Laser frequency stabilization method based on two-color circularly polarized light Doppler-free absorption spectroscopy

Abstract

A laser frequency stabilization method based on two-color circularly polarized light Doppler-free absorption spectroscopy uses two-color light to generate a coherent population capture (CPT) effect on the basis of a Doppler-free absorption optical path, reducing the absorption peak linewidth at the frequency locking point, thereby increasing the slope of the dispersion signal and improving the sensitivity and stability of the frequency system. The absorption peak of the circularly polarized light spectrum signal still has a large amplitude under the geomagnetic field, and no additional magnetic shielding measures are required, thereby simplifying the optical path structure and laying the foundation for miniaturization.

Description

Technical Field

[0001] The present invention relates to the technical field of laser frequency stabilization, and in particular to a laser frequency stabilization method based on a two-color circularly polarized light Doppler-free absorption spectrum. The method generates a coherent population capture (CPT) effect through two-color light on the basis of a Doppler-free absorption optical path, thereby reducing the absorption peak linewidth at the frequency locking point, thereby increasing the slope of the dispersion signal and improving the sensitivity and stability of the frequency system. The absorption peak of the circularly polarized light spectrum signal still has a large amplitude under the geomagnetic field, and no additional magnetic shielding measures are required, thereby simplifying the optical path structure and laying the foundation for miniaturization. Background Art

[0002] Laser frequency stabilization is crucial in optical experiments, and atomic spectral lines are often used as references for laser frequencies. Saturation absorption spectroscopy is a common method for frequency stabilization. By counterpropagating pump and detection light, a transmission peak is generated to eliminate the Doppler effect. However, the transmission peak linewidth in saturation absorption spectroscopy is large, resulting in a small slope change in the dispersion signal at the stabilization point, making it less sensitive to frequency fluctuations.

[0003] The CPT effect (coherent population trapping) is a quantum coherence effect. It generates a transmission peak carrying both magnetic field and frequency information through the reaction of a two-color laser with an alkali metal. Its linewidth is much smaller than that of a saturated absorption spectrum. By replacing the pump and detection beams with two-color light of opposite rotational directions based on a Doppler-free absorption optical path, we exploit the CPT effect to generate a narrower absorption peak, increase the slope of the dispersion signal at the frequency-locking point, enhance the frequency stabilization system's sensitivity to frequency fluctuations, and improve frequency stabilization performance.

[0004] The CPT effect will weaken as the magnetic field increases. However, from the perspective of energy level, compared with linearly polarized light, circularly polarized light can F = 0 produces a CPT effect that is unaffected by the magnetic field. Therefore, the Doppler-free absorption spectrum of the two-color circularly polarized light still has an absorption peak with a small line width under the geomagnetic field, which is used as a stabilization point for laser frequency stabilization. Summary of the Invention

[0005] In response to the defects or shortcomings of the existing technology, the present invention proposes a laser frequency stabilization method based on two-color circularly polarized light Doppler-free absorption spectroscopy. On the basis of the Doppler-free absorption optical path, the coherent population capture CPT effect is generated by two-color light, which reduces the absorption peak linewidth at the locking point, thereby increasing the slope of the dispersion signal and improving the sensitivity and stability of the frequency system; the absorption peak of the circularly polarized light spectrum signal still has a large amplitude under the geomagnetic field, and no additional magnetic shielding measures are required, thereby simplifying the optical path structure and laying the foundation for miniaturization.

[0006] The technical solutions of the present invention are as follows:

[0007] The laser frequency stabilization method based on two-color circularly polarized light Doppler-free absorption spectroscopy is characterized by comprising the following steps:

[0008] Step 1: Input a first-handed two-color circularly polarized light as pump light into a first end of the atomic gas cell; after the first-handed two-color circularly polarized light is emitted from a second end of the atomic gas cell, it is changed into a second-handed two-color circularly polarized light as detection light and input into the atomic gas cell from the second end; the second-handed two-color circularly polarized light is opposite to the first-handed one; and after the second-handed two-color circularly polarized light is emitted from the first end, it enters a photoelectric detection system;

[0009] Step 2, performing laser frequency scanning so that the second-handed two-color circularly polarized light with different frequencies forms a two-color circularly polarized light Doppler-free absorption spectrum in the photoelectric detection system;

[0010] Step 3: determining a frequency-locking point in the two-color circularly polarized light Doppler-free absorption spectrum, and obtaining a dispersion signal corresponding to the frequency-locking point by demodulating the two-color circularly polarized light Doppler-free absorption spectrum;

[0011] Step 4: Turn off the laser frequency scanning, input the dispersion signal as the error signal into the PID control module, and control the laser frequency change through the PID output signal to achieve laser frequency stabilization.

[0012] The first end of the atomic gas chamber is respectively connected to a photodetector and a first quarter wave plate through a depolarizing beam splitter, the first quarter wave plate is connected to a laser collimator through an optical isolator, the laser collimator is connected to an electro-optical modulator through a second polarization-maintaining fiber, the electro-optical modulator is respectively connected to a radio frequency signal generator and the first polarization-maintaining fiber, the first polarization-maintaining fiber is connected to a laser controller through a tunable external cavity semiconductor laser, the laser controller is connected to the output end of a lock-in amplifier through a proportional-integral-differential controller, the first input end of the lock-in amplifier is connected to the photodetector, the second input end of the lock-in amplifier is connected to a sine wave signal generator, the sine wave signal generator is connected to a first input end of an adder, the second input end of the adder is connected to a triangular wave signal generator, the output end of the adder is connected to the laser controller, and the second end of the atomic gas chamber is connected to a reflector through a second quarter wave plate.

[0013] Step 1 includes: using a laser and an electro-optical modulator to generate a frequency that satisfies 87The Rb atomic D1 line satisfies the two-ground state hyperfine energy level frequency difference of 6.834 GHz and the two-color circularly polarized light, wherein the D1 line wavelength is 795 nm. The 795 nm monochromatic linearly polarized light emitted by the tunable external cavity semiconductor laser is modulated into a two-color linearly polarized light with a frequency of 377 THz±3.417 GHz by an electro-optical modulator controlled by a radio frequency signal with a frequency of 3.417 GHz, wherein 377 THz corresponds to a wavelength of 795 nm. The two-color linearly polarized light is then converted into two-color circularly polarized light by a quarter wave plate.

[0014] Step 2 includes: turning on the triangle wave signal generator, inputting the triangle wave signal into the laser controller, scanning the laser frequency within a certain range, and observing the Doppler-free absorption spectrum of the two-color circularly polarized light generated by the coherent population capture CPT effect through an oscilloscope.

[0015] Step 3 includes: finding the absorption peak with large amplitude and small line width in the two-color circularly polarized light Doppler-free absorption spectrum as the stabilization point, and selecting 87 The ground state energy level F in the dual-color non-Doppler absorption spectrum of RbD1 line g =1 and F g =2 transition to the excited state energy level F e =2. The CPT three-level system consisting of two ground-state energy levels and one excited-state energy level is unaffected by the magnetic field. When the pump light and the detection light are two-color circularly polarized light propagating in opposite directions, constructive interference occurs, and the CPT absorption peak amplitude reaches its maximum. The dispersion signal slope is maximum when it serves as the frequency locking point. Therefore, in the geomagnetic field environment, the two-color circularly polarized light Doppler absorption spectrum still has an absorption peak with a large amplitude that can be used for laser frequency stabilization. After the frequency stabilization point is determined, the laser center frequency is adjusted so that the frequency locking point is at the center of the periodic signal.

[0016] Step 4 includes: turning on the sine wave signal generator, superimposing the sine signal on the triangular wave scanning signal through an adder, and outputting it to the laser controller to modulate the two-color circularly polarized light Doppler-free absorption spectrum, thereby obtaining the modulated two-color circularly polarized light Doppler-free absorption spectrum, and at the same time inputting the sine wave signal as a reference signal into the phase-locked amplifier, and converting the Doppler-free absorption spectrum signal into a dispersion signal through demodulation by the phase-locked amplifier, the zero point frequency in the dispersion signal corresponds to the frequency locking point frequency, and after obtaining the dispersion signal, adjusting the amplitude and frequency of the reference signal so that the Doppler-free absorption spectrum signal and the dispersion signal at the frequency locking point are clearly visible.

[0017] Step 4 includes the following formula:

[0018]

[0019] Where u(t) is the PID output signal, e(t) and e(τ) are both PID input signals, i.e., dispersion signals serving as error signals, and K p is the proportional gain, K i is the integral gain, K d is the differential gain, t and τ are both time.

[0020] The technical effects of the present invention are as follows: The present invention provides a laser frequency stabilization method based on two-color circularly polarized light without Doppler absorption spectrum, which uses two-color circularly polarized light without Doppler absorption spectrum as an error signal to achieve the laser frequency stabilization under the geomagnetic field. 87 The frequency of the RbD1 line is locked. To ensure the feasibility of laser frequency stabilization, the advantages of the two-color circularly polarized light without Doppler absorption spectrum are theoretically analyzed from the perspective of energy level. The wavelength generated by the tunable external cavity semiconductor laser (ECDL) is around 795nm (corresponding to 87 RbD1 linear atomic transition frequency) of the monochromatic linearly polarized laser, the electro-optic modulator (EOM) controlled by the 3.417GHz radio frequency signal converts the 795nm monochromatic light polarization into a two-color linearly polarized light with a frequency of 377THz (corresponding to 795nm) ±3.417GHz, and the two-color linearly polarized light is converted into two-color circularly polarized light through a 1 / 4 wave plate (QWP). The two-color circularly polarized light is incident on the gas chamber as the pump light, and after passing through the gas chamber, it is converted into two-color linear polarized light through the 1 / 4 wave plate. The linearly polarized light is reflected by the reflector and then passes through the 1 / 4 wave plate again to become two-color circularly polarized light with the opposite rotation direction to the pump light. The two-color circularly polarized light with the opposite rotation direction is input into the gas chamber again as the detection light, and the photodetector receives the light signal to obtain the two-color circularly polarized light Doppler-free absorption spectrum. The triangle wave signal is input to the laser controller to scan the laser frequency to obtain 87 The two-color circularly polarized light of the RbD1 line has a Doppler-free spectrum. Adjust the center frequency of the laser so that the frequency locking point is located at the center of the scanning signal. Output a sinusoidal wave signal to the laser controller to modulate the laser current. Input the sinusoidal wave signal as a reference signal to the phase-locked amplifier, and use the phase-locked amplifier to demodulate to obtain the dispersion signal corresponding to the spectral signal. Adjust the frequency and amplitude of the sinusoidal wave signal so that both the spectral signal and the dispersion signal are clearly visible. Turn off the triangular wave signal input to keep the laser frequency at the frequency locking point. Input the dispersion signal as an error signal into the proportional integral differential (PID) module, and the PID module outputs a signal to the laser control system to dynamically adjust the laser frequency. When the laser frequency offsets, the laser controller receives the error signal to adjust the laser current and the resonant cavity piezoelectric ceramic voltage to return the laser frequency to the stable frequency point again, thereby achieving 87Frequency locking of the RbD1 line. This method, based on a Doppler-free absorption optical path, uses two-color light to generate a coherent population trapping (CPT) effect, reducing the absorption peak linewidth at the frequency locking point, thereby increasing the slope of the dispersion signal and enhancing the sensitivity and stability of the frequency system. The circularly polarized light spectral signal absorption peak maintains a large amplitude in the geomagnetic field, eliminating the need for additional magnetic shielding measures. This simplifies the optical path structure and paves the way for miniaturization. This technology has strong applicability and practical value in fields such as CPT magnetometers and CPT atomic clocks. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 The present invention is a flow chart of a laser frequency stabilization method based on a two-color circularly polarized light Doppler-free absorption spectrum. Figure 1 The method includes steps 1: obtaining two-color circularly polarized light using a laser, an electro-optical modulator, and a quarter-wave plate; 2: using a polarization beam splitter and a reflector to achieve counter-propagation of the pump light and the detection light, and adjusting the circular polarization direction of the detection light to be opposite to that of the pump light using the quarter-wave plate, thereby obtaining a two-color circularly polarized light Doppler-free absorption spectrum; 3: turning on the laser scanning and modulation, receiving the absorption spectrum using a photodetector and transmitting it to a phase-locked amplifier for demodulation to obtain the dispersion signal corresponding to the spectrum, adjusting the laser current and scanning range to find the dispersion signal corresponding to the frequency locking point, and adjusting the amplitude and frequency of the laser modulation signal to make both the spectrum signal and the dispersion signal clearly visible. 4: turning off the laser scanning, inputting the dispersion signal as an error signal into a PID control module (PID, proportional-integral-derivative), and controlling the laser frequency change using the PID output signal to achieve laser frequency stabilization.

[0022] Figure 2 The present invention is a schematic diagram of the structure of a laser frequency stabilization system involved in the laser frequency stabilization method based on a two-color circularly polarized light Doppler-free absorption spectrum.

[0023] Figure 3 This is a diagram of a three-level system in the CPT effect that is invariant to magnetic fields. CPT stands for coherent population trapping. Figure 3 m in F is the magnetic quantum number; 5 2 S 1 / 2 and 5 2 P 1 / 2 express 87 Atomic energy level of Rb atom at D1 line; F g represents the ground state hyperfine level in a three-level system; F e represents the excited state hyperfine level in the three-level system; σ +represents left-handed circularly polarized light; σ - Represents right-handed circularly polarized light.

[0024] The accompanying drawings are marked as follows: 1-laser controller; 2-tunable external-cavity diode laser (ECDL); 3-first polarization-maintaining fiber; 4-RF signal generator; 5-electro-optical modulator (EOM, Electro-Optic Modulator, used to modulate monochromatic laser into dual-color laser with frequencies of 377THz (corresponding to 795nm) ± 3.417GHz); 6-second polarization-maintaining fiber; 7-laser collimator; 8-optical isolator; 9-first 1 / 4 wave plate (Quarter-waveplate, QWP); 10-reflector (the reflected light of which is incident on the atomic gas chamber again as detection light); 11-second 1 / 4 wave plate (used to reverse the circular polarization states of the two incident gas chamber lasers, for example, one is left-handed circularly polarized light and the other is right-handed circularly polarized light); 12-atomic gas chamber; 13-depolarizing beam splitter (NPBS, Non-Polarizing Beam Splitter) Splitter); 14-photodetector (PD, photodetector, used to obtain two-color circularly polarized light Doppler-free spectrum); 15-phase-locked amplifier; 16-proportional-integral-derivative controller (PID, proportional-integral-derivative); 17-triangle wave signal generator; 18-sine wave signal generator; 19-adder. DETAILED DESCRIPTION

[0025] Below is the attached figure ( Figure 1-Figure 3 ) and Examples illustrate the present invention.

[0026] Figure 1 The present invention is a flow chart of a laser frequency stabilization method based on a two-color circularly polarized light Doppler-free absorption spectrum. Figure 2 The present invention is a schematic diagram of the structure of a laser frequency stabilization system involved in the laser frequency stabilization method based on a two-color circularly polarized light Doppler-free absorption spectrum. Figure 3 This is a schematic diagram of a three-level system in the CPT effect that does not change with the magnetic field. Figures 1 to 3As shown, a laser frequency stabilization method based on a two-color circularly polarized light Doppler-free absorption spectrum comprises the following steps: step 1, inputting a first-handed two-color circularly polarized light as pump light into a first end of an atomic gas cell, the first-handed two-color circularly polarized light being emitted from a second end of the atomic gas cell and then being changed into a second-handed two-color circularly polarized light as detection light and inputting the atomic gas cell from the second end, wherein the second handing is opposite to the first handing, and the second-handed two-color circularly polarized light is emitted from the first end and then enters a photoelectric detection system; step 2, performing a laser frequency scan so that two-color circularly polarized light of second handings with different frequencies forms a two-color circularly polarized light Doppler-free absorption spectrum in the photoelectric detection system; step 3, determining a frequency locking point in the two-color circularly polarized light Doppler-free absorption spectrum, and obtaining a dispersion signal corresponding to the frequency locking point by demodulating the two-color circularly polarized light Doppler-free absorption spectrum; step 4, closing the laser frequency scan, inputting the dispersion signal as an error signal into a PID control module, and controlling the laser frequency change through the PID output signal to achieve laser frequency stabilization.

[0027] The first end of the atomic gas chamber 12 is respectively connected to the photodetector 14 and the first 1 / 4 wave plate 9 through the depolarization beam splitter prism 13, the first 1 / 4 wave plate 9 is connected to the laser collimator 7 through the optical isolator 8, the laser collimator 7 is connected to the electro-optical modulator 5 through the second polarization-maintaining fiber 6, the electro-optical modulator 5 is respectively connected to the radio frequency signal generator 4 and the first polarization-maintaining fiber 3, the first polarization-maintaining fiber 3 is connected to the laser controller 1 through the tunable external cavity semiconductor laser 2, the laser controller 1 is connected to the output end of the phase-locked amplifier 15 through the proportional-integral-differential controller 16, the first input end of the phase-locked amplifier 15 is connected to the photodetector 14, the second input end of the phase-locked amplifier 15 is connected to the sine wave signal generator 18, the sine wave signal generator 18 is connected to the first input end of the adder 19, the second input end of the adder 19 is connected to the triangular wave signal generator 17, the output end of the adder 19 is connected to the laser controller 1, and the second end of the atomic gas chamber 12 is connected to the reflector 10 through the second 1 / 4 wave plate 11.

[0028] Step 1 includes: using a laser and an electro-optical modulator to generate a frequency that satisfies 87The Rb atomic D1 line satisfies the frequency difference between the two ground-state hyperfine levels of 6.834 GHz, and the D1 line has a wavelength of 795 nm. The 795 nm monochromatic linearly polarized light emitted by a tunable external cavity semiconductor laser is modulated into a frequency-compliant two-color linearly polarized light of 377 THz ± 3.417 GHz by an electro-optical modulator controlled by a radio frequency signal of 3.417 GHz, where 377 THz corresponds to a wavelength of 795 nm. The two-color linearly polarized light is then converted into two-color circularly polarized light by a quarter-wave plate. Step 2 includes: turning on a triangular wave signal generator, inputting the triangular wave signal into a laser controller, sweeping the laser frequency within a certain range, and observing the Doppler-free absorption spectrum of the two-color circularly polarized light generated by the coherent population trapping (CPT) effect using an oscilloscope.

[0029] Step 3 includes: finding the absorption peak with large amplitude and small line width in the two-color circularly polarized light Doppler-free absorption spectrum as the stabilization point, and selecting 87 The ground state energy level F in the dual-color non-Doppler absorption spectrum of RbD1 line g =1 and F g =2 transition to the excited state energy level F e =2. The CPT three-level system consisting of two ground-state energy levels and one excited-state energy level is unaffected by the magnetic field. When the pump light and the detection light are two-color circularly polarized light propagating in opposite directions, constructive interference occurs, and the CPT absorption peak amplitude reaches its maximum. The dispersion signal slope is maximum when it serves as the frequency locking point. Therefore, in the geomagnetic field environment, the two-color circularly polarized light Doppler absorption spectrum still has an absorption peak with a large amplitude that can be used for laser frequency stabilization. After the frequency stabilization point is determined, the laser center frequency is adjusted so that the frequency locking point is at the center of the periodic signal.

[0030] Step 4 includes: turning on the sine wave signal generator, superimposing the sine signal on the triangular wave scanning signal through an adder, and outputting it to the laser controller to modulate the two-color circularly polarized light Doppler-free absorption spectrum, thereby obtaining the modulated two-color circularly polarized light Doppler-free absorption spectrum, and at the same time inputting the sine wave signal as a reference signal into the phase-locked amplifier, and converting the Doppler-free absorption spectrum signal into a dispersion signal through demodulation by the phase-locked amplifier, the zero point frequency in the dispersion signal corresponds to the frequency locking point frequency, and after obtaining the dispersion signal, adjusting the amplitude and frequency of the reference signal so that the Doppler-free absorption spectrum signal and the dispersion signal at the frequency locking point are clearly visible.

[0031] Step 4 includes the following formula:

[0032]

[0033] Where u(t) is the PID output signal, e(t) and e(τ) are both PID input signals, i.e., dispersion signals serving as error signals, and K pis the proportional gain, K i is the integral gain, K d is the differential gain, t and τ are both time.

[0034] The laser frequency stabilization method based on two-color circularly polarized light Doppler-free absorption spectroscopy uses two-color circularly polarized light as the frequency stabilization light source and combines it with the Doppler-free absorption optical path to obtain two-color circularly polarized light Doppler-free absorption spectroscopy. Two-color Doppler-free absorption spectroscopy uses the coherent population trapping (CPT) effect to lock the frequency point ( 87 The RbD1 line) is used to obtain an absorption peak with a narrow linewidth. The characteristics of circularly polarized light in the CPT effect are utilized to overcome the disadvantage of small signal amplitude in the geomagnetic field, thereby using the two-color circularly polarized light Doppler-free absorption spectrum for laser frequency stabilization in the geomagnetic field. After establishing the two-color circularly polarized light Doppler-free absorption optical path, a triangle wave signal is used to scan the laser frequency to obtain the two-color circularly polarized light Doppler-free absorption spectrum. The laser current is adjusted so that the frequency locking point is located at the center of the signal. A sine wave signal is superimposed on the triangle wave signal to modulate the spectrum signal. The sine wave signal is input as a reference signal into a phase-locked amplifier. The phase-locked amplifier demodulates the signal to obtain the dispersion signal corresponding to the absorption spectrum. The frequency and amplitude of the sinusoidal signal are adjusted to make both the spectrum signal and the dispersion signal clearly visible. The laser frequency triangle wave scanning is turned off, and the dispersion signal is input as an error signal into the proportional integral differential (PID) module for processing. The processed signal is output to the laser control module, which adjusts the laser frequency in real time to return it to the stable frequency point, thus achieving laser frequency stabilization.

[0035] The principle of the laser frequency stabilization method based on two-color circularly polarized light Doppler-free absorption spectroscopy, refer to Figure 1 , 1-Laser controller, used to adjust the frequency and intensity of the laser emitted by the laser. 2-Tunable external cavity semiconductor laser, to obtain monochromatic linearly polarized light with a frequency of about 795nm. 3-Polarization-maintaining fiber, to transmit the laser from the laser to the electro-optical modulator. 4-RF signal generator, to generate a radio frequency signal with a frequency of about 3.417GHz. 5-Electro-optical modulator, to modulate the monochromatic laser into a two-color laser with frequencies of 377THz (corresponding to 795nm) ±3.417GHz. 6-Polarization-maintaining fiber, to transmit the laser from the electro-optical modulator to the laser collimator. 7-Laser collimator, to emit the laser into space, so that the laser is converted from fiber light to spatial light. 8-Optical isolator, to make the light propagate in one direction only, to prevent the light from propagating in the opposite direction to the electro-optical modulator and causing damage to it. 9-1 / 4 wave plate, to convert linearly polarized light into circularly polarized light. 10-Reflector, which reflects the laser light and re-enters the atomic gas chamber as detection light. The laser light before reflection is marked in yellow, and the laser light after reflection is marked in blue.

[0036] 11-1 / 4 wave plate, which makes the circular polarization state of the two incident lasers in the gas chamber reverse (i.e. one is left-handed circularly polarized light and the other is right-handed circularly polarized light). 12-Atomic gas chamber, vacuum gas chamber, filled with natural rubidium ( 87 Rb accounts for 27.85, 85 Rb accounts for 72.15). 13-Depolarizing prism, the laser is divided into two beams of equal size and unchanged polarization state after transmission and reflection, in which the reflected light of the yellow laser and the transmitted light of the blue laser are retained. 14-Photodetector, used to receive the detection light, convert the optical signal into an electrical signal, and obtain a two-color circularly polarized light Doppler-free spectrum. 15-Phase-locked amplifier, uses the sinusoidal wave signal as a reference signal to modulate the spectrum signal to obtain a dispersion signal. 16-Proportional integral differential (PID) controller, performs proportional integral differential processing on the dispersion signal and outputs it to the laser controller. 17-Triangular wave signal generator, outputs a triangular wave signal to the laser controller to realize frequency scanning. 18-Sine wave signal generator, outputs a sine wave signal to the laser controller and the phase-locked amplifier to realize signal modulation and demodulation. 19-Adder, superimposes the triangular wave signal and the sine wave signal and inputs them to the laser controller.

[0037] When alkali metal atoms react with light of a specific frequency, the atoms absorb the energy of the light and undergo transitions. When two-color light reacts with alkali metal atoms, a coherent population trapping (CPT) effect occurs, and the atoms are trapped in the ground state energy level, so that the atoms no longer absorb the energy of light. This is reflected in the spectrum as a transmission peak at the atomic transition frequency point. However, when two beams of two-color circularly polarized light propagating in opposite directions (i.e., one beam is left-handed light and the other is right-handed light) react with atoms at the same time to produce the CPT effect, the atoms trapped in the ground state due to the CPT effect produce an enhanced absorption relative to the other beam, which in turn produces a sharp absorption peak in the spectrum. The apex of the absorption peak corresponds to the frequency at the frequency locking point, so the Doppler-free absorption spectrum of two-color circularly polarized light can be used for laser frequency stabilization. This article adopts 87 Ground state F in the two-color non-Doppler absorption spectrum of Rb atom D1 line g =1 and F g =2 transition to excited state F e =2 is used as the frequency stabilization point, and the ECDL laser is used to generate 87 The monochromatic linearly polarized laser corresponding to the RbD1 line (795nm) is half-wave modulated by the EOM controlled by a 3.417GHz RF signal to obtain a two-color linearly polarized light containing ±1-order sideband light. The frequency difference of the sideband light is 6.834GHz, which roughly meets 87The RbD1 line ground state hyperfine energy level difference. The obtained two-color linear polarized light is converted into two-color circularly polarized light through a 1 / 4 wave plate. The two-color circularly polarized light is respectively incident into the gas chamber as pump light and detection light through a reflector and a 1 / 4 wave plate. At this time, the rotation directions of the pump light and the detection light are opposite. Turn on the triangle wave signal generator to scan the laser frequency, and the optical signal of the detection light is received by the photodetector to obtain 87 The RbD1 line two-color circularly polarized light has no Doppler absorption spectrum. Adjust the laser current and the triangle wave scanning range to make the ground state F g =1 and F g =2 transition to excited state F e = 2, the corresponding absorption peak is located at the center of the periodic signal. The sinusoidal modulated signal is superimposed on the triangular wave sweep signal using an adder and then modulated and demodulated into a dispersion signal using a phase-locked amplifier. The frequency and amplitude of the sinusoidal signal are adjusted to ensure clarity of both the spectral and dispersion signals. The laser frequency sweep is turned off, and the dispersion signal is input as an error signal into the PID module, which then outputs the error signal to the laser control module. Based on the received error signal, the laser dynamically adjusts the laser current and the resonant cavity piezoelectric ceramic voltage to return the laser frequency to the locked frequency point, thereby achieving laser frequency stabilization.

[0038] This method requires five steps to achieve a laser frequency stabilization method based on two-color circularly polarized light Doppler-free absorption spectroscopy.

[0039] Step 1: Generation of two-color circularly polarized light

[0040] In order to find the corresponding frequency locking point, it is necessary to generate a frequency that satisfies 87 The laser frequency of the ECDL laser is usually adjusted to 87 Near the D1 line of the Rb atom, the emission of monochromatic linearly polarized light meets the requirements. The EOM, controlled by a 3.417 GHz radio frequency signal, converts the monochromatic linearly polarized light into two-color linearly polarized light with a frequency difference that meets the requirements. The quarter-wave plate then converts the two-color linearly polarized light into two-color circularly polarized light.

[0041] Step 2: Build a two-color circularly polarized light path without Doppler absorption

[0042] According to the Doppler effect, the actual transition frequency of light-atom interactions is affected by the relative velocity of the light and atoms, which increases the linewidth of the corresponding absorption peak. To eliminate the Doppler effect, we employ a saturated absorption optical path, in which two circularly polarized beams of light are transmitted into the gas cell in opposite directions, acting as pump and detection beams. Because the pump and detection beams have the same frequency and propagate in opposite directions, only atoms with zero velocity can react simultaneously with both beams. This eliminates the Doppler effect and reduces the absorption linewidth at the frequency-locking point.

[0043] When two-color light reacts with alkali metal atoms and the frequency matches the transition of two ground-state hyperfine energy levels to the same excited state, they form a three-level system and undergo the coherent population trapping (CPT) effect, trapping the atoms in the ground-state energy level. When the counter-propagating pump light and detection light simultaneously undergo the CPT effect with the atoms, the atoms trapped by the pump light will experience enhanced absorption of the detection light, and vice versa, resulting in a sharp absorption peak in the spectrum. The following is an analysis of the atomic energy levels involved in the CPT effect:

[0044] In a magnetic field, 87 The D1 line energy level of the Rb atom will undergo Zeeman splitting. F =0 ground state hyperfine level |F g ,m F =0>, the corresponding energy is:

[0045]

[0046] Where E(F g ,m F =0) represents the magnetic quantum number m F =0 87 The energy of the ground state hyperfine level of the D1 line of the Rb atom, F g express 87 The ground state hyperfine level of the D1 line of Rb atom, F g =1,2;m F represents the magnetic quantum number; h is the Planck constant, which is 6.626×10 -34 ;v hfs is the microwave frequency corresponding to the ground state energy levels when there is no external magnetic field, and its value is 6.834×10 9 ; I is the nuclear spin quantum number, which is 3 / 2.

[0047] The energy result is independent of the magnetic field size, so 87 The number of magnetic field sub-elements in the D1 line of Rb atom m F = 0, the ground state Zeeman self-level does not move with the magnetic field. g =1,m F =0> and |F g =2,m F =0> The CPT effect consisting of two ground-state energy levels can exist in a geomagnetic environment. Below we analyze the CPT three-level system consisting of these two ground-state energy levels.

[0048] Figure 3 Middle m F Represents the magnetic quantum number; 5 2 S 1 / 2 and 5 2 P1 / 2 represents the atomic energy level of 87Rb atom at D1 line; F g represents the ground state hyperfine level in a three-level system; F e represents the excited state hyperfine level in the three-level system; σ + represents left-handed circularly polarized light; σ - Represents right-handed circularly polarized light.

[0049] When left-handed and right-handed circularly polarized light 87 When Rb atoms interact with each other, they can form Figure 3 The two ground state energy levels in the three-level system are not affected by the magnetic field, and the two systems share the same ground state, so the left-handed and right-handed two-color light are respectively at |F g =1,m F =0>、|F g =2,m F =0> The dark state prepared at the energy level will interfere. Assume that the electric field vectors of the two sets of two-color light interacting with the atom are

[0050]

[0051] Represents the electric field vector of the two-color light, where the subscript j = 1, 2 is used to distinguish two-color light of different frequencies, and the positive and negative signs represent the left-handed and right-handed components respectively. Represents the electric field intensity of two sets of two-color light; is a unit vector; e is a natural constant, with a value of approximately 2.71828; i is an imaginary unit; ω j is the corresponding two-color light frequency; t is the time; Represents two sets of two-color light wave vectors, in vacuum there are represents the optical path length of the light field; Represents the initial phase of the light field. Then the Rabi frequencies corresponding to the resonance of different light fields at the corresponding energy levels are:

[0052]

[0053] represents the Rabi frequencies corresponding to the resonance of different circularly polarized two-color light fields at the corresponding energy levels, where the subscripts j = 1, 2 are used to distinguish two-color lights of different frequencies, and the positive and negative signs represent the left-handed and right-handed components, respectively; Represents the electric field intensity of two sets of two-color light; is a unit vector; represents the corresponding electric dipole moment; is the reduced Planck constant, e is a natural constant with a value of approximately 2.71828; i is an imaginary unit; ω j is the corresponding two-color light frequency; t is the time; Represents two sets of two-color light wave vectors, in vacuum there are represents the optical path length of the light field; represents the initial phase of the light field.

[0054] Two sets of two-color circularly polarized light in |F g =1,m F =0>、|F g =2,m F =0> The dark states formed by the energy levels are

[0055]

[0056] |D ± > indicates two sets of two-color circularly polarized light in |F g =1,m F =0>、|F g =2,m F =0>The dark state formed by the energy level, the positive and negative signs represent the left and right components respectively; Indicates different circularly polarized two-color light fields in |F g =1,m F =0>The Rabi frequency corresponding to the energy level resonance; Indicates different circularly polarized two-color light fields in |F g =2,m F =0>The Rabi frequency corresponding to the energy level resonance;

[0057]

[0058] for 87 The transition of the D1 line of Rb atom is

[0059]

[0060] is a unit vector; represents the corresponding electric dipole moment,

[0061] Assumptions Available

[0062]

[0063] represents the electric field intensity of two sets of two-color light; e is a natural constant with a value of approximately 2.71828; i is an imaginary unit; represents the optical path length of the light field; Represents two sets of two-color light wave vectors, in vacuum there are The initial phase of the light field represents the optical path difference between the left-handed and right-handed two-color light. When , the CPT effects produced by the left-handed and right-handed three-level systems interfere constructively, and when When , the two interferences cancel each other out.

[0064] for Figure 3 In a three-level system unaffected by magnetic fields, when the pump and detection beams are two-color circularly polarized and propagate in opposite directions (i.e., one is left-handed circularly polarized and the other is right-handed circularly polarized), they constructively interfere with each other, and the CPT absorption peak reaches its maximum amplitude. The dispersion signal slope is maximum at the frequency-locking point. When the pump and detection beams are two-color linearly polarized, we consider the linearly polarized light as a mixture of equal proportions of left-handed and right-handed circularly polarized light. At this point, the CPT effects caused by the left-handed and right-handed light interfere destructively, causing their contribution to the CPT peak to be almost zero. Therefore, in a geomagnetic environment, the Doppler absorption spectrum of two-color circularly polarized light still has a large absorption peak, which can be used for laser frequency stabilization. However, the absorption peak amplitude of the Doppler absorption spectrum of two-color linearly polarized light decreases rapidly, making it unsuitable for use as a reference for frequency stabilization.

[0065] Based on the above theory, we constructed an experimental optical path to obtain the Doppler-free absorption spectrum of two-color circularly polarized light. The two-color circularly polarized light changes its optical path through the depolarization beam splitter NPBS and is used as the pump light to enter the 87 The laser is then emitted and converted into two-color linear polarized light by a quarter wave plate. After being reflected by a reflector, it is converted into two-color circular polarized light with a rotation direction opposite to that of the pump light by a quarter wave plate. This light is then incident into the gas chamber again as the detection light. The detection light is then received by a photodetector PD after exiting the gas chamber. 87 Two-color circularly polarized light Doppler-free absorption spectrum of the RbD1 line.

[0066] Step 3: Find the appropriate frequency lock point

[0067] Turn on the laser frequency scan and find the absorption peak with large amplitude and small line width in the two-color circularly polarized light Doppler-free absorption spectrum as the stable frequency point. Here we choose 87 The ground state energy level F in the dual-color non-Doppler absorption spectrum of RbD1 line g =1 and F g =2 transition to the excited state energy level F e = 2 corresponding absorption peak. After the stable frequency point is determined, adjust the center frequency of the laser so that the frequency locking point is at the center of the periodic signal.

[0068] Step 4: Modulate and demodulate the spectral signal into a dispersion signal

[0069] The sine wave signal used for modulation is superimposed on the scanning signal, and the Doppler-free absorption spectrum of the two-color circularly polarized light is modulated and demodulated by a phase-locked amplifier to obtain the corresponding dispersion signal.

[0070] The two-color light Doppler-free absorption spectrum is simplified as:

[0071] G(ω)=f(ω)+g(ω)

[0072] f(ω)=-(aω 2 +bω+c)

[0073]

[0074] G(ω) is the functional expression for the absorption peak of the two-color light Doppler-free spectrum. f(ω) represents the Doppler background in the spectral line component, which is a binomial and is displayed as a Fokker profile. g(ω) represents the transition component of the hyperfine energy level of the spectral line, which is a Lorentz profile. a, b, c, and K are unknown coefficients. ω is the actual frequency of the laser. γ is the line width of the spectral line. g(ω) is axially symmetric, and its center point frequency ω0 corresponds to the atomic transition frequency, which is the reference frequency of the laser frequency stabilization. In the signal, it corresponds to the extreme point of the spectral line.

[0075] Add a sinusoidal signal Asin(Ωt) to the laser frequency ω0, which is called the modulation signal. If the modulation frequency is Ω, the frequency after modulation is:

[0076] ω′=ω0+Asin(Ωt) (8)

[0077] A is the modulation depth and |A|≤γ, γ is the spectral line width, Ω is the modulation frequency; t is time. Taylor expansion of G(ω) at ω0:

[0078]

[0079] Then multiply the two signals sin(Ωt) (called the reference signal, note that it is different from the reference frequency) and G(ω′) to extract their DC terms:

[0080]

[0081] Where T = 2π / Ω is the period of the modulation signal. It can be seen that this DC term is proportional to the product of the first harmonic (first differential) of the spectral signal G(ω) and the modulation depth A. This is the first harmonic (first differential) signal of the spectrum, commonly known as the error signal. The mathematical process of integration is implemented in the circuit using a lock-in amplifier.

[0082] The absorption peak in the spectral signal corresponds to the zero crossing point in the dispersion signal, making it easier to lock and determine the frequency offset of the laser. Adjust the frequency and amplitude of the sine wave signal to make both the spectral signal and the dispersion signal clearer.

[0083] Step 5: Implement closed-loop control of laser frequency stabilization

[0084] The scanning signal is turned off, and the dispersion signal is fed into the PID module as an error signal. The PID module then outputs a frequency-stabilized signal to the laser control system. The PID module's output is the sum of the three algorithms (proportional, integral, and differential). Its input is the error value e(t) (herein, the numerical change in the dispersion signal). Defining u(t) as the output value, the PID algorithm can be expressed as follows:

[0085]

[0086] where K p is the proportional gain; K i is the integral gain; K d is the differential gain; e(t) is the error.

[0087] Proportional regulation (P) refers to a controller whose output is proportional to the input error signal. When only proportional regulation is in effect, the system output will have a steady-state error. Proportional regulation responds proportionally to system deviations. Once a system deviation occurs, proportional regulation immediately takes effect to reduce the deviation. A large proportional parameter can speed up regulation and reduce errors, but an excessively large proportional parameter can reduce system stability and even cause instability.

[0088] In integral control (I), the output of the controller is proportional to the integral of the input error signal. For an automatic control system, if there is a steady-state error after entering the steady state, it is called a differential system. In order to eliminate the steady-state error, an "integral term" must be introduced in the controller. The integral term is the integral of the error depending on time, and as time increases, the integral term continues to accumulate. In this way, even if the error is very small, the integral term will increase with time, which will drive the output of the controller to increase and further reduce the steady-state error until it is equal to zero. When the error is zero, the integral control output is constant. The strength of the integral effect depends on the integral time constant K i ,K i The smaller it is, the stronger the integral effect is. i If the integral is too large, the integral effect will be weak. Adding integral regulation will reduce the stability of the system and slow down the dynamic response. It is often combined with the other two types of regulation to form a PI regulator or PID regulator.

[0089] In differential control (D), the controller output is proportional to the differential of the input error signal (i.e., the rate of change of the error). Automatic control systems may experience oscillation or even instability during the error control process. This is due to the presence of components (links) with significant inertia or hysteresis, which act to suppress the error, but whose changes always lag behind those of the error. To address this issue, the error suppression function can be made "ahead of the curve." In other words, simply introducing a proportional term into the controller is often insufficient, as the proportional term merely amplifies the error amplitude. Instead, a differential term is needed to predict the error's trend. Thus, a controller with both proportional and differential control can suppress error changes in advance, thus avoiding significant overshoot of the controlled variable. Therefore, for controlled objects with significant inertia or hysteresis, a proportional-plus-derivative (PD) controller can improve the system's dynamic characteristics during the control process. By using differential control to suppress or eliminate deviations before they develop, the system's dynamic performance is enhanced. Appropriate differential parameters can reduce overshoot and shorten control time. However, the differential action has an amplifying effect on noise interference, so excessive differential adjustment is detrimental to the system's anti-interference ability. The differential action cannot be used alone and needs to be combined with the other two adjustment rules to form a PID controller.

[0090] The laser control system dynamically adjusts the laser current or piezoelectric ceramic voltage according to the size and positive and negative of the obtained frequency stabilization signal, adjusts the laser frequency to the locking frequency point, and thus dynamically locks the laser frequency.

[0091] Any content not described in detail in this specification is prior art known to those skilled in the art. It should be noted that the above description is intended to help those skilled in the art understand the present invention, but does not limit the scope of protection of the present invention. Any equivalent substitution, modification, improvement, and / or simplification of the above description that does not depart from the essence of the present invention shall fall within the scope of protection of the present invention.

Claims

1. A laser frequency stabilization method based on two-color circularly polarized light Doppler-free absorption spectroscopy, characterized in that: The following steps are involved: Step 1: Input a first-handed two-color circularly polarized light as pump light into a first end of the atomic gas cell; after the first-handed two-color circularly polarized light is emitted from a second end of the atomic gas cell, it is changed into a second-handed two-color circularly polarized light as detection light and input into the atomic gas cell from the second end; the second-handed two-color circularly polarized light is opposite to the first-handed one; and after the second-handed two-color circularly polarized light is emitted from the first end, it enters a photoelectric detection system; Step 2, performing laser frequency scanning so that the second-handed two-color circularly polarized light with different frequencies forms a two-color circularly polarized light Doppler-free absorption spectrum in the photoelectric detection system; Step 3: determining a frequency-locking point in the two-color circularly polarized light Doppler-free absorption spectrum, and obtaining a dispersion signal corresponding to the frequency-locking point by demodulating the two-color circularly polarized light Doppler-free absorption spectrum; Step 4: Turn off the laser frequency scanning, input the dispersion signal as the error signal into the PID control module, and control the laser frequency change through the PID output signal to achieve laser frequency stabilization; Step 3 includes: finding the absorption peak with large amplitude and small line width in the two-color circularly polarized light Doppler-free absorption spectrum as the stabilization point, and selecting 87 The ground state energy level F in the dual-color non-Doppler absorption spectrum of RbD1 line g =1 and F g =2 transition to the excited state energy level F e =2, the CPT three-level system consisting of two ground-state energy levels and one excited-state energy level is not affected by the magnetic field. When the pump light and the detection light are two-color circularly polarized light propagating in opposite directions, they interfere constructively, and the CPT absorption peak amplitude reaches its maximum. When it serves as the frequency locking point, the dispersion signal slope is the largest. Therefore, in the geomagnetic field environment, the two-color circularly polarized light Doppler absorption spectrum still has a large absorption peak that can be used for laser frequency stabilization. After the frequency stabilization point is determined, the laser center frequency is adjusted so that the frequency locking point is at the center of the periodic signal. Step 4 includes: turning on a sine wave signal generator, superimposing a sine signal on a triangular wave scanning signal through an adder, and outputting the resultant signal to a laser controller to modulate the two-color circularly polarized light Doppler-free absorption spectrum, thereby obtaining a modulated two-color circularly polarized light Doppler-free absorption spectrum; simultaneously, inputting the sine wave signal as a reference signal into a phase-locked amplifier, converting the Doppler-free absorption spectrum signal into a dispersion signal through demodulation by the phase-locked amplifier, wherein the zero-point frequency in the dispersion signal corresponds to the frequency locking point frequency; after obtaining the dispersion signal, adjusting the amplitude and frequency of the reference signal so that both the Doppler-free absorption spectrum signal and the dispersion signal at the frequency locking point are clearly visible; Step 4 includes the following formula: Where u(t) is the PID output signal, e(t) and e(τ) are both PID input signals, i.e., dispersion signals serving as error signals, and K p is the proportional gain, K i is the integral gain, K d is the differential gain, t and τ are both time.

2. The laser frequency stabilization method based on two-color circularly polarized light Doppler-free absorption spectroscopy according to claim 1, characterized in that: The first end of the atomic gas chamber is respectively connected to a photodetector and a first quarter wave plate through a depolarizing beam splitter, the first quarter wave plate is connected to a laser collimator through an optical isolator, the laser collimator is connected to an electro-optical modulator through a second polarization-maintaining fiber, the electro-optical modulator is respectively connected to a radio frequency signal generator and the first polarization-maintaining fiber, the first polarization-maintaining fiber is connected to a laser controller through a tunable external cavity semiconductor laser, the laser controller is connected to the output end of a lock-in amplifier through a proportional-integral-differential controller, the first input end of the lock-in amplifier is connected to the photodetector, the second input end of the lock-in amplifier is connected to a sine wave signal generator, the sine wave signal generator is connected to a first input end of an adder, the second input end of the adder is connected to a triangular wave signal generator, the output end of the adder is connected to the laser controller, and the second end of the atomic gas chamber is connected to a reflector through a second quarter wave plate.

3. The laser frequency stabilization method based on two-color circularly polarized light Doppler-free absorption spectroscopy according to claim 1, characterized in that: Step 1 includes: using a laser and an electro-optical modulator to generate a frequency that satisfies 87 The Rb atomic D1 line satisfies the two-ground state hyperfine energy level frequency difference of 6.834 GHz and the two-color circularly polarized light, wherein the D1 line wavelength is 795 nm. The 795 nm monochromatic linearly polarized light emitted by the tunable external cavity semiconductor laser is modulated into a two-color linearly polarized light with a frequency of 377 THz±3.417 GHz by an electro-optical modulator controlled by a radio frequency signal with a frequency of 3.417 GHz, wherein 377 THz corresponds to a wavelength of 795 nm. The two-color linearly polarized light is then converted into two-color circularly polarized light by a quarter wave plate.

4. The laser frequency stabilization method based on two-color circularly polarized light Doppler-free absorption spectroscopy according to claim 1, characterized in that: Step 2 includes: turning on the triangle wave signal generator, inputting the triangle wave signal into the laser controller, scanning the laser frequency within a certain range, and observing the Doppler-free absorption spectrum of the two-color circularly polarized light generated by the coherent population capture CPT effect through an oscilloscope.

Images