Double-beam SERF atom magnetometer three-axis precision magnetic compensation method based on double observed quantities

Abstract

The invention discloses a double-beam SERF atom magnetometer three-axis precision magnetic compensation method based on double observed quantities, and the method comprises the steps: generating two observed quantities of a DC component and a first-order harmonic wave at the same time under the modulation of a single magnetic field: achieving the quick positioning of an interval in a wide magnetic field range through the single-peak characteristic of the first-order harmonic wave observed quantity, and determining a near zero point and a neighborhood of the near zero point; the effective magnetic field search range of the magnetic compensation point is obviously expanded; a zero point is quickly determined in a compensation interval, and the system complexity and the compensation time are reduced; the zero crossing point of the magnetic field abscissa of the direct-current component observed quantity is used as a residual magnetism point, the residual magnetism point is quickly locked in a fine compensation window positioned by the direct-current component, and pT-magnitude compensation precision is achieved. And three-axis iteration is combined, so that the influence of cross coupling is eliminated, the system compensation error is reduced, and the robustness and the compensation precision are met at the same time in a light-weight magnetic shielding or drifting magnetic environment. Convergence can be realized when iteration turns are equal to 3 times in a typical experiment.

Description

Technical Field

[0001] This invention belongs to the field of quantum precision measurement and magnetic field compensation technology, and relates to triaxial remanent magnetization compensation of atomic magnetometers in weak magnetic environments. In particular, it is a triaxial precision magnetic compensation method for a dual-beam SERF atomic magnetometer based on dual observations. By using a modulation-analytical solution-iteration method and allocating dual observations, it can achieve rapid positioning and zero-point locking of the zero magnetic point, achieving both robustness and accuracy. The dual observations refer to the first-order harmonic observation and the DC component observation. Background Technology

[0002] SERF atomic magnetometers can achieve extremely high sensitivity in very weak magnetic environments (SERF, Spin-Exchange Relaxation-Free), but low-frequency drift and other factors still exist within shielded systems, making their operating point prone to deviating from the linear operating region. Therefore, stable and fast triaxial active compensation is required. Existing technologies include cross-axis modulation schemes, unmodulated zero-field resonance schemes, and high-frequency modulation schemes under coarse compensation, but they generally suffer from difficulties in simultaneously achieving robustness and compensation accuracy, as well as slow convergence.

[0003] A search revealed that existing patent literature related to the technical objectives of this invention employs the following methods: quasi-static coarse compensation is performed first, followed by high-frequency modulation, and triaxial fine compensation is achieved by utilizing the zero-crossing point of the demodulated first-order harmonic dispersion curve. This method is only applicable to single-beam SERF atomic magnetometers, and the observations primarily rely on the first-order harmonic as the criterion; it is not suitable for dual-beam SERF atomic magnetometers. Summary of the Invention

[0004] This invention proposes a triaxial precision magnetic compensation method for a dual-beam SERF atomic magnetometer based on dual observations. This method obtains a complete analytical model of the atomic spin response under high-frequency magnetic field modulation through perturbation iteration. Under a single high-frequency magnetic field modulation, it simultaneously generates two observations: a DC component and a first-order harmonic. The single-peak characteristic of the first-order harmonic observation enables rapid interval localization over a wide magnetic field range, determining the near-zero point and its neighborhood, significantly expanding the effective search range and reducing system complexity and compensation time. The zero-crossing point of the DC component observation is used as the remanent magnetization point, rapidly locking the remanent magnetization point within the fine compensation window located by the DC component, achieving pT-level compensation accuracy. Combined with triaxial iteration, the method eliminates cross-coupling effects, reduces system compensation errors, and thus simultaneously satisfies robustness and compensation accuracy. In typical experiments, convergence is achieved in just three iterations.

[0005] The technical solution of the present invention is as follows:

[0006] A triaxial precision magnetic compensation method based on a dual-beam SERF atomic magnetometer with dual observations is characterized by the following steps: A single modulated magnetic field is applied along the sensitive axis direction of the dual-beam SERF atomic magnetometer system to simultaneously acquire DC component and first-order harmonic observations within the same demodulation framework. The single-peak characteristic of the first-order harmonic is used to rapidly locate each axis within a wide magnetic field range, determining the near-zero point and its neighborhood as a magnetic compensation fine-scan window. The DC component is demodulated, and the zero-crossing point of the first-order harmonic's abscissa within the magnetic compensation fine-scan window is found as the DC component's remanent magnetization point. The three axes sequentially complete the first-order harmonic interval location. After the DC component's remanent magnetization point is determined, triaxial iteration is performed. The first-round triaxial remanent magnetization is used as the initial value, updated, and applied to the triaxial coils. The next iteration is then performed based on the applied results until the iteration convergence condition is met, achieving a compensation accuracy on the order of pT.

[0007] Includes the following steps:

[0008] Step 1: Establish a right-handed coordinate system with the pump light direction as the z-axis, the detection light direction as the x-axis, and the sensing axis as the y-axis. Apply a single modulation magnetic field along the y-axis. B mod ω is the amplitude of the modulated magnetic field, t is the frequency of the modulated magnetic field, and DC component observations and first harmonic observations are established simultaneously under the same demodulation framework.

[0009] Step 2: While maintaining the single modulated magnetic field, demodulate the first harmonic component of the dual-beam SERF magnetometer system response using a lock-in amplifier. In the y-axis absorption curve with the y-axis magnetic field as the abscissa and the response signal amplitude as the ordinate, find the range of the maximum value of the y-axis absorption curve; this range is the y-axis remanent magnetization point. The magnetic field compensation interval is the y-axis interval. , These are the left and right boundary values ​​of the compensation region where the remanent magnetization point is located; similarly, the x-axis interval is obtained by finding the range of the maximum value point of the x-axis absorption curve. , The x-axis is the remanent magnetization point; similarly, the z-axis interval is obtained by finding the range of the minimum points of the z-axis absorption curve. , It is the remanent magnetization point along the z-axis;

[0010] Step 3: Keeping the single modulated magnetic field unchanged, scan the y-axis magnetic field region and demodulate the DC component of the dual-beam SERF magnetometer system response. In the y-axis dispersion curve with the y-axis magnetic field as the abscissa and the response signal amplitude as the ordinate, the y-axis interval is used as a fine compensation window. The zero-crossing point of the y-axis dispersion curve within this compensation window is used to obtain the y-axis remanence value. ;

[0011] Step 4: Keeping the single modulated magnetic field unchanged, apply an additional DC bias magnetic field along the z-axis. Demodulating the DC component of the dual-beam SERF magnetometer system response Scanning the x-axis interval, in the x-axis dispersion curve with the x-axis magnetic field as the abscissa and the response signal amplitude as the ordinate, using the x-axis interval as a fine compensation window, the zero-crossing point of the x-axis dispersion curve within this compensation window is found to obtain the remanence value of the x-axis. Next, the DC bias magnetic field along the z-axis is reduced to zero, and an additional DC bias magnetic field is applied along the x-axis. The remanence value along the z-axis is obtained by using the zero-crossing point of the z-axis dispersion curve. Then, the DC bias magnetic field along the x-axis is reduced to zero;

[0012] Step 5, calculate the triaxial remanence value. As the initial value for the system, it is applied to the triaxial coil. Steps 2 to 4 are repeated to begin triaxial iteration until the triaxial remanent magnetization value of the last round, i.e., the i-th round, is reached. When the system convergence requirements are fully met, take The iteration terminates when the final remanence value is output.

[0013] Step 1 includes the following formula:

[0014]

[0015]

[0016]

[0017] in, It is the electron spin polarization component in the x-axis direction. It is the DC component response value obtained by demodulating the detection signal. Let β be the 0th order Bessel function, β be an intermediate quantity, and p be a preset value. The value of determines the series expansion of the analytical solution, and K1 is the first harmonic response value obtained by demodulating the detection signal. It is the (2p+1)th order Bessel function, and K2 is the harmonic response value corresponding to the even-order harmonics. It is the 2p-th order Bessel function. It is the light pumping rate. It is the relaxation rate. It is the electron gyromagnetic ratio. It is to broaden, It is the residual magnetic field along the x, y, and z axes, and q is the nuclear slowing factor;

[0018] Step 1 includes the following expression:

[0019]

[0020] The above DC component and first harmonic All analytical solutions are correct sensitive.

[0021] Step 2 includes the following formula:

[0022]

[0023]

[0024]

[0025] in, It is the first-order response harmonic value demodulated after y-axis field sweep. It is a y-axis scanning magnetic field. These are the first-order harmonic response values ​​demodulated after the x-axis sweep. It is the x-axis scanning magnetic field. These are the first-order harmonic response values ​​demodulated after z-axis sweep. It is the z-axis scanning magnetic field.

[0026] Step 3 includes the following formula:

[0027]

[0028] in, It is the first-order response harmonic value demodulated after y-axis field sweep. It is the y-axis scanning magnetic field.

[0029] Step 4 includes the following formula:

[0030]

[0031]

[0032] in These are the first-order harmonic response values ​​demodulated after the x-axis sweep. It is the x-axis scanning magnetic field. It involves applying an additional DC bias magnetic field along the z-axis. These are the first-order harmonic response values ​​demodulated after z-axis sweep. It is a z-axis scanning magnetic field. It applies an additional DC bias magnetic field along the x-axis.

[0033] Step 5 includes The following formula, when it has already been applied:

[0034]

[0035] Repeat steps 2-4, that is, calculate the remanence value of each axis in the fine compensation window in the order of y, x, and z, to obtain the three-axis remanence values ​​for the second round. The system is iterated using the method described above. When the difference between the triaxial remanence values ​​of two iterations... Less than or equal to the threshold ,Right now:

[0036]

[0037] in Let be the number of iterations, where B is determined based on the magnetic shielding environment of the system and the resolution of the coil current source. th = 0.5~5pT, if the triaxial remanence values ​​all meet the system convergence requirements, take The iteration terminates when the final remanence value is output.

[0038] The dual-beam SERF atomic magnetometer system includes a dual-beam SERF atomic magnetometer housing located within a magnetically shielded container. The housing contains, in sequence, a pump laser collimator, a pump light polarizer, a mirror, a quarter-wave plate, and an alkali metal gas chamber within a gas chamber heating oven. The input end of the pump laser collimator is connected to the first channel of the dual-beam SERF atomic magnetometer's two-channel laser. The second channel of the dual-beam SERF atomic magnetometer's two-channel laser is connected to an output acquisition and display system via a detection laser collimator, a detection light polarizer, an alkali metal gas chamber, a lateral displacement beam splitter, and a photodetector.

[0039] The technical effects of this invention are as follows: This invention is based on a triaxial precision magnetic compensation method using a dual-beam SERF atomic magnetometer with dual observations. Under single modulation, it simultaneously generates two observations: a DC component and a first-order harmonic. The first-order harmonic observation, with its single-peak characteristics, achieves rapid interval localization within a wide magnetic field range, determining the near-zero point and its neighborhood, significantly expanding the effective magnetic field search range of the magnetic compensation point. It also rapidly determines the zero point within the compensation interval, reducing system complexity and compensation time. Using the zero-crossing point of the magnetic field abscissa of the DC component observation as the remanent magnetization point, it quickly locks the remanent magnetization point within the fine compensation window located by the DC component, achieving pT-level compensation accuracy. Combined with triaxial iteration, it eliminates the influence of cross-coupling, reducing system compensation errors, thus simultaneously satisfying robustness and compensation accuracy in lightweight magnetic shielding or drift magnetic environments. In typical experiments, convergence is achieved with only 3 iterations.

[0040] The advantages of this invention compared to the prior art are:

[0041] (1) Two observations, DC component and first harmonic, are used for compensation. The first harmonic is used as the observation to achieve global interval positioning, and the DC component is used as the observation to achieve accurate compensation. Compared with the compensation scheme that only uses a single observation, this expands the effective magnetic field search range of the magnetic compensation point, ensures that the compensation zero point is found quickly within the search range, and can also achieve the compensation accuracy of a single observation.

[0042] (2) Since the first harmonic component has a global extremum and is a single-peak function, it can quickly converge to the near-zero interval within a wide magnetic field range; because of its single-peak characteristic, it can avoid getting trapped in local optimal solutions and improve robustness.

[0043] (3) The compensation structure of first-order harmonic observation positioning-DC component observation measurement iteration is adopted. Under typical experimental conditions, convergence can be achieved in 3 iterations. Compared with the traditional axis-by-axis repeated field scanning, the number of scanning points and waiting time are significantly reduced, and the complexity of the compensation process is reduced. Attached Figure Description

[0044] Figure 1 This is a schematic diagram of the dual-beam SERF atomic magnetometer system structure involved in the present invention's triaxial precision magnetic compensation method based on dual observations of a dual-beam SERF atomic magnetometer.

[0045] Figure 2 This is a schematic diagram of the process of the triaxial precision magnetic compensation method based on a dual-beam SERF atomic magnetometer with dual observations, according to the present invention. Figure 2 The process includes step 1, applying a modulated magnetic field in the y-axis direction. B mod ω is the amplitude of the modulated magnetic field, t is the frequency of the modulated magnetic field, and t is time. The demodulated signal is obtained from the modulation of the magnetic field amplitude. Sensitive DC component and first harmonic analytical solution, B x It is the x-axis magnetic field, B y It is the y-axis magnetic field, B z The z-axis magnetic field; Step 2, keeping the modulated magnetic field unchanged, use the first harmonic component of the dual-beam SERF magnetometer system response demodulated by the lock-in amplifier to find the remanent magnetization point on the y-axis. The magnetic field compensation region, y-axis interval , These are the left and right boundary values ​​of the compensation region where the remanent magnetization point is located. Keeping the modulation magnetic field constant, repeat the above process on the other two axes to find the remanent magnetization point on the x-axis. and z-axis remanent magnetization point The magnetic field compensation region, x-axis interval z-axis interval Step 3: Keeping the modulated magnetic field constant, use the DC component of the dual-beam SERF magnetometer system response demodulated by the lock-in amplifier to find the remanent magnetization point on the y-axis; Step 4: Keeping the high-frequency modulated magnetic field constant, use the DC component of the dual-beam SERF magnetometer system response demodulated by the lock-in amplifier to apply a DC magnetic field in the z-axis direction to find the remanent magnetization point on the x-axis. Then, repeat the above process in the z-axis direction, apply a DC magnetic field in the x-axis direction to find the remanent magnetization point on the z-axis; Step 5: Repeat steps 2 to 4 iteratively until the convergence condition is met.

[0046] The following are the annotations in the attached diagram: 1-Magnetic shielding barrel; 2-Dual-beam SERF atomic magnetometer housing; 3-Dual-beam SERF atomic magnetometer two-channel laser; 4-Pump polarizer; 5-1 / 4 wave plate; 6-Reflector; 7-Detection polarizer; 8-Lateral displacement beam splitter; 9-Gas chamber heating oven; 10-Alkali metal gas chamber; 11-Photodetector; 12-Output acquisition and display system; 13-Pump laser collimator; 14-Detection laser collimator; 15-Polarization-maintaining fiber; 16-Cable. Detailed Implementation

[0047] The following is in conjunction with the attached diagram ( Figures 1-2 The present invention will be described in conjunction with the examples.

[0048] Figure 1 This is a schematic diagram of the dual-beam SERF atomic magnetometer system structure involved in the present invention's triaxial precision magnetic compensation method based on dual observations of a dual-beam SERF atomic magnetometer. Figure 2 This is a schematic diagram of the triaxial precision magnetic compensation method based on a dual-beam SERF atomic magnetometer with dual observations, as per the present invention. (Reference) Figures 1 to 2 As shown, a triaxial precision magnetic compensation method based on a dual-beam SERF atomic magnetometer with dual observations includes applying a single modulated magnetic field along the sensitive axis direction of the dual-beam SERF atomic magnetometer system to simultaneously acquire DC component observations and first-order harmonic observations within the same demodulation framework. Utilizing the single-peak characteristic of the first-order harmonic, the method performs rapid interval positioning of each axis within a wide magnetic field range, determining the near-zero point and its neighborhood as a magnetic compensation fine-scan window. The DC component is demodulated, and within the magnetic compensation fine-scan window, the zero-crossing point of the first-order harmonic's abscissa is found as the remanent magnetization point of the DC component. The three axes sequentially complete the first-order harmonic interval positioning. After the remanent magnetization point of the DC component is determined, triaxial iteration is performed. The remanent magnetization of the first round is used as the initial value, updated, and applied to the triaxial coils. Based on the applied results, the next iteration begins until the iteration convergence condition is met, achieving a compensation accuracy on the order of pT.

[0049] The steps include: Step 1, establishing a right-handed coordinate system with the pump light direction as the z-axis, the detection light direction as the x-axis, and the sensing axis as the y-axis, and applying a single modulation magnetic field along the y-axis. B mod ω is the amplitude of the modulated magnetic field, t is the frequency of the modulated magnetic field, and t is time. Under the same demodulation framework, DC component observations and first-order harmonic observations are established simultaneously. Step 2: While maintaining the single modulated magnetic field, a lock-in amplifier is used to demodulate the first-order harmonic component of the dual-beam SERF magnetometer system response. In the y-axis absorption curve with the y-axis magnetic field as the abscissa and the response signal amplitude as the ordinate, find the range of the maximum value of the y-axis absorption curve; this range is the y-axis remanent magnetization point. The magnetic field compensation interval is the y-axis interval. , These are the left and right boundary values ​​of the compensation region where the remanent magnetization point is located; similarly, the x-axis interval is obtained by finding the range of the maximum value point of the x-axis absorption curve. , The x-axis is the remanent magnetization point; similarly, the z-axis interval is obtained by finding the range of the minimum points of the z-axis absorption curve. , It is the remanent magnetization point along the z-axis;

[0050] Step 3: Keeping the single modulated magnetic field unchanged, scan the y-axis magnetic field region and demodulate the DC component of the dual-beam SERF magnetometer system response. In the y-axis dispersion curve with the y-axis magnetic field as the abscissa and the response signal amplitude as the ordinate, the y-axis interval is used as a fine compensation window. The zero-crossing point of the y-axis dispersion curve within this compensation window is used to obtain the y-axis remanence value. Step 4: Keeping the single modulated magnetic field unchanged, apply an additional DC bias magnetic field along the z-axis. Demodulating the DC component of the dual-beam SERF magnetometer system response Scanning the x-axis interval, in the x-axis dispersion curve with the x-axis magnetic field as the abscissa and the response signal amplitude as the ordinate, using the x-axis interval as a fine compensation window, the zero-crossing point of the x-axis dispersion curve within this compensation window is found to obtain the remanence value of the x-axis. Next, the DC bias magnetic field along the z-axis is reduced to zero, and an additional DC bias magnetic field is applied along the x-axis. The remanence value along the z-axis is obtained by using the zero-crossing point of the z-axis dispersion curve. Then, the DC bias magnetic field along the x-axis is returned to zero; step 5, the remanence values ​​of the three axes are... As the initial value for the system, it is applied to the triaxial coil. Steps 2 to 4 are repeated to begin triaxial iteration until the triaxial remanent magnetization value of the last round, i.e., the i-th round, is reached. When the system convergence requirements are fully met, take The iteration terminates when the final remanence value is output.

[0051] Step 1 includes the following formula:

[0052]

[0053]

[0054]

[0055] in, It is the electron spin polarization component in the x-axis direction. It is the DC component response value obtained by demodulating the detection signal. Let β be the 0th order Bessel function, β be an intermediate quantity, and p be a preset value. The value of determines the series expansion of the analytical solution, and K1 is the first harmonic response value obtained by demodulating the detection signal. It is the (2p+1)th order Bessel function, and K2 is the harmonic response value corresponding to the even-order harmonics. It is the 2p-th order Bessel function. It is the light pumping rate. It is the relaxation rate. It is the electron gyromagnetic ratio. It is to broaden, It is the residual magnetic field along the x, y, and z axes, and q is the nuclear slowing factor;

[0056] Step 1 includes the following expression:

[0057]

[0058] The above DC component and first harmonic All analytical solutions are correct sensitive.

[0059] Step 2 includes the following formula:

[0060]

[0061]

[0062]

[0063] in, It is the first-order response harmonic value demodulated after y-axis field sweep. It is a y-axis scanning magnetic field. These are the first-order harmonic response values ​​demodulated after the x-axis sweep. It is the x-axis scanning magnetic field. These are the first-order harmonic response values ​​demodulated after z-axis sweep. It is the z-axis scanning magnetic field.

[0064] Step 3 includes the following formula:

[0065]

[0066] in, It is the first-order response harmonic value demodulated after y-axis field sweep. It is the y-axis scanning magnetic field.

[0067] Step 4 includes the following formula:

[0068]

[0069]

[0070] in These are the first-order harmonic response values ​​demodulated after the x-axis sweep. It is the x-axis scanning magnetic field. It involves applying an additional DC bias magnetic field along the z-axis. These are the first-order harmonic response values ​​demodulated after z-axis sweep. It is a z-axis scanning magnetic field. It applies an additional DC bias magnetic field along the x-axis.

[0071] Step 5 includes The following formula, when it has already been applied:

[0072]

[0073] Repeat steps 2-4, that is, calculate the remanence value of each axis in the fine compensation window in the order of y, x, and z, to obtain the three-axis remanence values ​​for the second round. The system is iterated using the method described above. When the difference between the triaxial remanence values ​​of two iterations... Less than or equal to the threshold ,Right now:

[0074]

[0075] in Let be the number of iterations, where B is determined based on the magnetic shielding environment of the system and the resolution of the coil current source. th = 0.5~5pT, if the triaxial remanence values ​​all meet the system convergence requirements, take The iteration terminates when the final remanence value is output.

[0076] The dual-beam SERF atomic magnetometer system includes a dual-beam SERF atomic magnetometer housing 2 located inside a magnetically shielded barrel 1. The dual-beam SERF atomic magnetometer housing 2 includes, in sequence, a pump laser collimator 13, a pump light polarizer 4, a reflector 6, a quarter-wave plate 5, and an alkali metal gas chamber 10 inside a gas chamber heating oven 9. The input end of the pump laser collimator 13 is connected to the first channel of the dual-beam SERF atomic magnetometer's two-channel laser 3. The second channel of the dual-beam SERF atomic magnetometer's two-channel laser 3 is connected to the output acquisition and display system 12 via a detection laser collimator 14, a detection light polarizer 7, an alkali metal gas chamber 10, a lateral displacement beam splitter 8, and a photodetector 11.

[0077] Figure 1 The overall system consists of a magnetically shielded barrel, a dual-beam SERF atomic magnetometer system, and an electrical control and acquisition section. The outer layer is the magnetically shielded barrel, and the inner layer is the dual-beam SERF atomic magnetometer system, which includes a three-dimensional magnetic compensation coil with x, y, and z-axis coils capable of superimposing DC and modulated magnetic fields. The gas chamber is located inside a heating oven and positioned at the center of the coils. The pump laser along the z-axis is polarized by a polarizer and a quarter-wave plate to form circularly polarized light, which then passes through the alkali metal gas chamber for pumping. The detection laser emits detection light along the x-axis after collimation, passes through the gas chamber via a polarizer, and is incident on a photodetector via a lateral displacement beam splitter. The light is then converted into first-order and DC component signals by a cross-group amplifier and a lock-in amplifier for readout.

[0078] The dual-beam SERF atomic magnetometer system of this invention includes a pump laser and a detection laser. The pump laser is connected to a laser collimator via a polarization-maintaining fiber. The laser emitted from the collimator passes through a polarizer and a reflector, then through a quarter-wave plate and passes along the z-axis through an alkali metal gas cell to pump alkali metal. The detection laser is connected to the laser collimator via a polarization-maintaining fiber. The laser emitted from the collimator passes through a polarizer, passes along the x-axis through the alkali metal gas cell, and reaches two photodetectors via a lateral displacement beam splitter. The photodetectors are connected differentially and then connected to a transimpedance amplifier via a cable. The transimpedance amplifier is connected to a lock-in amplifier, which is connected to a data acquisition and output display. The alkali metal gas cell is located inside a gas cell heating oven, which is located inside a magnetic compensation coil. The magnetic compensation coil is located inside a magnetic shielding container and is connected to a signal generator via a cable.

[0079] A triaxial precision magnetic compensation method based on a dual-beam SERF atomic magnetometer with dual observations is proposed, and the specific implementation steps are as follows:

[0080] Step 1: Define the pump beam direction of the dual-beam SERF atomic magnetometer as the z-axis, the detection beam direction as the x-axis, and the sensing axis direction as the y-axis. Apply a high-frequency magnetic field modulation along the y-axis. Introducing dual observations of DC component and first harmonic, It modulates the amplitude of the magnetic field. , It modulates the magnetic field frequency. , It's time.

[0081] The three-axis magnetic fields are respectively represented as follows: An analytical model of the dual-beam SERF magnetometer under a high-frequency modulated magnetic field along the y-axis was obtained by solving the Bloch equations using a perturbation iterative method. Synchronization references, phases, and time constants for the DC component and first harmonic channels of the lock-in amplifier were established, and the demodulated response signal was used to extract the corresponding... The analytical solution for the sensitive DC component and first harmonic is shown in the following complete form:

[0082]

[0083]

[0084] in, It is the electron spin polarization component in the x-axis direction. and These are the 0th and 1st order Bessel functions, respectively. It depends on the nuclear slowdown factor and modulation magnetic field amplitude frequency The parameters, and These are the DC component and the first harmonic response value, respectively, obtained by demodulating the detection signal. Light pumping rate, It is the relaxation rate. It is the electron gyromagnetic ratio. It is the residual magnetic field along the x, y, and z axes.

[0085] Furthermore, the dual-beam SERF magnetometer required for this method is obtained under a y-axis modulated magnetic field. The analytical solutions for the sensitive DC component and first harmonic provide the basis for subsequent magnetic compensation methods:

[0086]

[0087] Step 2: In order to quickly obtain the near-zero range of the compensated axis over a wide magnetic field range, the DC component is... Precise locking provides the initial compensation range; this step maintains the high-frequency modulated magnetic field from step 1. Without changing the position, scan the y-axis magnetic field region and use the first harmonic channel of the lock-in amplifier to demodulate the first harmonic component of the dual-beam SERF magnetometer system response. In a two-dimensional curve with the y-axis magnetic field value on the x-axis and the response signal amplitude on the y-axis, the curve shape is an absorption line. The maximum point corresponding to the absorption curve and its neighborhood are searched and identified. This range is used as the magnetic field compensation region for the remanent magnetization point on the y-axis. The y-axis interval is... . It is the left and right neighbor values ​​of the compensation region where the remanent magnetization point is located, which is approximately 100 to 500 pT.

[0088]

[0089] in, It is the first-order response harmonic value demodulated after y-axis field sweep. It is the y-axis scanning magnetic field.

[0090] Keeping the high-frequency magnetic field constant, repeat the above process on the other two axes to find the range of the maximum points of the x-axis absorption curve and the minimum points of the z-axis absorption curve. This determines the magnetic field compensation regions for the x and z axes. The x-axis interval is... The z-axis interval is .

[0091]

[0092]

[0093] in, These are the first-order harmonic response values ​​demodulated after the x-axis sweep. It is the x-axis scanning magnetic field. These are the first-order harmonic response values ​​demodulated after z-axis sweep. It is the z-axis scanning magnetic field.

[0094] Step 3: This step is based on the magnetic field compensation range where the remanent magnetization point is located, which has already been obtained. By utilizing the zero-crossing point of the DC component and combining iterative triaxial magnetic field measurements, high-precision determination of the target axis zero point is achieved. The high-frequency modulated magnetic field from step 1 is maintained. Keeping the y-axis magnetic field region unchanged, the DC component of the dual-beam SERF magnetometer system response is demodulated. In the two-dimensional curve with the y-axis magnetic field value as the abscissa and the response signal amplitude as the ordinate, the curve is a dispersive line. The y-axis magnetic field compensation interval obtained in step 2 is taken as the fine compensation window. Find the zero-crossing point (the intersection of the curve and the horizontal axis) of the dispersion curve corresponding to the DC component within the compensation window. The horizontal axis of this point is the remanence value on the y-axis. .

[0095]

[0096] in, It is the first-order response harmonic value demodulated after y-axis field sweep. It is the y-axis scanning magnetic field.

[0097] Step 4: Maintain the high-frequency modulated magnetic field from Step 1. The operation remains unchanged; in addition, an extra DC bias magnetic field is applied along the z-axis. The DC component of the dual-beam SERF magnetometer system response is demodulated, and the x-axis magnetic field region is scanned. In the two-dimensional curve with the x-axis magnetic field as the abscissa and the response signal amplitude as the ordinate, the curve is a dispersive line. The x-axis magnetic field compensation interval obtained in step 2 is taken as the fine compensation window. Find the zero-crossing point (the intersection of the curve and the horizontal axis) of the dispersion curve corresponding to the DC component within the compensation window; the horizontal axis of this point is the remanence value on the x-axis. Next, the DC bias magnetic field along the z-axis is reduced to zero. Then, an additional DC bias magnetic field is applied along the x-axis, and the above process is repeated along the z-axis to obtain the remanence value along the z-axis. Then, the DC bias magnetic field along the x-axis is reduced to zero.

[0098]

[0099]

[0100] in, These are the first-order harmonic response values ​​demodulated after the x-axis sweep. It is the x-axis scanning magnetic field. These are the first-order harmonic response values ​​demodulated after z-axis sweep. It is the z-axis scanning magnetic field.

[0101] Step 5 is performed after steps 2-4. It retains and applies the triaxial remanent magnetization value obtained in the previous round to the system, and then repeats steps 2-4 again to bring the remanent magnetization value as close as possible to the true zero point. Keeping the high-frequency modulated magnetic field from step 1 unchanged, the triaxial remanent magnetization value obtained in steps 2-4 is applied... As the initial value for the system, it is applied to the triaxial coil, and this iteration is number 1.

[0102]

[0103] middle, It is the initial first-order response harmonic value after applying initial values ​​to the system.

[0104] In triaxial remanence If the application has already been performed, repeat steps 2-4, that is, calculate the remanence value of each axis in the fine compensation window in the order of y, x, and z to obtain a new round of triaxial remanence values. The system is iterated using the method described above. When the difference in the triaxial remanence values ​​between two iterations is sufficiently small, that is... , Let be the number of iterations, where The value is usually determined based on the magnetic shielding environment of the system and the resolution of the coil current source, typically ranging from 0.5 to 5 pT. If the triaxial remanence values ​​all meet the system convergence requirements, then... The iteration terminates when the final remanence value is output.

[0105] The dual-beam SERF atomic magnetometer system, as shown in Figure 1 As shown, the outer side of the system is a magnetically shielded barrel 1; the inner side of the system is a dual-beam SERF atomic magnetometer, including a three-dimensional magnetic compensation coil (containing three sets of coils for x / y / z, supporting DC and modulation superposition) 2; an alkali metal gas chamber 10 is placed in the center, located inside a gas chamber heating oven 9. The oven ensures that the alkali metal atoms reach the temperature required for the SERF state and guarantees temperature and field uniformity. The dual-channel laser 3 of the dual-beam SERF atomic magnetometer emits pump light along the z-axis, which enters the gas chamber after passing through a polarization-maintaining fiber 15, a pump laser collimator 13, a polarizer 4, and a quarter-wave plate 5. The wavelength of the laser beam satisfies the center of the D1 line of the alkali metal atoms, achieving circularly polarized pumping. The dual-channel laser 3 of the dual-beam SERF atomic magnetometer emits detection light along the x-axis, which enters the gas chamber after passing through a detection laser collimator 14 and a polarizer 7. The wavelength of the laser beam satisfies the differential detection detuning frequency. After the beam is split by a lateral displacement beam splitter prism 8, it is differentially read out by two photodetectors 12. The detection signal is input to the output acquisition and display system 12, which simultaneously outputs a DC / modulated hybrid current to the dual-beam SERF atomic magnetometer device; all connections are completed via cable 16. The above components and their connections correspond. Figure 1 The arrows and traces are shown.

[0106] A triaxial precision magnetic compensation method based on a dual-beam SERF atomic magnetometer with dual observations is proposed. This method utilizes perturbation iteration to obtain a complete analytical model of the atomic spin response under high-frequency magnetic field modulation. Under single modulation, it simultaneously generates two observations: a DC component and a first-order harmonic. The first-order harmonic observation, with its single-peak characteristic, enables rapid interval localization over a wide magnetic field range, determining the near-zero point and its neighborhood, significantly expanding the effective magnetic field search range for the magnetic compensation point. Furthermore, it rapidly determines the zero point within the compensation interval, reducing system complexity and compensation time. Using the zero-crossing point of the magnetic field abscissa of the DC component observation as the remanent magnetization point, it quickly locks the remanent magnetization point within the fine compensation window located by the DC component, achieving pT-level compensation accuracy. Combined with triaxial iteration, this eliminates cross-coupling effects, reducing system compensation errors and thus simultaneously satisfying robustness and compensation accuracy under lightweight magnetic shielding or drift magnetic environments. In typical experiments, convergence is achieved with only 3 iterations.

[0107] Contents not described in detail in this specification are prior art known to those skilled in the art. It is hereby indicated that the above description is intended to help those skilled in the art understand this invention, but does not limit the scope of protection of this invention. Any equivalent substitutions, modifications, improvements, and / or simplifications of the above descriptions that do not depart from the essential content of this invention fall within the scope of protection of this invention.

Claims

1. A triaxial precision magnetic compensation method based on a dual-beam SERF atomic magnetometer with dual observations, characterized in that, This method involves applying a single modulated magnetic field along the sensitive axis of a dual-beam SERF atomic magnetometer system to simultaneously acquire DC component and first-order harmonic observations within the same demodulation framework. Utilizing the single-peak characteristic of the first-order harmonic, the system performs rapid interval localization of each axis over a wide magnetic field range, determining the near-zero point and its neighborhood as a magnetic compensation fine-scan window. The DC component is then demodulated, and the zero-crossing point of the first-order harmonic's abscissa within the magnetic compensation fine-scan window is identified as the remanent magnetization point of the DC component. The three axes sequentially complete the first-order harmonic interval localization. After determining the remanent magnetization point of the DC component, a three-axis iteration is performed. The remanent magnetization of the first round is used as the initial value, updated, and applied to the three-axis coils. The next iteration is then initiated based on the applied results until the iteration convergence condition is met, achieving a compensation accuracy on the order of pT.

2. The triaxial precision magnetic compensation method for a dual-beam SERF atomic magnetometer based on dual observations as described in claim 1, characterized in that, Includes the following steps: Step 1: Establish a right-handed coordinate system with the pump light direction as the z-axis, the detection light direction as the x-axis, and the sensing axis as the y-axis. Apply a single modulation magnetic field along the y-axis. B mod ω is the amplitude of the modulated magnetic field, t is the frequency of the modulated magnetic field, and DC component observations and first harmonic observations are established simultaneously under the same demodulation framework. Step 2: While maintaining the single modulated magnetic field, demodulate the first harmonic component of the dual-beam SERF magnetometer system response using a lock-in amplifier. In the y-axis absorption curve with the y-axis magnetic field as the abscissa and the response signal amplitude as the ordinate, find the range of the maximum value of the y-axis absorption curve; this range is the y-axis remanent magnetization point. The magnetic field compensation interval is the y-axis interval. , These are the left and right boundary values ​​of the compensation region where the remanent magnetization point is located; similarly, the x-axis interval is obtained by finding the range of the maximum value point of the x-axis absorption curve. , The x-axis is the remanent magnetization point; similarly, the z-axis interval is obtained by finding the range of the minimum points of the z-axis absorption curve. , It is the remanent magnetization point along the z-axis; Step 3: Keeping the single modulated magnetic field unchanged, scan the y-axis magnetic field region and demodulate the DC component of the dual-beam SERF magnetometer system response. In the y-axis dispersion curve with the y-axis magnetic field as the abscissa and the response signal amplitude as the ordinate, the y-axis interval is used as a fine compensation window. The zero-crossing point of the y-axis dispersion curve within this compensation window is used to obtain the y-axis remanence value. ; Step 4: Keeping the single modulated magnetic field unchanged, apply an additional DC bias magnetic field along the z-axis. Demodulating the DC component of the dual-beam SERF magnetometer system response Scanning the x-axis interval, in the x-axis dispersion curve with the x-axis magnetic field as the abscissa and the response signal amplitude as the ordinate, using the x-axis interval as a fine compensation window, the zero-crossing point of the x-axis dispersion curve within this compensation window is found to obtain the remanence value of the x-axis. Next, the DC bias magnetic field along the z-axis is reduced to zero, and an additional DC bias magnetic field is applied along the x-axis. The remanence value along the z-axis is obtained by using the zero-crossing point of the z-axis dispersion curve. Then, the DC bias magnetic field along the x-axis is reduced to zero; Step 5, calculate the triaxial remanence value. As the initial value for the system, it is applied to the triaxial coil. Steps 2 to 4 are repeated to begin triaxial iteration until the triaxial remanent magnetization value of the last round, i.e., the i-th round, is reached. When the system convergence requirements are fully met, take The iteration terminates when the final remanence value is output.

3. The triaxial precision magnetic compensation method for a dual-beam SERF atomic magnetometer based on dual observations according to claim 2, characterized in that, Step 1 includes the following formula: in, It is the electron spin polarization component in the x-axis direction. It is the DC component response value obtained by demodulating the detection signal. Let β be the 0th order Bessel function, β be an intermediate quantity, and p be a preset value. The value of determines the series expansion of the analytical solution, and K1 is the first harmonic response value obtained by demodulating the detection signal. It is the (2p+1)th order Bessel function, and K2 is the harmonic response value corresponding to the even-order harmonics. It is the 2p-th order Bessel function. It is the light pumping rate. It is the relaxation rate. It is the electron gyromagnetic ratio. It is to broaden, q is the residual magnetic field along the x, y, and z axes, and q is the nuclear slowing factor.

4. The triaxial precision magnetic compensation method for a dual-beam SERF atomic magnetometer based on dual observations according to claim 2, characterized in that, Step 1 includes the following expression: The above DC component and first harmonic All analytical solutions are correct sensitive.

5. The triaxial precision magnetic compensation method for a dual-beam SERF atomic magnetometer based on dual observations according to claim 2, characterized in that, Step 2 includes the following formula: in, It is the first-order response harmonic value demodulated after y-axis field sweep. It is a y-axis scanning magnetic field. These are the first-order harmonic response values ​​demodulated after the x-axis sweep. It is the x-axis scanning magnetic field. These are the first-order harmonic response values ​​demodulated after z-axis sweep. It is the z-axis scanning magnetic field.

6. The triaxial precision magnetic compensation method for a dual-beam SERF atomic magnetometer based on dual observations according to claim 2, characterized in that, Step 3 includes the following formula: in, It is the first-order response harmonic value demodulated after y-axis field sweep. It is the y-axis scanning magnetic field.

7. The triaxial precision magnetic compensation method for a dual-beam SERF atomic magnetometer based on dual observations according to claim 2, characterized in that, Step 4 includes the following formula: in These are the first-order harmonic response values ​​demodulated after the x-axis sweep. It is the x-axis scanning magnetic field. It involves applying an additional DC bias magnetic field along the z-axis. These are the first-order harmonic response values ​​demodulated after z-axis sweep. It is a z-axis scanning magnetic field. It applies an additional DC bias magnetic field along the x-axis.

8. The triaxial precision magnetic compensation method for a dual-beam SERF atomic magnetometer based on dual observations according to claim 2, characterized in that, Step 5 includes The following formula, when it has already been applied: Repeat steps 2-4, that is, calculate the remanence value of each axis in the fine compensation window in the order of y, x, and z, to obtain the three-axis remanence values ​​for the second round. The system is iterated using the method described above. When the difference between the triaxial remanence values ​​of two iterations... Less than or equal to the threshold ,Right now: in Let be the number of iterations, where B is determined based on the magnetic shielding environment of the system and the resolution of the coil current source. th = 0.5~5pT, if the triaxial remanence values ​​all meet the system convergence requirements, take The iteration terminates when the final remanence value is output.

9. The triaxial precision magnetic compensation method for a dual-beam SERF atomic magnetometer based on dual observations according to claim 1, characterized in that, The dual-beam SERF atomic magnetometer system includes a dual-beam SERF atomic magnetometer housing located within a magnetically shielded container. The housing contains, in sequence, a pump laser collimator, a pump light polarizer, a mirror, a quarter-wave plate, and an alkali metal gas chamber within a gas chamber heating oven. The input end of the pump laser collimator is connected to the first channel of the dual-beam SERF atomic magnetometer's two-channel laser. The second channel of the dual-beam SERF atomic magnetometer's two-channel laser is connected to an output acquisition and display system via a detection laser collimator, a detection light polarizer, an alkali metal gas chamber, a lateral displacement beam splitter, and a photodetector.

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