CN108008531A - A kind of raman laser light path matching system based on Mach-Zehnder interferometer - Google Patents

Abstract

The invention discloses a kind of raman laser light path matching system based on Mach-Zehnder interferometer, the light path in phase feedback loop between two beam laser is realized using the Mach-Zehnder interferometer of an optical fiber to match, so that phase feedback loop is consistent with the phase noise from laser light source that atomic group detects, so as to which influence of the phase noise to raman laser of laser can be suppressed by backfeed loop, the present invention realizes the light path matching system of all -fiber, inhibit influence of the phase noise of laser light source to cold atom gravimeter, and the present invention realizes that light path matches using optic fibre light path, the extra phase noise that it is introduced is very low.

Description

A Raman laser optical path matching system based on Mach-Zehnder interferometer

technical field

The invention relates to a Raman laser optical path matching system based on a Mach-Zehnder interferometer, and belongs to the technical field of cold atom gravimeters.

Background technique

The Raman laser is two laser beams with a fixed frequency difference and phase difference used in the cold atom gravimeter. The phase noise of the beat frequency of the two laser beams is called the phase noise of the Raman laser. Based on the interference effect of matter waves, the cold atom gravimeter can perform high-precision measurements of gravitational acceleration and gravitational gradient. Ultra-high-precision cold-atom gravimeters require Raman lasers with ultra-low phase noise.

One method is to use two independent lasers to generate two laser beams, and lock their beat frequency to the output signal of an ultra-stable crystal oscillator through an optical phase-locked loop method, thereby realizing Raman laser with low phase noise. Another method is to use only one laser, and split its output laser into two beams through a beam splitter, one of which is shifted in frequency by an electro-optic modulator driven by an ultra-stable crystal oscillator to generate a laser beam with a certain Two laser beams with different frequencies. Then, the beat frequency of the two laser beams is locked to the ultra-stable crystal oscillator through the phase feedback system to suppress the noise caused by the laser light source, vibration and temperature changes.

The cold atom gravimeter has two working modes. One is the speed-insensitive mode. In this mode, the propagation direction of the two laser beams acting on the atomic group is the same, so the Doppler frequency shift of the two laser beams caused by the falling speed of the atoms is almost the same and cancels each other out. As a result, the falling velocity of the atoms and the velocity distribution of the atomic cluster itself have little effect on the measurement accuracy of the gravimeter. However, since the directions of the two laser beams are the same, the directions of the stimulated absorption and stimulated emission of photons of the atoms are also the same, resulting in the atoms gaining very little total momentum. The result is very little separation in momentum space between excited and unexcited atoms, making the gravimeters very insensitive.

The other is velocity-sensitive mode. In this mode, the propagation direction of the two laser beams interacting with the atomic group is opposite. The Doppler frequency shift of the two laser beams caused by the falling velocity of the atoms is almost the same, but the sign is opposite. Therefore, it is necessary to adjust the frequency of one of the laser beams in order to counteract the influence of the Doppler frequency shift during the working process. However, since the directions of the two laser beams are opposite, the directions of the stimulated absorption and stimulated emission of photons of the atoms are also opposite, so the total momentum acquired by the atoms is very large. The result is a large separation in momentum space between excited and unexcited atoms, which makes the gravimeter highly sensitive.

General cold atom gravimeters use velocity sensitive mode. In order to realize two laser beams with opposite transmission directions, usually the two laser beams are transmitted in the same direction through the atomic group, and then the mirrors are used to reflect the two laser beams vertically, and then pass through the atomic group again. The lasers that interact with the atoms are an initial beam of laser light and another beam of laser light that is reflected. During this process, the reflected laser light experiences additional optical paths, and the phase jitter accumulated by the laser during these additional optical paths deteriorates the phase noise of the Raman laser. Moreover, since the extra optical path does not appear in the phase feedback loop, the phase noise cannot be suppressed by the phase feedback loop. Ultimately, the inherent noise of the atomic gravimeter increases and the measurement accuracy decreases.

Contents of the invention

The purpose of the present invention is to solve the above problems, and propose a Raman laser optical path matching system based on a Mach-Zehnder interferometer. The optical path is matched, so that the phase feedback loop is consistent with the phase noise from the laser source detected by the atomic group, so that the influence of the phase noise of the laser on the Raman laser can be suppressed through the feedback loop.

A Raman laser optical path matching system based on Mach-Zehnder interferometer, including laser light source, first 1/2λ wave plate, first polarization beam splitter prism, electro-optic modulator, first 45° mirror, Fabry-Perot standard Tool, the second 1/2λ wave plate, the second 45° mirror, the third 1/2λ wave plate, the second polarization beam splitter prism, the first fiber coupler, the first polarization maintaining fiber, fiber collimator, laser splitter Beamer, acousto-optic modulator, laser beam expander, first 1/4λ wave plate, first atomic group, second atomic group, second 1/4λ wave plate, zero-degree mirror, second fiber coupler, fiber polarization splitter Beamer, second polarization-maintaining fiber, third polarization-maintaining fiber, high-speed optical switch, fourth polarization-maintaining fiber, fifth polarization-maintaining fiber, Y waveguide, fiber polarization beam combiner, high-speed photodetector, feedback circuit system.

The output laser light from the laser light source passes through the first 1/2λ wave plate and enters the first polarization beam splitter prism, and the first polarization beam splitter prism divides the input laser light into transmitted laser light and reflected laser light. The transmitted laser light passing through the first polarization splitter prism enters the electro-optic modulator, and the output laser light of the electro-optic modulator is composed of a carrier wave, required first-order modulation sidebands and high-order modulation sidebands. The output laser of the electro-optic modulator is reflected by the first 45° mirror and enters the Fabry-Perot etalon. The Fabry-Perot etalon filters out the redundant laser frequency components, and the output laser is the required first-order modulation sideband. The output laser light of the Fabry-Perot etalon is reflected by the second polarization beam splitter after passing through the second 1/2λ wave plate, and the reflected laser light is input to the first fiber coupler; wherein the laser light reflected by the first polarization beam splitter is sent by the second 45 After being reflected by the °reflector, it passes through the third 1/2λ wave plate, and the output laser light from the third 1/2λ wave plate passes through the second polarization beam splitter and then is input to the first fiber coupler. The output end of the first fiber coupler is connected to the fiber collimator through the first polarization-maintaining fiber, and the output laser light of the fiber collimator enters the laser beam splitter, and the laser beam splitter divides the input laser light into reflected laser light with higher power and A transmitted laser with less power. Among them, the reflected laser light enters the acousto-optic modulator, and the acousto-optic modulator acts as a high-speed optical pulse modulator to generate the required pulsed laser light. The output laser of the acousto-optic modulator enters the laser beam expander, and the output laser of the laser beam expander passes through the first 1/4λ wave plate, the first atomic group, the second atomic group, and the second 1/4λ wave plate, and then is zero-degree reflector reflection, and then successively pass through the second 1/4λ wave plate, the second atomic group, and the first atomic group; where the transmitted laser light enters the second fiber coupler, the output end of the second fiber coupler and the input end of the fiber polarization beam splitter The left output end of the fiber polarization beam combiner is connected to the left input end of the fiber polarization beam combiner through the second polarization maintaining fiber. The right output end of the fiber polarization beam combiner is connected to the input end of the high-speed optical switch through the third polarization-maintaining optical fiber, and the left and right output ends of the high-speed optical switch are respectively connected to the fourth polarization-maintaining optical fiber, the fifth polarization-maintaining optical fiber and the Y waveguide The left and right inputs are connected. The output end of the Y waveguide is connected to the right input end of the fiber polarization beam combiner, and the output laser light of the fiber polarization beam combiner enters the high-speed photodetector. The output end of the high-speed photodetector is connected with the input end of the feedback circuit system, and the output end of the feedback circuit system is connected with the modulation signal input end of the electro-optic modulator.

In a common Raman laser system, in order to eliminate the influence of the laser light source, vibration and temperature on the phase noise, the phase difference of the two laser beams is generally locked to an ultra-stable crystal oscillator through a phase-locked loop. The optimal solution is to make the phase difference of the two laser beams detected by the atom and the photodetector exactly the same, so that the phase noise of the Raman laser is completely determined by the phase noise of the ultra-stable crystal oscillator and the performance of the phase-locked loop. However, the cold atom gravimeter working in the speed-sensitive mode will inevitably produce an extra optical path due to a laser beam undergoing a vertical reflection process; function, which makes this extra optical path have two fixed values. Because the laser light source has phase noise, this extra optical path will cause the phase noise of the laser light source to not cancel each other out and be transferred to the phase noise of the Raman laser. For this reason, it is necessary to generate an optical path difference between the two laser beams received by the photodetector, which is equal to the additional optical path caused by vertical reflection. And the optical path difference is variable, so that the atomic group can achieve optical path matching at the highest point and the lowest point. At this time, the phase noise detected by the photodetector is consistent with the phase noise felt by the atomic group, so that the phase noise can be suppressed through the feedback circuit system.

Here, an all-fiber Mach-Zehnder interferometer is used. The input end of the interferometer splits the input two beams of laser light through a fiber optic polarization beam splitter and enters the two arms of the interferometer respectively. The right arm of the interferometer passes through a micromechanical optical The switch enables rapid switching between the two lengths. The optical path difference caused by vertical reflection is matched by setting the fiber length difference between the right arm and the left arm, and then the phase noise from the laser light source is suppressed by using the phase feedback loop, thereby suppressing the laser light source The effect of phase noise on the measurement accuracy of a cold-atom gravimeter.

Advantages of the present invention:

(1) An all-fiber optical path matching system is realized, which suppresses the influence of the phase noise of the laser light source on the cold atom gravimeter;

(2) The optical path matching is realized by using the optical fiber optical path, and the additional phase noise introduced by it is very low;

Description of drawings

Figure 1 is a block diagram of a Raman laser optical path matching system based on a Mach-Zehnder interferometer;

Fig. 2 is a schematic diagram of optical path matching;

Figure 3 is a schematic diagram of the time sequence of the throw-up atomic gravimeter;

In the picture:

1-Laser light source 2-The first 1/2λ wave plate 3-The first polarization beam splitter prism

4-Electro-optic modulator 5-First 45° mirror 6-Fabry-Perot etalon

7-Second 1/2λ wave plate 8-Second 45° mirror 9-Third 1/2λ wave plate

10-Second polarization beam splitter 11-First fiber coupler 12-First polarization maintaining fiber

13-Fiber optic collimator 14-Laser beam splitter 15-Acousto-optic modulator

16- Laser beam expander 17- The first 1/4λ wave plate 18- The first atomic group

19-Second atomic group 20-Second 1/4λ wave plate 21-Zero-degree mirror

22-Second Fiber Coupler 23-Fiber Polarization Beam Splitter 24-Second Polarization Maintaining Fiber

25-The third polarization-maintaining fiber 26-High-speed optical switch 27-The fourth polarization-maintaining fiber

28-Fifth polarization maintaining fiber 29-Y waveguide 30-Fiber polarization beam combiner

31-High-speed photodetector 32-Feedback circuit system

Detailed ways

The present invention will be further described in detail below in conjunction with the accompanying drawings.

A Raman laser optical path matching system based on Mach-Zehnder interferometer, as shown in Fig. A 45° reflector 5, a Fabry-Perot etalon 6, a second 1/2λ wave plate 7, a second 45° reflector 8, a third 1/2λ wave plate 9, a second polarizing beam splitter 10, and a first optical fiber Coupler 11, first polarization maintaining fiber 12, fiber collimator 13, laser beam splitter 14, acousto-optic modulator 15, laser beam expander 16, first 1/4λ wave plate 17, first atomic group 18, the first Diatomic group 19, second 1/4λ wave plate 20, zero-degree mirror 21, second fiber coupler 22, fiber polarization beam splitter 23, second polarization-maintaining fiber 24, third polarization-maintaining fiber 25, high-speed optical switch 26 , the fourth polarization-maintaining optical fiber 27, the fifth polarization-maintaining optical fiber 28, the Y waveguide 29, the optical fiber polarization beam combiner 30, the high-speed photodetector 31, the feedback circuit system 32;

The output laser light from the laser light source 1 passes through the first 1/2λ wave plate 2 and then enters the first polarization beam splitter 3. The first polarization beam splitter prism 3 divides the input laser light into transmitted laser light and reflected laser light. The laser light passing through the first polarization splitter prism 3 enters the electro-optic modulator 4, and the output laser light of the electro-optic modulator 4 is composed of a carrier wave, required first-order modulation sidebands and higher-order modulation sidebands. The output laser of the electro-optic modulator 4 enters the Fabry-Perot etalon 6 after being reflected by the first 45° reflector 5, and the Fabry-Perot etalon 6 filters out redundant laser frequency components, and the output laser is the required first-order modulation edge bring. The output laser light of the Fabry-Perot etalon 6 is reflected by the second polarization beam splitter prism 10 after passing through the second 1/2λ wave plate 7, and the reflected laser light is input into the first fiber coupler 11; The laser light is reflected by the second 45° reflector 8 and passes through the third 1/2λ wave plate 9, and the output laser light of the third 1/2λ wave plate 9 passes through the second polarization beam splitter prism 10 and then is input to the first fiber coupler 11 . The output end of the first fiber coupler 11 is connected with the fiber collimator 13 through the first polarization-maintaining fiber 12, and the output laser light of the fiber collimator 13 enters the laser beam splitter 14, and the laser beam splitter 14 divides the input laser light into power Larger reflected laser and less powerful transmitted laser. Wherein, the reflected laser light enters the acousto-optic modulator 15, and the acousto-optic modulator 15 acts as a high-speed optical switch to generate the required pulsed laser light. The output laser light of the acousto-optic modulator 15 enters the laser beam expander 16, and the output laser light of the laser beam expander 16 successively passes through the first 1/4λ wave plate 17, the first atomic group 18, the second atomic group 19, and the second 1/4λ wave plate The plate 20 is reflected by the zero-degree reflector 21, and then successively passes through the second 1/4λ wave plate 20, the second atomic group 19, and the first atomic group 19; wherein, the transmitted laser light enters the second fiber coupler 22, and the second fiber coupler The output end of 22 is connected to the input end of the fiber polarization beam splitter 23, and the left output end of the fiber polarization beam splitter 23 is connected to the left input end of the fiber polarization beam combiner 30 through the second polarization maintaining fiber 24. The right output end of the fiber polarization beam splitter 23 is connected to the input end of the high-speed optical switch 26 through the third polarization-maintaining optical fiber 25, and the left and right output ends of the high-speed optical switch 26 respectively pass through the fourth polarization-maintaining optical fiber 27 and the fifth polarization-maintaining optical fiber 27. The optical fiber 28 is connected to the left and right input ends of the Y waveguide 29 . The output end of the Y waveguide 29 is connected to the right input end of the fiber polarization beam combiner 30 , and the output laser light of the fiber polarization beam combiner 30 enters the high-speed photodetector 31 . The output end of the high-speed photodetector 31 is connected to the input end of the feedback circuit system 32 , and the output end of the feedback circuit system 32 is connected to the modulation signal input end of the electro-optic modulator 4 .

work process:

A Raman laser optical path matching system based on Mach-Zehnder interferometer, the output laser frequency of the laser light source is ω, and the EOM modulation frequency is ω _m . Assume that the modulated laser (denoted by L _up in Figure 2) excites atoms from bottom to top at time t, while the unmodulated laser (denoted by L _down in Figure 2) excites atoms from top to bottom after vertical reflection For atoms, the additional optical path caused by vertical reflection is denoted as ΔL. Here, the optical path difference of the two laser beams before beam expansion is ignored, and only the influence of the phase noise of the laser light source is considered, then the two laser beams interacting with atoms at the same time can be expressed as:

Among them, E ₁ and E ₂ are the amplitudes of the laser that excite atoms from bottom to top and from top to bottom respectively, φ ₀ (t) is the phase jitter of the laser light source, which is a random variable; τ ₀ =ΔL/c is the vertical reflection The resulting time delay, c is the speed of light. Then, the phase difference between the two laser beams felt by the atom is:

ΔΦ(t)＝ω _m t+ωτ ₀ +φ ₀ (t)-φ ₀ (t-τ ₀ ) (3)

Among them, ΔФ is the phase difference between the two laser beams, and φ ₀ (t)-φ ₀ (t-τ ₀ ) is an error term affecting the measurement accuracy of the gravimeter. On the one hand, this item can be reduced by reducing the delay τ ₀ , that is, reducing the distance of the vertical reflection. However, due to the limitation of the geometric structure of the gravimeter and the separation time, the delay τ ₀ is difficult to reduce. On the other hand, the error term can be fed back to the phase of a laser beam through the feedback system to realize real-time tracking compensation of the error term. Here, the photodetector is first used to detect the beat frequency of the two laser beams, and then the beat frequency signal and the reference frequency source are subjected to frequency discrimination and phase discrimination, and the phase error signal is extracted, and then the phase error signal is fed back through the feedback circuit The modulation signal of the EOM is returned, thereby changing the phase of the laser on the upper road, and realizing the elimination of the phase error. Specifically, at the same time as the atom, the phases of the two laser beams received by the photodetector are:

Here, the aforementioned L _up is used as a reference laser. Among them, E ₁ ′, E ₂ ′ are the amplitudes of the two laser beams received by the photodetector respectively, and τ ₁ is the time difference between the modulated laser light reaching the photodetector and the reference laser through the left arm of the fiber Mach-Zehnder interferometer; _τ2 is the time difference between the unmodulated laser passing through the right arm of the fiber Mach-Zehnder interferometer and reaching the photodetector and the reference laser. Then, the phase difference between the two laser beams felt by the detector is:

ΔΦ′(t)＝ω _m (t-τ ₁ )+ω(τ ₁ -τ ₂ )+φ ₀ (t-τ ₁ )-φ ₀ (t-τ ₂ ) (6)

Among them, ΔФ′ is the phase difference between the two laser beams felt by the detector, the ω _m t term is eliminated in the frequency discrimination process, and the constant phase term does not need to be considered, only φ ₀ (t-τ ₁ )-φ ₀ (t-τ ₂ ). In order to make the feedback phase error signal consistent with the phase error felt by the atoms, τ ₁ = 0 and τ ₂ = τ ₀ must be made, which requires careful design of the length of the two arms of the fiber optic Mach-Zehnder interferometer and their optical path difference , making it equal to the extra optical path of the unmodulated laser due to vertical reflection. Considering that the atomic group interacts with the laser at the upper and lower positions respectively, at this time, the switching of the two optical path differences of the fiber Mach-Zehnder interferometer can be realized by switching the high-speed optical switch. Specifically, the setup of the fiber optic Mach-Zehnder interferometer is shown in Figure 2, and the length of its two arms should satisfy the following formula:

L _a =L ₀ +2ΔL _a (7)

L _b ＝L ₀ +2ΔL _b (8)

Among them, L ₀ is the optical path of the left arm of the fiber optic Mach-Zehnder interferometer, L _a and L _b are the optical paths of the right arm of the fiber optic Mach-Zehnder interferometer when the high-speed optical switch is turned on on the left and on the right, respectively, ΔL _a and ΔL _b are the distances from the zero-degree reflector when the atomic group is at the highest point and the lowest point, respectively.

If the feedback loop gain is K in the frequency band of interest, then the remaining phase error term after feedback is approximately:

Among them, φ _r is the residual phase error. At this point, the remaining phase error is determined only by the loop gain.

Claims (2)

1. a kind of raman laser light path matching system based on Mach-Zehnder interferometer, including laser light source, the one 1/2 λ wave plates, First polarization splitting prism, electrooptic modulator, the one 45 ° of speculum, Fabry-Perot etalons, the 2nd 1/2 λ wave plates, the secondth 45 ° of speculums, the 3rd 1/2 λ wave plates, the second polarization splitting prism, the first fiber coupler, the first polarization maintaining optical fibre, fiber optic collimator Device, laser beam splitter, acousto-optic modulator, laser beam expander, the one 1/4 λ wave plates, the first atomic group, the second atomic group, the 2nd 1/ 4 λ wave plates, zero degree speculum, the second fiber coupler, fibre optic polarizing beam splitter, the second polarization maintaining optical fibre, the 3rd polarization maintaining optical fibre, height Fast photoswitch, the 4th polarization maintaining optical fibre, the 5th polarization maintaining optical fibre, Y waveguide, optical fiber polarisation bundling device, high-speed photodetector, feedback electricity Road system；

Laser light source exports laser will by entering the first polarization splitting prism, the first polarization splitting prism after the one 1/2 λ wave plates Input laser is divided into transmission laser and reflection laser；Wherein enter electrooptic modulator through the laser of the first polarization splitting prism, The output laser of electrooptic modulator is made of carrier wave, required single order modulation sideband, and high order modulation sideband；Electrooptic modulator Output laser reflected by the one 45 ° of speculum after enter Fabry-Perot etalons, Fabry-Perot etalons filter out more Remaining laser frequency composition, it is required single order modulation sideband, that it, which exports laser,；The output laser warp of Fabry-Perot etalons Reflected after crossing the 2nd 1/2 λ wave plates by the second polarization splitting prism, which is input to the first fiber coupler；Wherein by The laser of first polarization splitting prism reflection passes through the 3rd 1/2 λ wave plates, the 3rd 1/2 λ wave plates after being reflected by the 2nd 45 ° of speculum The second polarization splitting prism of output laser light after be input to the first fiber coupler；The output terminal of first fiber coupler leads to Cross the first polarization maintaining optical fibre with optical fiber collimator to be connected, the output laser of optical fiber collimator enters laser beam splitter, laser beam splitter Input laser is divided into reflection laser and transmission laser；Wherein, reflection laser enters acousto-optic modulator, and acousto-optic modulator is as high Fast photoswitch produces required pulse laser；The output laser of acousto-optic modulator enters laser beam expander, laser beam expander it is defeated It is successively anti-by zero degree speculum after the one 1/4 λ wave plates, the first atomic group, the second atomic group, the 2nd 1/4 λ wave plates to go out laser Penetrate, then successively pass through the 2nd 1/4 λ wave plates, the second atomic group, the first atomic group again；Wherein, transmission laser enters the second optical fiber Coupler, the output terminal of the second fiber coupler are connected with the input terminal of fibre optic polarizing beam splitter, a left side for fibre optic polarizing beam splitter Output terminal is connected by the second polarization maintaining optical fibre with the left input terminal of optical fiber polarisation bundling device；The right output terminal of fibre optic polarizing beam splitter It is connected by the 3rd polarization maintaining optical fibre with the input terminal of high-speed optical switch, the output terminal of left and right two of high-speed optical switch passes through respectively Four polarization maintaining optical fibres, the 5th polarization maintaining optical fibre are connected with the input terminal of left and right two of Y waveguide；The output terminal of Y waveguide is closed with optical fiber polarisation The right side input terminal of beam device is connected, and the output laser of optical fiber polarisation bundling device enters high-speed photodetector；High speed optoelectronic detects The output terminal of device is connected with the input terminal of feedback circuitry, and the modulation of the output terminal and electrooptic modulator of feedback circuitry is believed Number input terminal is connected.

2. a kind of raman laser light path matching system based on Mach-Zehnder interferometer according to claim 1, described The frequency of the output laser of laser light source is ω, and EOM modulating frequencies are ω_m；Assuming that the laser modulated in t moment from the bottom up Excited atom, and not modulated laser excited atom from top to bottom after vertical reflection, extra light caused by vertical reflection Cheng Jiwei Δs L；The influence of the phase noise of laser light source is only considered, in synchronization and two beam laser point of atomic interaction It is not expressed as：

Wherein, E₁, E₂The respectively from the bottom up and from top to bottom amplitude of the laser of excited atom, φ₀(t) it is laser light source Phase jitter；τ₀=Δ L/c is time delays caused by vertical reflection, and c is the light velocity；The phase for this two beams laser that atom is experienced Potential difference is：

ΔΦ (t)=ω_mt+ωτ₀+φ₀(t)-φ₀(t-τ₀) (3)

Wherein, Δ Ф be two beam laser phase difference, φ₀(t)-φ₀(t-τ₀) it is the error term for influencing gravimeter measurement accuracy； The beat frequency of this two beams laser is detected first by photodetector, beat signal and reference frequency source are then subjected to frequency discrimination, mirror Phase, which is extracted, and then modulation which is fed back to EOM by feedback circuit is believed Number, so as to change the phase of upper road laser, realize the elimination of the phase error；

Specifically, the phase of the two beam laser received with atom synchronization, photodetector is respectively：

If L_upFor reference laser, E '₁, E '₂The respectively amplitude for the two beam laser that photodetector receives, τ₁Modulated Laser reaches the time difference of photodetector and reference laser by the left arm of fiber Mach -Zehnder interferometer；τ₂It is not modulated Laser reaches the time difference of photodetector and reference laser by the right arm of fiber Mach -Zehnder interferometer；What detector was experienced The phase difference of this two beams laser is：

ΔΦ ' (t)=ω_m(t-τ₁)+ω(τ₁-τ₂)+φ₀(t-τ₁)-φ₀(t-τ₂) (6)

Wherein, the phase difference for this two beams laser that Δ Ф ' experiences for detector, ω_mT are eliminated during frequency discrimination；

So that τ₁=0 and τ₂=τ₀, two kinds of optical path differences of fiber Mach -Zehnder interferometer are realized by switching high-speed optical switch Switching；Specifically, two arm lengths of fiber Mach -Zehnder interferometer should meet following formula：

L_a=L₀+2ΔL_a (7)

L_b=L₀+2ΔL_b (8)

Wherein, L₀For the light path of fiber Mach -Zehnder interferometer left arm, L_a、L_bRespectively high-speed optical switch is on left side conducting and the right side The light path of fiber Mach -Zehnder interferometer right arm, Δ L when side turns on_a、ΔL_bWhen respectively atomic group is at the highest notch with minimum point With the distance of zero degree speculum；

If it is K in the band limits inner feedback loop gain of concern, then remaining phase error term is about after feedback：

Wherein, φ_rFor residual phase error；At this time, remaining phase error is only determined by loop gain.