicular to the beam propagation direction. If exciton phenomena are not targeted, Coulomb interactions do not play a major role in the fundamental physics of interband optical transitions (except in the case of excitons), and thus, the framework for the theoretical free-carrier form is limited. Referring now to FIG. 74, as a first step, the mean field of the twisted light can be derived and solved first at step 7402, and then at step 7404 the same equation as the collision term can be derived. The mean field of the twisted light is critical, which can be modified with the collision term. The collision term describes the scattering process that occurs by collisions of photoexcited electrons (electron-electron, electron-phonon, and electron-impurity scattering). The collision term in the relaxation time approximation can be added to the framework to describe those scattering processes, and the resulting numerical solution of the equations of motion will allow us to explore the impact of collision on the effect at step 7406. Furthermore, note that although the discussion focuses on bulk systems, the framework can be easily applied to two-dimensional systems excited at normal incidence.

Typically, photoexcitation in bulk systems is handled theoretically by assuming that the system is cubic, using Cartesian coordinates to quantify the electrons, and applying the limits of the large system size at the right moment of derivation. Due to symmetry, this approach allows for simple calculations with excitation with plane-wave light. However, in the case of excitation by twisted light applied with OAM, it leads to a complicated formulation. The twisted beam has inherent cylindrical properties, and it is the coordinate system used in our formulation.

In the framework of the bulk system, this simple but critical idea is used for the calculations shown in Figure 75. At step 7502, the solid body with which the beam interacts is imagined as a cylinder. At step 7504, the electronic states are quantified in cylindrical coordinates. Finally, at step 7506 the limits of the large system are taken. Bulk properties are independent of the geometry of the solid. To maintain the desired microstructure of the Bloch wave function to characterize the valence and conduction band states, the periodic parts of the Bloch states are approximated by their value at zero crystal momentum, a common term called effective mass Approximate practice. Using cylindrical coordinates instead of Cartesian coordinates allows decoupling the Heisenberg equations of motion in terms of the value of electron angular momentum, which greatly reduces the complexity of the problem. Using these generalized Bloch states can predict the dynamics of electrons, look for the emergence of currents with complex distributions, and demonstrate the transfer of OAMs from beams to electrons.

In this framework, direct bandgap semiconductors or insulators can be considered and an attempt is made to form interband transitions induced by irradiation with a twisted beam. It is assumed that the frequency of the light is such that interband transitions mainly occur, making exciton production unimportant. In this case, it is satisfactory to propose a theory that does not include Coulomb interactions between charge carriers. Therefore, the framework can potentially describe electron dynamics from irradiation to a fraction of picoseconds to avoid strong shifts due to decoherence. This framework is applicable to many physical systems, from semiconductors with band gaps of a fraction of the eV to insulators with larger band gaps, as long as the frequency of the torsional field is tuned above the band gap. This requires the use of torsional fields in the NIR to UV spectrum. This procedure describes a system and method for describing the transfer of orbital angular momentum between twisted light and electrons, and describes what the electron distribution looks like as a result of photoexcitation. Although several valence bands may be involved in interband optical transitions, for simplicity, the two-band model is considered here. From this 2-level framework it is straightforward to generalize the theory to cases involving more than one valence band.

The solutions to the given equations are the building blocks used to construct the mean of the observables of interest. In the standard theory of optical transitions, where light is assumed to be a plane wave and a dipole approximation is made, once the time and momentum dependent density matrices are obtained, the macroscopic optical polarization and thus, for example, the optical sensitivity are calculated. Under these assumptions, macroscopic polarization is only a spatially uniform, time-dependent function.

Conversely, if field inhomogeneities (eg, finite beam waists and oscillatory dependencies in the direction of propagation) are considered, the electronic variables obtain spatial dependencies of interest. Excitation of solids by twisted beams also produces a space-dependent carrier dynamics that requires local variables to describe. The motion patterns of photoexcited electrons can be visualized by calculating and using spatially inhomogeneous current densities. Another useful variable, the transferred angular momentum, is the global magnitude that characterizes the twisted light-matter interaction. On the one hand, the contributions of inter-band coherence and intra-band coherence to angular momentum and current can be investigated separately. This separation is conceptually useful because the interband coherence contribution has fast (possibly femtosecond) oscillations around the zero value of the current or angular momentum, similar to what happens with interband polarization, whereas population or intraband coherence The contribution comes from a slower (perhaps picosecond) process where a net transfer of momentum from light to matter occurs. However, interband coherence contributions are slower processes in which we transfer momentum from light to matter. The latter is related to the photon drag effect, which is now generalized to incorporate rotational drag in a plane perpendicular to the direction of propagation due to the "slow" transfer of angular momentum.

方程开始，该方程包括：The mathematical model is based on Schrödinger

The equation begins, which consists of:

总能量的哈密顿量的算符，其定义如下：in

Operator for the Hamiltonian of total energy, defined as follows:

and where T includes kinetic energy and V is potential energy.

The classic representation of the Hamiltonian of total energy is:

是动能，V是势能。in

is kinetic energy and V is potential energy.

For the simplest interaction (hydrogen):

库伦

Cullen

两体问题可以作为具有减小的质量的一体问题来解决。因此：Use reduced mass

The two-body problem can be solved as a one-body problem with reduced mass. therefore:

Laplace can be provided in spherical coordinates as follows:

Suppose:

Ψ _nlm (r, θ, φ) = R _nl (r) Y _lm (θ, φ)

where R _nl (r) includes the radial part and Y _lm (θ, φ) includes the angular part.

The radial portion is solved according to:

The angle portion is solved according to the following equation:

在两个量化状态之间转换，转换率根据下式定义：Now

Transitions between two quantization states, the transition rate is defined according to:

The transition rate between the two states is proportional to the coupling strength between the two states including the initial state (i) and the final state (f). Fermi's golden rule is defined as:

in

Using a semiclassical approach to light-matter interactions, where atoms are handled by quantum mechanics and photons are handled classically, the QED Hamiltonian is

in:

H _matter = Schrodinger Hamiltonian

H _int = -P ∈ ₀

_Hint includes dipole transitions, where -P equals the atomic electric dipole and ∈ ₀ includes the optical field.

For atomic electric dipoles:

For single electron:

P=-er

In the context of semiconductors, the Bohr radius _a0 is the distance between an electron and a hole that binds an exciton. The Hamiltonian of the excitonic state:

(m₀是自由电子质量)而不是a₀。Use a similar solution for R _nl (r) and Y _lm (θ,φ), where

(m ₀ is the free electron mass) instead of a ₀ .

In a box of length L, quantify the eigenenergy as:

Using the exciton Hamiltonian above:

Now know from OAM of Light:

包括偏振矢量，偏振矢量定义为：in

Including the polarization vector, the polarization vector is defined as:

A(r,t)=A _a (r,t)+A _e (r,t)

where A _a (r,t) includes the absorption from the valence band to the conduction band (v→c), and A _e (r,t) includes the emission from the conduction band to the valence band (c→v).

Next is the paraxial approximation:

Use the LG beam solution from the cylindrical Laplacian:

z _R = Rayleigh length, usually a few meters

where z _R >> z

For z _R >> z approximation

w(z)→w ₀

Then

where f(r) includes

Assuming the wave function of the electronic state of the semiconductor

Ψ(r,θ,φ)＝Φ(r,φ)Z(z)

Has a lattice periodic structure defined by u _b (r) and spin ξ

Ψ _c (r)=[Φ(r,φ)Z(z)]U _c (r)ξ conduction band

Ψ _v (r)＝[Φ(r,φ)Z(z)]U _v (r)ξ Valence band

Φ _nm (r,φ)＝R _nm (r,φ)e ^imφ

in

L is the characteristic confinement length of the electron.

We know that interact

Mechanical Momentum → Quantum Momentum - qA; and

So the one-electron interaction Hamiltonian will be:

q=-e

算符

operator

For minimal interaction:

Therefore, the transition matrix from the initial state to the final state is:

conduction band → valence band

M _if =<i|H|f>=<cα′|H|vα>

where α = collective exponent including all quantum numbers

use

we make

where R _nm (r,φ)e ^imφ includes Φ ^* (r,φ); U _c (r) includes the unit cell period; and ξ includes the spin.

due to orthogonality

Ψ _v =Φ(r,φ)Z(z)U _v ξ _v

It has spin orthogonality ∫ξ'ξd ³ r=δ _ξ'ξ .

Then, the transition matrix for transition from conduction to valence band consists of:

M _cv =<cα′|H _a |vα>

where _Ha is the absorber.

The matrix of valence band and conduction band transitions includes:

M _vc =<vα|He|cα′>

where He is the _emitter .

where P _ij is the matrix element.

The transfer matrix can be further defined as:

where f(r) is the radial component for ∈ _lp

∫e ^-ilφ e ^-i(m′-m)φ dφ＝2πδ _l,(m′-m)

∫ξ′ξd ³ r=d _ξ′ξ

The transition rate between 2 states:

Quadratic Quantification of Multibody Dynamics

Quadratic quantization enables multibody dynamics. Referring now to Figure 76, a system composed of many identical particles forms most of the physical world. Typical examples are electrons 7602 in ionic lattices 7604 in solids or nucleons in heavy nuclei. Although the classical treatment of identical particles is no different from the classical treatment of non-identical particles, classical theory relies on the assumption that the motion of each particle can always be followed. Indistinguishability imposes an additional requirement on the quantum theory of identical particles: the vectors representing states must have definite symmetries with respect to the interchanged labels of identical particles. It is complicated to impose this requirement in ordinary methods based on multi-particle wave functions. A convenient formulation called "quadratic quantization" is proposed here, consisting of many identical particles, allowing these symmetry requirements to be automatically taken into account. Its most typical feature is the use of generation operators and annihilation operators, according to which any operator can be expressed, and its effect on the state of the system is particularly simple. The real essence of this formulation is the introduction of a "large" Hilbert space, the vector of which can represent the states of an arbitrary, also infinite, even infinite number of particles. This is the Hilbert space, in which the roles of the generation and annihilation operators are naturally defined. When restricted to the subspace of H corresponding to the fixed number N of particles (which is possible if the Hamiltonian of the system is exchanged with the particle number operator), quantum mechanics formulated using this form is exactly equivalent to that based on the complement Quantum mechanics of the N-particle Schrodinger equation with proper symmetry requirements. However, quadratic quantization also opens up fundamentally new possibilities. Thus, quadratic quantification of the connection between ordinary quantum mechanics and relativistic quantum field theory that make up many-particle systems.

The primary quantization framework treats observables as operators and states as wave functions. In quadratic quantization, states must also be considered operators. For the general multiband case, the complete electronic Hamiltonian in quadratic quantization is:

where b, b' are energy bands.

α,α′ are the set indices of quantum numbers.

产生算符

generate operator

湮没算符

annihilation operator

_The Hermitian operators _γ1 and γ2 can also be expressed as:

Majorana Photon

Photons in structured beams (i.e. photons with OAM (orbital angular momentum) + SAM (spin angular momentum)) and photons with finite lateral dimensions were observed to travel at significantly slower speeds than light, including in a vacuum. However, photons traveling in a vacuum still have to travel at the speed of light. This behavior can be explained as a projection effect of the effective motion of the photons on the propagation axis of the diverging beam and depends on the geometrical properties of the beam. In this case, a structured beam carrying OAM, more specifically a hypergeometric beam, exhibits a group velocity (Vg) that obeys a relativistic particle similar to that proposed by Majorana for bosons and fermions The relationship between the spin and mass, which in turn involves the OAM, the propagation velocity, and the virtual mass parameter characterizing the beam.

Majorana proposed an efficient alternative solution for boson and fermion relativistic particles with zero or positive definite rest mass to avoid the problem of negative square mass solutions resulting from the Dirac equation, which is Caused by the antielectron discovered experimentally by Anderson. In the process of generalizing the Dirac equation to a spin value other than that of an electron, Majorana found a solution with a Bose-Einstein or Fermi-Dirac statistic A spectrum of infinite particles with a precise relationship between spin and mass. The infinite spin solution of the Dirac equation proposed by Majorana gives the spectrum of particles with positive definite or zero finite square mass. The particle spectrum described by the Majorana solution does not have any correspondence with the particle spectrum of the Standard Model. In this case, the particle and its corresponding antiparticle cannot be distinguished from each other. Since any particle and antiparticle must have opposite charges, this type of solution is only valid for known neutral particles. This relationship holds only for bosons such as gravity and photons, which are zero rest-mass particles in a vacuum, and for a small number of possible classes of fermions, the so-called Majorana neutrinos exception. Obviously, elementary particles such as electrons and positrons cannot be Majorana particles.

From Majorana's writings, he gradually thought of a relativistic theory of particles with arbitrary angular momentum. He first studied the finite case of complex systems, in particular the Dirac-like equations of photons, in which he started directly from Maxwell's classical fields, using the three-dimensional complex vector F=E+iH, where E and H are the electric and magnetic fields, respectively . This expression sets two invariants for the electromagnetic tensor, one is the real part of F and the other is the imaginary part of F, and introduces the photon wave function Ψ=E+iH, the probability interpretation of which is very simple and straightforward, And directly relies on Einstein-Born's initial intuition: the electromagnetic energy density is proportional to the probability density of photons. Maxwell's equations can be written with this wave function; the first is the typical transverse state in quantum mechanics for spin-1 particles, while the second Majorana is able to write the photon wave equation as a special case of Dirac's equation, which is shown to be equal to Effective in quantum electrodynamics (Quantum Electrodynamics, QED). Majorana's theory is ideal for studying bound or photonic systems in structured beams (ie, photons with OAM+SAM are called vector beams).

Examples of Majorana-like "particles" can be found in different situations, such as in condensed matter physics, where the composite state of particles behaves like a Majorana fermion, and for Majorana fermions, The particle and its antiparticle must coincide and gain mass from the self-interacting mechanism. This is different from the Standard Model which follows the Higgs mechanism. These quasiparticles are the product of electromagnetic interactions between electrons and atomic structure that exist in the case of condensed matter.

Quasiparticle excitations similar to Majorana particles have been observed in topological superconductors characterized by carrying zero charge and energy. Other types of quasiparticles called Majorana zero modes are observed in Josephson junctions and solid-state systems. They have potential future applications in information processing and photonic systems.

Furthermore, structured light beams and other photonic systems can work like Majorana particles. They involve not only spin angular momentum but also total angular momentum. Photons actually carry energy, momentum, and angular momentum J. The amount of conserved angular momentum carried by the photon is given by the (vector) sum of spin angular momentum (SAM) and orbital angular momentum (OAM).

An example is photons carrying OAMs propagating in structured plasmons. They acquire effective Proca mass through the Anderson-Higgs mechanism and obey a mass/OAM relationship similar to Majorana's mathematical structure. The difference between Majorana's original solution based on the space-time symmetry of the Lorentz group applied to the Dirac equations in vacuum and the space-time symmetry of photons in structured plasmas is the Anderson-Higgs Mechanism and the role of OAM on the mass/total angular momentum relationship of structured electromagnetic beams.

OAM is used as a term for reducing the mass of total proca photons in a plasma, as happens in the original spin/mass relationship of Majorana. What causes the Proca mass in the photons in the plasma is the disruption of the spatial uniformity and characteristic scale lengths introduced by the plasmonic structure at the frequencies of the plasmonic resonance. The presence of characteristic-scale lengths and structures in plasmas presents a strong analogy to spatiotemporal models characterized by the correction of the Lorentzian group, and the presence of characteristic-scale lengths, when present, exhibits inconsistencies with the dynamics described by the Dirac equations. Deep analogy. Fermions and anion-like behaviors with non-Abelian gauge structures are obtained by coherent superposition of OAM states. There are possible formulations with non-Abelian gauge theories.

OAM and Majorana Photons

The slowdown of structured beams in vacuum is related to the geometric divergence of the beam. This is a different mechanism in which light is slowed down by the presence of matter. Structured beam photons propagating in a vacuum can behave differently than plane waves due to field confinement induced by the finite range and the structure of the beam that changes the wave vector, which results in changing the group velocity V _g measured along the axis of propagation .

For different OAM modes, the phase velocity _Vp is also different. The core idea about the propagation velocity of OAM eigenmodes is that _Kz is not the only component of the wave vector that must be considered in order to fully describe the system.

In cylindrical coordinates of OAME(ρ,φ,z), where ρ=radial, φ=azimuth, z=vertical

In general, E(ρ,φ,z,t)=R(ρ)Φ(φ)Z(z)T(t)E ₀

In any particular radial mode:

and phase velocity:

But we also know v _g v _p =c ² , where v _p =phase velocity and v _g =group velocity.

For OAM beams:

给出，其中Φ(r)表示波相位波前。对于拉盖尔-高斯模式，沿z的群速度(其具有对传播距离z的显式依赖性)由下式给出：The precise group velocity of a paraxial beam at any point in space can be calculated using the wave diagram description. In the wave description, the group velocity is given by

is given, where Φ(r) represents the wave phase wavefront. For the Laguerre-Gaussian mode, the group velocity along z (which has an explicit dependence on the propagation distance z) is given by:

(瑞利距离)。in

(Rayleigh distance).

This relationship reflects the strange geometry of these beams. The time delay or better the different group velocities can be explained by the effect of the virtual mass m _v of the quasi-particle state, which characterizes the dynamics of the beam and is described by the Schrödinger-like equation at low velocities propagating with the group velocity V _g :

therefore:

This virtual mass term results in the Majorana mass M. Any of these quasiparticle states have a precise relationship between their angular momentum value and their virtual mass in a vacuum, similar to the behavior of a Proka photon with OAM in a plasma.

This means that the process of beam confinement and structuring acts like the Anderson-Higgs mechanism that induces the Proca mass on the photon and its angular momentum/mass relationship in the Majorana model, similar to that even if the beam is in space The role of free propagation in the waveguide also occurs.

Therefore, photons propagating in vacuum belonging to such structured beams follow the mathematical rules of the Majorana model of quasiparticle states. In fact, the relationship involving the wave vector K and the virtual mass term m _v is obtained by comparing the two group velocities

The corresponding energy is:

其中

是虚拟质量的角动量部分。Each of these beams behaves as a particle in the low energy limit obeying the Schrödinger/Dirac equations with a virtual Majorana mass M and Majorana-model OAM/virtual mass relation, like Majorana Nathan in his 1932 paper. The M in Majorana's original work is

in

is the angular momentum part of the virtual mass.

Thus, the dynamics and structure of the beam are uniquely characterized in space and time by the rules of the Poincare group that establish the Majorana model. Even though particles with opposite OAM values propagate with the same group velocity, their chirality is different. Through the projection effect along the propagation axis, the size and shape of the beam can be adjusted arbitrarily to obtain different apparent sublight speeds for different OAM values, and to obtain spatial buffering information in time.

Weaving of Majorana fermions with Majorana photons (vector vortex beams with OAM)

Braided non-Abelian anyons are needed in topological quantum informatics and quantum computing to improve the entanglement properties of quantum computing components. A promising class of non-Abelian anyons are the Majorana bound states (MBS) that appear as zero-energy quasiparticles in topological superconductors. In recent years, there have been many demonstrations of detecting and manipulating MBS in condensed matter platforms. Implementations based on one-dimensional (1D) semiconducting wires (SWs) are the most obvious demonstrations. Some experiments report characteristic transport signatures in the form of zero-bias conductance peaks that are compatible with the presence of zero-energy MBSs.

The most important feature of MBS is their exchange or weaving statistics: moving these Majorana quasiparticles around each other and swapping their positions will achieve a non-Abelian unitary transformation that depends only on the trajectory topology. In this way, information can be encoded in the twist of the state function (wave function). This is shown generally in FIG. 77 . Beam 7702 is provided to the OAM generator to have OAM values applied to the beam. The OAM-infused beam is then applied to the weaving process 7706 to weave anyons of the solid state material 7708, thereby encoding information in the twist of the state function. Compared to quantum computing using conventional qubits, this unitary transformation is more robust to decoherence and phase shifting due to the local environment, which will make this method of interest for topological quantum computing. In order to detect Majorana signatures and manipulate the weaving of MBSs, it is necessary to find interference schemes (boosting ground-state degradation) so that the MBSs interact.

Suppose there is a Clifford algebraic generalization of quaternions and their relation to the braided group representation associated with Majorana fermions. That is, topological quantum computing is based on the fusion rule of Majorana fermions. In this configuration, Majorana fermions can be seen not only in the cooperative structure of electrons (i.e., the quantum Hall effect), but also by algebraically decomposing the fermion's operator into two Majorana operators The Clifford algebra of symbol generation is seen in the one-electron structure. These braided representations have important applications in quantum informatics and topology. The Majorana operator leads to a particularly robust representation of the braided group, which is then further represented to find the phase of the fermions under their exchange in plane space. The braided group (represented by the Majorana operator) represents the exchange of Majoranas in space.

An example of weaving of anyons 7802 is shown in FIG. 78 . Here, mathematics will form a bridge between theoretical models of anyons and their application to quantum computing components. The braiding of Majorana fermions is a natural representation of the Clifford algebra, and also represents the quaternion as SU(2) to the braiding group. This could also explain the vortex of the quantum Hall effect. It may not work for electrons in one-dimensional nanowires. However, there are three Majorana operators that generate copies of quaternions.

Referring now to FIG. 79, a braid 7902 is an inset of a collection of strands 7904 with their ends 7906 in two rows of points arranged one above the other with respect to the choice of vertical. The wire harnesses 7904 are not individually knotted, and they do not intersect each other. The braid 7902 can be multiplied by attaching the bottom row 7906B of one braid to the top row 7904A of the other braid. This multiplication of braid 7902 forms a group under this concept of multiplication. Therefore, weaving theory is crucial for both the electromagnetic knot and the knot and link theory of quantum wave functions or state knots.

Braiding using a Y junction of a vector beam with orbital angular momentum

Majorana fermions can be woven with Majorana photons, which are beams of vortex vectors carrying orbital angular momentum. In this case, there will be four Majoranas (M ₀ , M ₁ , M ₂ , M ₃ ), where M ₁ , M ₂ , M ₃ are considered to be at the end of the Y junction, M ₀ is at the center of the Y-junction (Y-junction waveguide). Complex weaving can be performed by placing a superconducting Y-junction in a cavity with an OAM beam acting on the Y-junction. In this setup there will be a Berry phase contribution to the dynamics. The Hamiltonian can then be constructed using the rotating wave approximation. For this case, the Hamiltonian couples states to photons in the cavity at the frequency of the cavity.

Quaternion implementation of wave function knots and electromagnetic knots

Fermions

For fermions:

并且

and

If there are two Majorana fermions, then:

xy=-yx

Majoranas are their own antiparticles, so

x²＝1

x ² = 1

xy+yx=0y ² =1

So if:

Then you can make a fermion with two Majoranas, and then:

Furthermore, two Majoranas can be made from one fermion according to the following formula:

Now about three majoranas, three majoranas can represent a quaternion group. If there are Majorana subs x, y, z:

Then x ² =1, y ² =1, z ² =1

Let I=yxJ=zy K=xz

but:

I ² =-1 J ² =-1K ² =-1 IJK=-1

Then the operator can be defined as:

woven into each other

ABA=BAB BCB=CBC ACA=CAC

These weaving operators are entangled and can be used for general-purpose quantum computing.

The Clifford algebra of Majoranas corrects the representation of braiding. The weaving of Majorana seeds is not limited to nanowires and can in principle be applied to 2, 3, 4 or n-strands. 3 shares will represent the quaternion case.

In the two-qubit state:

When ad-bc≠0,

|φ＞=a|00＞+b|01＞+c|10＞+d|11＞

entangled.

SU(2) braided frame

The matrix SU(2) has the following form:

Det(M)=1 in SU(2) and

if z=a+ib and

but

where a ² +b ² +c ² +d ² =1

but:

并且

in

and

and I ² =-1J ² =-1K ² =-1 IJK=-1

IJ=K JK=I KI=J

JI=-K KJ=-I IK=-J

1. The algebras of I, J, and K are quaternions. Generally speaking:

q=a+bI+cJ+dK

If U&V are pure quaternions, (a=0), then:

uv=-u·v+u×v

Quaternions are closely linked to topology, and weaving is the basis of Majoranas and their applications in quantum computing. The same quaternion algebra can also be used to generate electromagnetic knots.

Referring now to Tables 1 and 2 below, there are electromagnetic equations in traditional U(1) symmetry and SU(2) symmetry. With temperature control, it is possible to go from one symmetric space to another, and these states can also be described using quaternion algebra for weaving wave functions.

Interaction of new OAMs with substances with graphene honeycomb lattices

Due to its crystal structure, graphene behaves as a semi-metallic material whose low-energy excitations behave as massless Dirac fermions. Therefore, graphene exhibits unusual transport properties, like the unusual quantum Hall effect and Klein tunneling. Its optical properties are bizarre: Although graphene is a single atom thick, it absorbs a lot of white light, and its transparency is governed by a fine structural constant, which is usually associated with quantum electrodynamics rather than condensed matter physics.

Current efforts to study structured light serve to understand and generate twisted beams on the one hand, and to study interactions with particles, atoms and molecules, and Bose-Einstein condensates on the other.

Thus, as shown in FIG. 81 , the OAM beam 8102 can be made to interact with the graphene 8104 to enable the OAM-processed photons to change the state of the particles in the graphene 8104 . The interaction of graphene 8104 with light 8102 has been theoretically studied in different ways, such as by calculating photoconductivity or controlling photocurrent. The study of the interaction of graphene 8104 with light-carrying OAM 8102 is interesting as the world is moving towards using the properties of graphene for many different applications. Because twisted light 8102 has orbital angular momentum, OAM transfer from photons to electrons in graphene 8104 can be expected. However, the analysis is complicated by the fact that the lower excitations of graphene 8104 are Dirac fermions, the OAM of Dirac fermions is not well defined. However, there is another angular momentum associated with the honeycomb lattice of graphene 8104, called pseudo-spin, and the total angular momentum (orbital plus pseudo-spin) is conserved.

The interaction Hamiltonian described in this paper can be used to study the interaction of graphene with twisted light and to calculate related physical observables, such as the photo-induced current and the transfer of angular momentum from light to electron particles in the material.

The low energy state of graphene is a two-component optically active body. These spin bodies are not spin states of electrons, but are related to the physical lattice. Each component is related to the relative magnitude of the Bloch function in each sublattice of the honeycomb lattice. They have SU(2) algebras. This degree of freedom is a pseudo-spin. It works in the Hamiltonian as it does in the Dirac Hamiltonian by the canonical spin. It has the same SU(2) algebra, but instead of the isospin symmetry connecting protons and neutrons, the pseudospin is angular momentum. In a state where all electrons are in the A-site, this pseudo-spin will point upward in the z-direction (out of the plane containing the graphene disk), whereas if the electrons are in the B sublattice, it will be in the z-direction Down.

Interacting Hamiltonian OAM (Honeycomb) with Graphene Lattice

Referring now to Figure 82, a graphene lattice in a honeycomb structure is shown. If T1 and T2 are the basis vectors _of the Bravais lattice, and _k and k' are the corners of the first Brillouin zone, then the Hamiltonian is:

如果将该矩阵对角化，则得到代表石墨烯能带的能量本征值。The degree of separation of carbon atoms on the lattice is

If this matrix is diagonalized, the energy eigenvalues representing the graphene energy bands are obtained.

If k=K+(qx, q _y )

对于q_xa《1but

For q _x a < 1

q _y 0 < 1

So for a 2D Hamiltonian:

泡利矩阵

Pauli matrix

m=±1

where the Fermi velocity is equal to:

比c慢约300倍

~300 times slower than c

The eigenstates of these Hamiltonians are spinors with 2 components, which are the 2 elements of the lattice basis.

For circular graphene with radius _r0 , the low energy state can be found in cylindrical coordinates, where

where J _m (x) of x _mv is zero.

的z分量，则哈密顿量与OAM之间的交换关系为：To study the interaction of graphene with OAM beams, the OAM operator was examined

The z component of , then the exchange relationship between the Hamiltonian and OAM is:

To construct conserved angular momentum, pseudo-spin is added to L _z , and the total angular momentum is:

The operator is indeed commutative with the Hamiltonian, and

接近k或k′

close to k or k′

Interacting Hamiltonian

We know that the vector potential of an OAM beam in Coulomb gauge is:

偏振矢量σ＝±1in

Polarization vector σ=±1

The radial parts of the beam are the Bessel functions J _l (qr) and J _l+r (qr). It is also possible to use the Laguerre-Gaussian function instead of the Bessel function. Here q _z and q are for structured light, q _x , q _y , q _mv for electrons.

To construct the interacting Hamiltonian:

but

Since graphene is 2D, the EM field has only x, y values.

At z=0 (graphene disk), the vector potential is:

Let us make A ₊ =A ₀ e ^-iωt J _l (qr)e ^ilθ 1 photon absorption

A-=A ₀ e ^-iωt J _l (qr)e ^-ilθ 1 photon emission

Then the interaction Hamiltonian close to the Dirac point α is:

For α=1 (closer to K) and σ=+1

For α=-1 (closer to K') and σ=+1

Then the transition matrix becomes:

where close to K:

如前所述in

as mentioned

跃迁率

transition rate

OAM-assisted embrittlement for gene editing and molecular manipulation (a novel OAM and matter interaction)

The current state-of-the-art CRISPR technology is CRISPR-Cas9. CRISPR-Cas9 is a technology that uses an enzyme that uses the CRISPR sequence as a guide to recognize and cut a specific strand of DNA that is complementary to the CRISPR sequence. It is produced by a genome editing system that occurs naturally in bacteria. Bacteria capture DNA fragments from the attacking virus and use them to generate DNA fragments (CRISPR arrays). Bacteria produce RNA fragments from CRISPR arrays to target viral DNA. The bacteria then use Cas9 to cut open the DNA, rendering the virus ineffective. Cas9 is also working in the lab. Scientists generate short pieces of RNA with short "guide sequences" that attach (bind) to specific DNA target sequences in the genome. The laboratory creation of this engineered guide sequence is where OAM can come into play. Like bacteria, modified RNAs are used to recognize DNA sequences, and the engineered sequences cut the DNA at target locations. Once the DNA is cut, the cell's own DNA repair machinery can be used to add or remove fragments of genetic material, or to alter the DNA by replacing existing fragments with custom-made DNA sequences. Therefore, OAM-assisted CRISPR can be used to modify RNA or cut DNA at a target location.

Currently, most research into genome editing is done to understand disease using cells and animal models. A variety of diseases are currently being studied, including monogenic diseases such as cystic fibrosis, hemophilia, and sickle cell disease. It can also be used to treat and prevent more complex diseases such as cancer, heart disease, mental illness and HIV infection.

Most of the changes introduced through gene editing are limited to somatic cells, which are cells other than egg and sperm cells. These changes only affect certain organizations and are not passed from one generation to the next. However, changes to genes in egg cells or sperm cells (germline cells) or embryonic genes can be passed on to offspring.

OAM can be used in the laboratory to generate "guide sequences" called OAM-assisted CRISPR for gene editing. The non-bacterial method of using OAM to generate "guide sequences" in the laboratory is a good approximation to OAM-assisted CRISPR. OAM-assisted CRISPR could impact precision genetics and the precision pharmaceutical industry.

Thus, as shown in FIG. 83, the combination of CRISPR-Cas9 system 8302 and OAM-infused beam 8304 can be applied to gene sequence 8306. The OAM-assisted CRISPR-Cas9 system will result in the removal of the desired gene sequence 8308 and provide a revised gene sequence 8310 with the removed sequence 8308, which can be replaced by another sequence in the desired manner.

Those skilled in the art will appreciate that this quantum-mechanical framework for the interaction of OAM with applications in solid state, biological science and quantum computing provides an improved way to allow the use of OAM-processed beams to impart Electronic OAM for various types of materials. It is to be understood that the drawings and detailed description herein are to be regarded in an illustrative rather than a restrictive sense, and are not intended to be limiting to the particular forms and examples disclosed. On the contrary, included are any further modifications, changes, rearrangements, substitutions, substitutions, design choices and embodiments apparent to those of ordinary skill in the art without departing from the spirit and scope of the invention as defined by the following claims. Accordingly, the following claims are to be construed to include all such further modifications, changes, rearrangements, substitutions, substitutions, design choices and embodiments.

Claims (30)

1. A method for imparting orbital angular momentum (OAM) to electrons of a semiconductor material, comprising: Generate a plane wave beam; applying at least one orbital angular momentum to the plane wave beam to generate an OAM beam; controlling transitions of electrons between quantized states within the semiconductor material in response to the at least one orbital angular momentum applied to the plane wave beam; and The OAM beam is emitted at the semiconductor material to induce the transitions of the electrons between the quantized states within the semiconductor material. 2. The method of claim 1, wherein the step of controlling further comprises controlling the level of free carrier generation within the semiconductor material in response to the interaction of the OAM beam with the semiconductor material rather than Control the level of exciton production. 3. The method of claim 1, wherein the step of controlling the transition further comprises defining the quantized state as a two-band model and controlling the transition of electrons between a first band and a second band. 4. The method of claim 1, wherein the step of controlling further comprises: constructing a semiclassical Hamiltonian, wherein a quantum mechanical operator defines the behavior of electrons within the semiconductor material, and the bare electron energy and The interaction Hamiltonian defines the behavior of photons within the OAM beam. 5. The method of claim 4, wherein the interacting Hamiltonian of photons with electrons provides eigenvectors with expected values of the OAM of the OAM beam. 6. The method of claim 1, wherein the step of transferring further transfers the OAM of the beam from the photons of the OAM beam to the electrons of the semiconductor material. 7. The method of claim 6, further comprising generating an electric current and a magnetic field by transferring the OAM of the light beam from the photons of the light beam to the electrons of the semiconductor material. 8. The method of claim 7, further comprising determining a total current and total magnetic field of the current generated and the magnetic field generated. 9. The method of claim 8, wherein the step of determining comprises the steps of: determining the total number of photoexcited electrons within the semiconductor material; determining a first current and a first magnetic field produced by the single electron; and The total number of photoexcited electrons is multiplied by each of the first current and the first magnetic field to determine the total current and the total magnetic field. 10. The method of claim 1, wherein the step of controlling further comprises: determining the OAM applied by the OAM beam to electrons of the semiconductor material, the step of determining further comprising: determining the mean field of the OAM beam; and The mean field of the OAM beam modified by a collision term is determined, wherein the collision term describes a scattering process that occurs in response to collisions of photoexcited electrons. 11. The method of claim 1 , wherein the step of controlling further comprises determining where the OAM is directed from the photons of the OAM beam to the semiconductor material by treating the semiconductor as a bulk system. The application of the electrons, the step of determining further comprises: imagine the semiconductor material as a cylinder; quantifying the electronic state of the electrons in the semiconductor material in cylindrical coordinates; A limit of a large system including the semiconductor material is determined in response to the quantified electronic state. 12. The method of claim 1, wherein the controlling step further comprises determining the OAM from the photons of the OAM beam to the semiconductor material by treating the semiconductor as a bulk system the application of electrons, the step of determining further comprising: determining the generalized bulk state of the electrons of the semiconductor material; and predicting the dynamics of electrons in the semiconductor material in response to the generalized Bloch state; and A current of the electrons in the semiconductor material is determined. 13. The method of claim 1, wherein the step of controlling further comprises using quadratic quantization to control transitions of the electrons between quantized states within the semiconductor material. 14. The method of claim 1, wherein the step of controlling further comprises: controlling the electrons between quantized states within the semiconductor material using photon behavior based on Majorana particle modeling 's transition. 15. The method of claim 14, wherein the controlling step further comprises the step of weaving electrons within the semiconductor material using photons within the OAM beam modeled based on Majorana particles, Therein, information is stored within the woven electronics. 16. The method of claim 15, wherein the step of braiding further comprises the step of attaching a bottom row of a first braid to a top row of a second braid to form a cluster. 17. The method of claim 15, wherein the step of weaving is performed using a Y-knot in a cavity in which a Hamiltonian constructed by a rotational wave approximation converts electrons at the cavity's frequency. state and photon coupling. 18. The method of claim 14, wherein the step of weaving is further responsive to temperature control and quaternion algebra describing the electronic state of weaving. 19. A system for imparting orbital angular momentum (OAM) to electrons of a semiconductor material, comprising: a light source generator for generating a plane wave beam; an orbital angular momentum (OAM) processing circuit for applying at least one orbital angular momentum to a plane wave beam to generate an OAM beam, wherein the OAM processing circuit is responsive to the at least one orbital angular momentum applied to the plane wave beam controlling the transition of electrons between quantized states within the semiconductor material; and a transmitter for emitting the OAM beam at the semiconductor material to induce transitions of the electrons between the quantized states within the semiconductor material. 20. The system of claim 19, wherein the OAM processing circuit controls the generation level of free carriers within the semiconductor material in response to the interaction of the OAM beam with the semiconductor material rather than controlling the laser sub-production level. 21. The system of claim 19, wherein the OAM processing circuit controls the transition of electrons between a first band and a second band within a two band model. 22. The system of claim 19, wherein the OAM of the beam is transferred from the photons of the OAM beam to the electrons of the semiconductor material. 23. The system of claim 22, wherein transferring the OAM of the beam from the photons of the OAM beam to the electrons of the semiconductor material generates an electric current and a magnetic field. 24. The system of claim 19, wherein the OAM processing circuit determines the application of OAM from photons of the OAM beam to the electrons of the semiconductor material by determining the semiconductor material generalized bulk states of electrons treating the semiconductor as a bulk system; predicting the dynamics of electrons in the semiconductor material in response to the generalized Bloch state; and determining the current flow of the electrons in the semiconductor material . 25. The system of claim 19, wherein the OAM processing circuit uses quadratic quantization to control transitions of the electrons between quantized states within the semiconductor material. 26. The system of claim 19, wherein the OAM processing circuit controls transitions of the electrons between quantized states within the semiconductor material using photon behavior based on Majorana particle modeling. 27. The system of claim 26, wherein the OAM processing circuit uses photons within the OAM beam modeled based on Majorana particles to weave electrons within the semiconductor material, wherein information is Stored within the woven electronics. 28. The system of claim 27, wherein the OAM processing circuit attaches a bottom row of a first braid to a top row of a second braid to form a cluster. 29. The system of claim 27, further comprising a Y-junction in a cavity for applying the emitted OAM beam to the semiconductor material, wherein the Hamiltonian constructed by the rotating wave approximation is at the frequency of the cavity Electronic states are coupled to photons in the cavity. 30. The system of claim 27, wherein the OAM processing circuit controls the weave in response to temperature control and quaternion algebra describes the state of the electron's weave.

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