A method for measuring the polarization rate of a relaxation-based atomic magnetometer

Abstract

A method for measuring the polarization rate of a relaxation-based atomic magnetometer, with the atomic magnetometer as the main research object, uses the dispersion curve to obtain the magnetic linewidth of the magnetometer, and then obtains the total relaxation rate of the magnetometer. By varying the pump optical power density of the magnetometer over a large range, the relationship between the total relaxation rate and the optical power density is obtained. At the same time, the saturated part of the relaxation rate is considered, and this relationship is fitted to obtain the pumping rate and other relaxation rates respectively. At this time, the polarization rate of the atomic magnetometer can be obtained. This method greatly improves the accuracy and reliability of polarization rate measurement because it considers the saturation of the relaxation rate, and can be applied to single-axis magnetometers, biaxial magnetometers and triaxial magnetometers simultaneously without any additional auxiliary or calibration equipment. The accurate measurement of the polarization rate will ensure the optimization process of the magnetometer, which is of great significance for improving the performance of the magnetometer, improving its stability and ensuring its practical application in the field of biomagnetic measurement.

Description

Technical Field

[0001] The present invention relates to a method for measuring the polarization rate of an atomic magnetometer based on relaxation, belonging to the field of atomic magnetometers and can also be used in the field of atomic inertial measurement systems. Background Art

[0002] Atomic magnetometers based on Spin-Exchange Relaxation-Free (SERF) technology have received extensive attention at home and abroad in the field of high-precision magnetic field measurement due to their ultra-high theoretical precision beyond existing related measurement means. Among them, integrated atomic magnetometers have been applied to biomagnetic measurement. In addition to the advantage of high sensitivity, SERF atomic magnetometers also have flexible characteristics such as no need for cryogenic cooling, wearable by humans and movable measurement, and are expected to achieve major breakthroughs in the fields of magnetocardiogram measurement and magnetoencephalogram measurement. High-efficiency and high-stability electron polarization determine the performance of atomic magnetometers, and the level of the polarization rate directly affects the output signal intensity of the magnetometer. A high-precision method for measuring the polarization rate ensures the efficient and accurate parameter optimization and performance analysis, and is of great significance for improving the sensitivity and stability of the system.

[0003] Currently, the measurement methods of the polarization rate mainly consider the atomic measurement system with double beams and large gas chambers, and the measurement method for the polarization rate of single-beam and small gas chambers is still blank. At the same time, solving the polarization rate measurement of single-beam atomic magnetometers can be easily extended to biaxial or even triaxial atomic measurement systems, with high application prospects. In summary, with the development and popularization of atomic spin magnetic field / inertial measurement technology, it is necessary to accurately measure the polarization rate, but the practical research in this area is relatively lacking. The present invention mainly studies the relaxation-based method for measuring the polarization rate of atomic magnetometers, which can be carried out simultaneously during the daily optimization of atomic magnetometers without any additional equipment. At the same time, due to considering the part of relaxation rate saturation, the measurement accuracy of the polarization rate is very high. A high-precision method for measuring the polarization rate ensures the efficient and accurate parameter optimization and performance analysis, and is of great significance for improving the sensitivity and stability of the magnetic field measurement system. Starting from the overall situation, the present invention studies the measurement method of atomic magnetometers, which will provide guidance and reference for the polarization rate measurement of similar atomic measurement devices. Summary of the Invention

[0004] The problem solved by the present invention is to provide a method for measuring the polarization rate of an atomic magnetometer based on relaxation, which belongs to a high-precision and high-accuracy method for measuring the polarization rate, can be carried out simultaneously during the daily optimization of atomic magnetometers without any additional equipment. A high-precision method for measuring the polarization rate ensures the efficient and accurate parameter optimization and performance analysis, and is of great significance for improving the sensitivity and stability of the magnetic field measurement system.

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

[0006] A method for measuring the polarization rate of an atomic magnetometer based on relaxation, characterized by comprising the following steps:

[0007] Step 1: Start the experimental system for measuring the polarization rate of the atomic magnetometer, heat the alkali metal gas cell to 150 °C using a non-magnetic electric heating system, and make the atomic magnetometer work in a "near-zero magnetic state" using multi-layer magnetic shielding and magnetic field cross-modulation compensation technology;

[0008] Step 2: Apply a sinusoidal modulation magnetic field of 1 kHz on the x-axis, detect the information of the light passing through the alkali metal gas cell using a photodetector to obtain an output signal, and demodulate the first harmonic of the output signal using a lock-in amplifier;

[0009] Step 3: Apply a scanning magnetic field from -60 nT to +60 nT on the basis of the 1 kHz sinusoidal modulation magnetic field on the x-axis, obtain the dispersion curve of the magnetometer, and obtain the total relaxation rate of the magnetometer in the current state using the relationship between the magnetic linewidth of the dispersion curve and the relaxation of the magnetometer;

[0010] Step 4: Change the incident light power density multiple times, fit the relationship between the total relaxation rate and the incident light power density, obtain the relationship between the optical pumping rate and other relaxation rates, where the other relaxation rate is equal to the total relaxation rate minus the optical pumping rate, thereby obtaining the variation relationship of the polarization rate with the incident light power density, and repeat multiple times to take the average value and error bars;

[0011] Step 5: The selected incident light power density includes the saturation region of the relaxation rate, and obtain the variation relationship of the polarization rate with temperature by changing the temperature.

[0012] In step 1, the outer diameter of the alkali metal gas cell is 4 mm, the inner diameter is 3 mm, the alkali metal gas cell contains rubidium and nitrogen, and circularly polarized laser with a 2.7 mm light spot of rubidium atom D1 line is used to pump and polarize the atoms in the gas cell. A three-axis magnetic field coil with a known coil constant is used for magnetic field cross-modulation compensation, and the multi-layer magnetic shielding shields the geomagnetic field to the nT level.

[0013] In step 2, it includes converting the optical signal into an electrical signal, amplifying it 100,000 times using a transimpedance amplifier, and then demodulating the first harmonic of the output signal using a lock-in amplifier.

[0014] In step 4, it includes changing the incident light power density ≥ 10 times and without repetition. The more the light power density points, the higher the accuracy.

[0015] It includes the following relational expressions:

[0016]

[0017] where P0 is the polarizability, Rop is the optical pumping rate, and Rrel is other relaxation rates;

[0018]

[0019]

[0020] where R tot is the total relaxation rate, is the spin-exchange collision relaxation rate, which is proportional to its spin-exchange rate, R SD is the spin-destruction collision relaxation rate, R wall is the wall collision relaxation rate, R trap is the spin capture relaxation rate.

[0021]

[0022]

[0023] where ρ(-1 / 2) is the atomic number density of the bright state energy level in the saturation region of the relaxation rate, ρ(+1 / 2) is the atomic number density of the dark state energy level in the saturation region of the relaxation rate, a is the optical pumping efficiency, and the optical pumping efficiency refers to the probability of being excited from the m J =-1 / 2 sublevel and decaying to the m J =+1 / 2 sublevel, or is expressed as the average angular momentum increase per atom per absorbed photon. m J =-1 / 2 and m J =+1 / 2 are the two Zeeman sublevels of the ground state, representing the bright state and the dark state respectively, and t is time.

[0024] It includes that the pumping light is emitted by a distributed feedback laser with a blue detuning of 20 GHz, and the pumping light is coupled to the prototype through a polarization-maintaining fiber. The output end of the fiber is equipped with a collimator, and the diameter of the collimated output spot is 2.7 mm. Then, it passes through an adjusted linear polarizer and a λ / 4 wave plate in sequence. After converting the linearly polarized light into circularly polarized light, it is input into the gas chamber to polarize the atoms. The three-dimensional magnetic field coil is composed of an X-direction magnetic field coil, a Y-direction magnetic field coil, and a Z-direction magnetic field coil. The driving voltage in the coil is controlled by a signal generator. One set of three-dimensional magnetic field coils is used for magnetic field cross-modulation compensation, and another set of magnetic field coils is used to apply a calibration magnetic field when measuring the sensitivity. The magnetic field cross-modulation compensation is achieved by driving the three-dimensional magnetic field coil with a signal generator. First, the X-direction coil is used to apply a sinusoidal magnetic field modulation with a fundamental frequency in the X direction, and the driving voltage of the X-direction magnetic field coil is changed. When the output signal of the magnetometer becomes the second harmonic frequency, the X-direction magnetic field compensation point is found. The same principle applies to the other two axes.

[0025] In the atomic magnetometer polarizability measurement experimental system in Step 1, a distributed feedback laser is included. The distributed feedback laser is sequentially connected to a lock-in amplifier through a polarization-maintaining fiber, an optical fiber collimator, a linear polarizer, a λ / 4 wave plate, an alkali metal gas cell, a photodetector, and a transimpedance amplifier. The lock-in amplifier is respectively connected to a waveform generator and a data processing system. The waveform generator is connected to a magnetic field coil. The alkali metal gas cell is located inside an oven, the oven is located inside the magnetic field coil, and the magnetic field coil is located inside a multi-layer magnetic shielding barrel.

[0026] The technical effects of the present invention are as follows: A method for measuring the polarizability of an atomic magnetometer based on relaxation in the present invention takes the atomic magnetometer as the main research object, obtains the magnetic linewidth of the magnetometer using the dispersion curve, and then obtains the total relaxation rate of the magnetometer. By greatly changing the pump optical power density of the magnetometer, the relationship between the total relaxation rate and the optical power density is obtained. At the same time, the saturated part of the relaxation rate is considered, and this relationship is fitted to respectively obtain the pumping rate and other relaxation rates. At this time, the polarizability of the atomic magnetometer can be obtained. Since this method considers the saturation of the relaxation rate, it greatly improves the accuracy and reliability of polarizability measurement, and can be simultaneously applied to common atomic magnetometers such as single-axis magnetometers, biaxial magnetometers, and triaxial magnetometers without any additional auxiliary or calibration equipment. As an important index of the atomic magnetometer, the accurate measurement of the polarizability will ensure the optimization process of the magnetometer, which is of great significance for improving the performance of the magnetometer, enhancing its stability, and ensuring its practical application in the field of biomagnetic measurement. Description of the Drawings

[0027] Figure 1 is a schematic flow chart of implementing a method for measuring the polarizability of an atomic magnetometer based on relaxation in the present invention. Figure 1 It includes Step 1: Start the atomic magnetometer, heat the gas cell to 150 °C using a non-magnetic electric heating system, and make it work in a "near-zero magnetic state" using a multi-layer magnetic shielding and magnetic field cross-modulation compensation technique; Step 2: Apply a 1 kHz sinusoidal modulation magnetic field on the x-axis, detect the information of the light passing through the gas cell using a photodetector, and demodulate the first harmonic of the output signal using a lock-in amplifier; Step 3: Apply a scanning magnetic field from -60 nT to +60 nT on the x-axis, obtain the dispersion curve of the magnetometer, and obtain the total relaxation rate of the magnetometer in the current state using the relationship between the full width at half maximum (magnetic linewidth) of the dispersion curve and the relaxation of the magnetometer; Step 4: Change the incident optical power density multiple times, fit the relationship between the total relaxation rate and the optical power density, obtain the relationship between the optical pumping rate and other relaxation rates, obtain the change of the polarizability with the optical power density, and repeat multiple times to take the average value and error bars; Step 5: The selected optical power density includes the saturation region of the relaxation rate. Change the temperature and repeat the above process to obtain the relationship between the polarizability and the temperature. At this time, the relationship between the polarizability and the optical power density and temperature is obtained.

[0028] Figure 2 It is a schematic diagram of the optical pumping principle of alkali metal atoms involved in the present invention. Figure 2 It is used to illustrate the optical pumping principle and the bright and dark states of the ground state sub-levels, facilitating the understanding of the concept of polarization. Figure 2 In 2 S 1 / 2 represents the atomic ground state (such as the ground state of rubidium atoms), 2 P 1 / 2 represents the atomic excited state (such as the excited state of rubidium atoms), m J = +1 / 2 and m J = -1 / 2 respectively represent the two Zeeman sub-levels of the ground state. The circularly polarized laser pumping action pumps the atoms from the bright state m J = -1 / 2 to the excited state 2 P 1 / 2 . Collision mixing causes the atoms in the excited state to mix in its two Zeeman sub-levels and be equally probabilistically distributed. The quenching effect causes the atoms in the excited state to finally return to the two sub-levels of the ground state equally probabilistically. In this process, the number of atoms in the dark state will gradually increase. Due to the relaxation effect, finally, there will be a certain number of atoms in the bright state and they will not be completely emptied. From Figure 2 it can be seen that the action of optical pumping ultimately changes the atomic population between the two sub-levels of the ground state, macroscopically showing a certain directivity.

[0029] Figure 3 It is a schematic diagram of the dispersion curve involved in the present invention. Figure 3 It includes the implementation method of the dispersion curve and the position of the magnetic linewidth in the dispersion curve, facilitating the understanding of the theory of the polarization rate measurement method. Figure 3 In it, the abscissa, i.e., the sensitive axis x-axis, is the scanning magnetic field (nT, -60~-40···60), and the ordinate is the response signal (V, -0.15~-0.1···0.15). Figure 3 In it, 15.66 nT and -15.66 nT are the magnetic linewidth values of the magnetometer, and 0.075 V and -0.074 V are the magnitudes of the output response signals of the magnetometer. The dispersion curve is obtained by applying a scanning magnetic field from -60 nT to +60 nT on the sensitive axis x-axis and recording the output response signals of the magnetometer. The magnetic linewidth of the magnetometer is the full width at half maximum of the magnetometer, that is, the magnetic field value at the peak of the output response signal.

[0030] Figure 4 It is a schematic diagram of the experimental system for measuring the polarization rate of an atomic magnetometer adopted in implementing a method for measuring the polarization rate of an atomic magnetometer based on relaxation according to the present invention.

[0031] The descriptions of the reference numerals are as follows: 1 - multi-layer magnetic shielding barrel; 2 - magnetic field coil; 3 - magnetic field coil; 4 - alkali metal gas cell; 5 - photodetector; 6 - oven; 7 - fiber optic collimator; 8 - linear polarizer; 9 - λ / 4 wave plate; 10 - polarization-maintaining fiber; 11 - distributed feedback laser; 12 - waveform generator; 13 - lock-in amplifier; 14 - data processing system; 15 - transimpedance amplifier. Detailed implementation manners

[0032] The present invention will be described below with reference to the accompanying drawings ( Figures 1 - 4 ).) and embodiments.

[0033] Figure 1 is a schematic flow chart of a method for measuring the polarization rate of a relaxation-based atomic magnetometer for implementing the present invention. Figure 2 is a schematic diagram of the optical pumping principle of alkali metal atoms related to the present invention. Figure 3 is a schematic diagram of the dispersion curve related to the present invention. Figure 4 is a schematic diagram of an experimental system for measuring the polarization rate of an atomic magnetometer adopted by a method for measuring the polarization rate of a relaxation-based atomic magnetometer for implementing the present invention. Refer to Figures 1 to 4 As shown, a method for measuring the polarization rate of a relaxation-based atomic magnetometer includes the following steps: Step 1, start the experimental system for measuring the polarization rate of the atomic magnetometer, heat the alkali metal gas cell to 150 °C by using a non-magnetic electric heating system, and make the atomic magnetometer work in the "near-zero magnetic state" by using multi-layer magnetic shielding and magnetic field cross-modulation compensation technology; Step 2, apply a 1 kHz sinusoidal modulation magnetic field on the x-axis, detect the information of the light passing through the alkali metal gas cell by using a photodetector to obtain an output signal, and demodulate the first harmonic of the output signal by using a lock-in amplifier; Step 3, apply a scanning magnetic field from -60 nT to +60 nT on the basis of applying a 1 kHz sinusoidal modulation magnetic field on the x-axis, obtain the dispersion curve of the magnetometer, and obtain the total relaxation rate of the magnetometer in the current state by using the relationship between the magnetic line width of the dispersion curve and the relaxation of the magnetometer; Step 4, change the incident light power density multiple times, fit the relationship between the total relaxation rate and the incident light power density, obtain the relationship between the optical pumping rate and other relaxation rates, where the other relaxation rate is equal to the total relaxation rate minus the optical pumping rate, thereby obtaining the variation relationship of the polarization rate with the incident light power density, and repeat multiple times to take the average value and error bars; Step 5, the selected incident light power density includes the saturation region of the relaxation rate, and the variation relationship of the polarization rate with temperature is obtained by changing the temperature.

[0034] In Step 1, the outer diameter of the alkali metal gas cell is 4 mm, and the inner diameter is 3 mm. The alkali metal gas cell contains rubidium and nitrogen. Circularly polarized laser with a 2.7-mm spot of the rubidium atom D1 line is used to pump and polarize the atoms in the cell. A three-axis magnetic field coil with a known coil constant is used for magnetic field cross modulation compensation. The multi-layer magnetic shielding shields the geomagnetic field to the nT level. In Step 2, it includes converting the optical signal into an electrical signal and then amplifying it by 100,000 times using a transimpedance amplifier, and then demodulating the first harmonic of the output signal using a lock-in amplifier. In Step 4, it includes changing the incident optical power density ≥ 10 times and without repetition. The more optical power density points, the higher the accuracy.

[0035] The following relationships are included:

[0036]

[0037] where P0 is the polarization rate, Rop is the optical pumping rate, and Rrel is other relaxation rates;

[0038]

[0039]

[0040] where R tot is the total relaxation rate, is the spin-exchange collision relaxation rate, proportional to its spin-exchange rate, R SD is the spin-destruction collision relaxation rate, R wall is the wall collision relaxation rate, R trap is the spin capture relaxation rate.

[0041]

[0042]

[0043] where ρ(-1 / 2) is the atomic number density of the bright state energy level in the saturation region of the relaxation rate, ρ(+1 / 2) is the atomic number density of the dark state energy level in the saturation region of the relaxation rate, a is the optical pumping efficiency, and the optical pumping efficiency refers to the probability of being excited from the m J =-1 / 2 sub-level and decaying to the m J =+1 / 2 sub-level or is expressed as the average angular momentum increase per atom per absorbed photon. m J =-1 / 2 and m J =+1 / 2 are the two Zeeman sub-levels of the ground state, referring to the bright state and the dark state respectively, and t is time.

[0044] The pumping light is emitted by a distributed feedback laser with a blue detuning of 20 GHz. The pumping light is coupled to the prototype through a polarization-maintaining fiber. The output end of the fiber is equipped with a collimator, and the diameter of the collimated output spot is 2.7 mm. Then, it passes through an adjusted linear polarizer and a λ / 4 wave plate in sequence. After converting the linearly polarized light into circularly polarized light, it is input into the gas cell to polarize the atoms. The three-dimensional magnetic field coil is composed of an X-direction magnetic field coil, a Y-direction magnetic field coil, and a Z-direction magnetic field coil. The driving voltage in the coil is controlled by a signal generator. One set of three-dimensional magnetic field coils is used for magnetic field cross-modulation compensation, and another set of magnetic field coils is used to apply a calibration magnetic field when measuring the sensitivity. The magnetic field cross-modulation compensation is achieved by driving the three-dimensional magnetic field coil with a signal generator. First, use the X-direction coil to apply a sinusoidal magnetic field modulation with a fundamental frequency in the X direction. By changing the driving voltage of the X-direction magnetic field coil, when the output signal of the magnetometer becomes a second harmonic frequency, the magnetic field compensation point in the X direction is found. The same principle applies to the other two axes.

[0045] In the atomic magnetometer polarizability measurement experimental system in step 1, it includes a distributed feedback laser. The distributed feedback laser is connected to a lock-in amplifier through a polarization-maintaining fiber, a fiber collimator, a linear polarizer, a λ / 4 wave plate, an alkali metal gas cell, a photodetector, and a transimpedance amplifier in sequence. The lock-in amplifier is connected to a waveform generator and a data processing system respectively. The waveform generator is connected to the magnetic field coil. The alkali metal gas cell is located inside an oven, the oven is located inside the magnetic field coil, and the magnetic field coil is located inside a multi-layer magnetic shielding barrel.

[0046] The technical solution of the present invention is: a method for measuring the polarizability of a relaxation-based atomic magnetometer, and its implementation method and steps are as follows:

[0047] (1) Place the SERF (spin-exchange relaxation-free) atomic magnetometer in a magnetic shielding environment (a multi-layer permalloy magnetic shielding barrel shields the geomagnetic field to a few nT). Heat a rubidium nitrogen gas cell with an outer diameter of 4 mm and an inner diameter of 3 mm to 150 °C using a non-magnetic electric heating system. At the same time, use circularly polarized laser light with a 2.7 mm spot of the rubidium atomic D1 line to pump and polarize the atoms in the gas cell. Use a three-axis magnetic field coil with a known coil constant to perform magnetic field cross-modulation compensation to make the atomic magnetometer work in a "near-zero magnetic state". Thus, the high temperature, high alkali metal density, and non-magnetic conditions required for the SERF state are satisfied;

[0048] (2) Apply a sinusoidal modulation magnetic field with a frequency of 1 kHz on the x-axis, and use a photodetector to detect the information of the light passing through the gas cell. After converting the optical signal into an electrical signal, it is amplified 100,000 times using a transimpedance amplifier, and then the first harmonic of the output signal is demodulated using a lock-in amplifier. At this time, additionally apply a scanning magnetic field from -60 nT to +60 nT on the x-axis to obtain the dispersion curve of the magnetometer;

[0049] (3) Obtain the total relaxation rate of the magnetometer in its current state by using the relationship between the full width at half maximum (magnetic line width) of the dispersion curve and the relaxation of the magnetometer. Then change the incident optical power density and obtain the current total relaxation rate again. Since only the optical pumping rate in the relaxation rate is affected by the optical power density, continuously change the incident optical power density (more than 10 times without repetition, and the more optical power density points, the higher the accuracy), and the relationship between the total relaxation rate and the optical power density can be fitted to obtain the relationship between the optical pumping rate and other relaxation rates;

[0050] (4) Using the formula of the polarizability, substitute the optical pumping rate and other relaxation rates to obtain the variation of the polarizability with the optical power density. Repeat multiple times and take the average value and error bars. The selected optical power density covers a wide range. At a relatively large optical power density, the optical absorption of atoms will saturate and its relaxation rate will also saturate. Therefore, the polarizability will first increase and then change little;

[0051] (5) Change the temperature and repeat the above process to obtain the relationship between the polarizability and the temperature. At this time, the relationship between the polarizability and the optical power density and temperature is obtained, which is beneficial to further experimental research.

[0052] (6) The core of the measurement scheme involved is: apply a scanning magnetic field to the magnetometer to obtain the dispersion curve of its output signal, and perform a modeling analysis on the output signal of the magnetometer. Finally, obtain the total relaxation rate of the magnetometer in its current state by using the relationship between the full width at half maximum (magnetic line width) of the dispersion curve and the relaxation of the magnetometer. Then continuously change the incident optical power density to obtain the relationship between the optical pumping rate and other relaxation rates. Using the formula of the polarizability, obtain the variation of the polarizability with the optical power density. Repeat multiple times and take the average value and error bars. At the same time, the application of a wide range of optical power densities covers the saturation region of the relaxation rate, which greatly improves the accuracy of polarizability measurement.

[0053] (7) It can be carried out simultaneously during the daily optimization of the atomic magnetometer and does not require any additional equipment. The high-precision polarizability measurement method ensures the efficient and accurate parameter optimization and performance analysis, which is of great significance for improving the sensitivity and stability of the magnetic field measurement system. The higher the polarizability, the better the system stability, the larger the scale factor and output signal intensity, and the better the signal-to-noise ratio. Ensuring the improvement of the polarizability also guarantees the improvement of the magnetic measurement sensitivity, further promoting the application of the atomic magnetometer in heart and brain magnetic measurement.

[0054] The principle of the present invention lies in:

[0055] The interaction between alkali metal atoms, pumping light and magnetic field is described by wave functions. However, the atomic number density involved when the atomic magnetometer works is between 10 12 per cm 3 and 10 14 per cm 3Between them, the behavior of an ensemble with a high atomic number density can be accurately described using the density matrix. When the magnetometer operates in the SERF state, the precession frequency of the atomic spins in the magnetic field is very slow, and the behavior of the alkali metal atomic ensemble can be described using the Bloch equation. If the pumping rate and polarization rate are considered as spatial functions in the gas cell, the spin evolution process of the alkali metal atoms can be described by combining the Bloch equation with the standard diffusion function:

[0056]

[0057] where P is the electron spin, t is time, q is the electron slowing factor, γ e is the gyromagnetic ratio of the electron, B is the external magnetic field, R op is the pumping rate of the pumping light, s is the polarization degree vector of the pumping light, indicating that the pumping light is along the z-axis direction, R tot is the total relaxation rate of the electrons, D is the diffusion coefficient, is the vector differential operator, which represents the gradient operator in higher mathematics.

[0058] The SERF atomic magnetometer operates in a near-zero magnetic environment. Therefore, first, the magnetic field compensation for the three-axis residual magnetism needs to be carried out to reduce the DC residual magnetism to less than 1 nT. When a modulation magnetic field is applied and the magnetic field of the non-sensitive axis completely returns to zero, since the modulation frequency is usually on the order of kHz, at this time, the high-order resonance terms tend to zero, and only the zero-order resonance term needs to be considered, which is also called the zero-field (Zero Field, ZF) resonance. The zero-field resonance output signal of the SERF atomic magnetometer is

[0059]

[0060] J n (u) is the Bessel function of the first kind of order n, n is an integer greater than or equal to 0, B x is the magnetic field of the x-axis, and w is the angular frequency. After the output current of the magnetometer is converted into a voltage signal by a transimpedance amplifier, the output signal is input to a lock-in amplifier, and the first harmonic of the signal is demodulated to obtain the output signal equation V of the magnetometer

[0061]

[0062] where K PDA is the amplification factor of the transimpedance amplifier, K PD is the optoelectronic conversion coefficient of the photodetector, I in is the optical power of the pumping light, η is the transmittance of the gas cell, e is the natural constant, and OD(v) is the optical depth of the gas cell. This is a function of B xis the dispersion curve of the variable. The full width at half maximum of the dispersion curve is called the magnetic linewidth ΔB of the magnetometer, and can be obtained by the formula ΔB = R tot / γ e to establish the relationship with the total relaxation rate. By applying a scanning signal, the current dispersion curve of the magnetometer can be obtained, and then the total relaxation rate can be obtained. The total relaxation rate of the magnetometer can be written as

[0063]

[0064] where is the spin-exchange collision relaxation rate, which is proportional to its spin-exchange rate. It basically disappears under the conditions of high atomic number density and weak magnetic field. R SD is the spin-destruction collision relaxation rate, R wall is the bubble-wall collision relaxation rate, R trap is the spin-trapping relaxation rate. The pumping rate R op (0) when the pumping light is incident on the gas cell can be expressed as

[0065]

[0066] where K is the proportionality coefficient, Φ is the optical power density of the pumping light, c is the speed of light, r e is the classical electron radius, f is the oscillation coefficient of the D1 line, h is Planck's constant, v is the frequency of the pumping light, Γ L is the pressure broadening related to the gas pressure, and v0 is the resonance frequency of the atom. Considering the attenuation of the pumping light intensity along the z direction caused by the absorption of the pumping light by the atoms, using the Lambert W function and the mean polarizability model, the optical pumping rate R op can be written as

[0067]

[0068] where L is the inner diameter of the gas cell, R rel is other relaxation rates, defined as the part obtained by subtracting the optical pumping rate from the total relaxation rate, n Rb is the number density of rubidium atoms, σ s is the collision cross-sectional area, and z is the distance that the pumping light advances along the z-axis. The spin-destruction collision relaxation rate R SD of the atomic magnetometer can be written as

[0069]

[0070] where is the spin-destruction collision cross-sectional area of rubidium atoms themselves, v Rb is the relative motion speed of rubidium atoms, is the number density of nitrogen molecules, is the spin-destruction collision cross-sectional area between rubidium atoms and the buffer gas nitrogen, is the relative motion speed between rubidium atoms and nitrogen molecules. The relaxation rate R of the cell wall of the atomic magnetometer wall can be written as

[0071]

[0072] where T is the temperature of the gas chamber, T0 is the temperature when calculating the standard atmospheric pressure, p stp is the standard atmospheric pressure, is the pressure of nitrogen, and π is the pi. The relaxation rate R of radiation trapping trap can be written in a form related only to the number density of nitrogen As described above, it can be seen that the relaxation rate related to the optical power density in the relaxation rate is only the optical pumping rate. Therefore, when keeping other conditions as consistent as possible and only changing the optical power density, the change in the total relaxation rate will only be related to the pumping rate. By fitting the relationship between the total relaxation rate and the optical power density, the relationship between the optical pumping rate and other relaxation rates can be obtained.

[0073] Next, the saturation region of the relaxation rate is described. This saturation region is caused by optical absorption saturation in a small gas chamber. Atoms can be excited from the ground state sublevel (bright state) and gradually fall into the dark state. Without an external mechanism, atoms will eventually all fall into the dark state. Assuming that the atomic number densities of the bright state and the dark state energy levels are ρ(-1 / 2) and ρ(+1 / 2) respectively, their change rules are

[0074]

[0075] where the optical pumping efficiency a refers to the probability of being excited from the m J =-1 / 2 sublevel and decaying to the m J =+1 / 2 sublevel, and can also be expressed as the average angular momentum increase of an atom per absorbed photon. m J =-1 / 2 and m J =+1 / 2 are the two Zeeman sublevels of the ground state, representing the bright state and the dark state respectively. Considering that the total atomic number density is constant, the polarization <P z > of the atoms and its change rate are

[0076]

[0077] Due to the existence of mechanisms such as collision relaxation and cell wall relaxation, the ground state energy level rearranges the atoms, and the atoms in the dark state will be rearranged at other relaxation rates R rel The minimum value of R rel is the limit lowest relaxation rate of the magnetometer. At this time, we can write the saturation parameter as where Ω R is the Rabi frequency, Γ is the relaxation rate; at the same time, we introduce Rrel Correct the polarization change rate as follows:

[0078]

[0079] As the saturation parameter continually increases, the population of the dark state continuously rises, and 〈P z 〉 will gradually increase. At this time, its change rate will also correspondingly decrease. As the dark state reaches saturation, the change rate of polarization approaches zero, and the magnetometer also enters the saturation region. When there is sufficient buffer gas and quenching gas to achieve sufficient collision mixing, a = 1 / 2. At this time, the equilibrium electron polarization rate P0 is

[0080]

[0081] Under the combined action of the relaxation mechanism and the saturation of the dark state population, the relaxation of the magnetometer will have a saturation region, which is determined by the upper limit of the polarization rate.

[0082] Figure 2 This mainly introduces the principle of optical pumping and the bright and dark states of the ground state sublevels to facilitate the understanding of the concept of polarization. The optical pumping method of the atomic magnetometer uses a circularly polarized laser beam to pump disordered atoms to a specific Zeeman sublevel, so that the atoms have a macroscopic orientation. The ground state of rubidium atoms is denoted as 2 S 1 / 2 , and the excited state is denoted as 2 P 1 / 2 . The two Zeeman sublevels of the ground state are denoted as m J = +1 / 2 and m J = -1 / 2. A specific circularly polarized laser pumps the atoms from the bright state m J = -1 / 2 to the excited state. Due to the collision of the buffer gas with the excited state alkali metal atoms, the atoms in the excited state will mix and be equally distributed among its two Zeeman sublevels. And through the quenching effect, they will finally return to the two sublevels of the ground state with equal probability. In this process, the number of atoms in the dark state will gradually increase. Due to the relaxation effect, finally, there will be a certain number of atoms in the bright state and they will not be completely emptied. It can be seen that the role of optical pumping ultimately changes the atomic population between the two sublevels of the ground state, and macroscopically shows a certain orientation.

[0083] Figure 3This mainly introduces the implementation method of the dispersion curve and the position of the magnetic linewidth in the dispersion curve, which is convenient for understanding the theory of the polarizability measurement method. The dispersion curve is obtained by applying a scanning magnetic field from -60 nT to +60 nT on the sensitive axis x-axis and recording the output response signal of the magnetometer. The full width at half maximum of the magnetometer, that is, the magnetic field value at the peak of the output response signal, is the magnetic linewidth of the magnetometer, as shown in the figure. In the figure, 15.66 nT and -15.66 nT are the magnetic linewidth values of the magnetometer, and 0.075 V and -0.074 V are the magnitudes of the output response signals of the magnetometer.

[0084] As Figure 1 shown, the specific implementation steps of the present invention are as follows:

[0085] (1) Place the SERF (Spin-Exchange Relaxation-Free) atomic magnetometer in a magnetic shielding environment (a multi-layer μ-metal magnetic shielding barrel shields the geomagnetic field to a few nT). Heat a rubidium-nitrogen gas cell with an outer diameter of 4 mm and an inner diameter of 3 mm to 150 °C using a non-magnetic electric heating system controlled by PID. At the same time, use circularly polarized laser with a 2.7 mm spot of the rubidium atom D1 line to pump and polarize the atoms in the gas cell. Use a three-axis magnetic field coil with a known coil constant to perform magnetic field cross-modulation compensation to make the atomic magnetometer work in the "near-zero magnetic state". Thus, the high temperature, high alkali metal density, and non-magnetic conditions required for the SERF state are satisfied;

[0086] Among them, the pumping laser is emitted by a distributed feedback laser (DFB) with a blue detuning of 20 GHz. The pumping light is coupled to the prototype through a polarization-maintaining fiber. The output end of the fiber is equipped with a collimator, and the diameter of the collimated output spot is 2.7 mm. Then, it passes through an adjusted linear polarizer and a λ / 4 wave plate in sequence to convert the linearly polarized light into circularly polarized light and then input it into the gas cell to polarize the atoms. The three-dimensional magnetic field coil is composed of an X-direction magnetic field coil, a Y-direction magnetic field coil, and a Z-direction magnetic field coil. The driving voltage in the coil is controlled by a signal generator. One set of three-dimensional magnetic field coils is used for magnetic field cross-modulation compensation, and another set of magnetic field coils is used to apply a calibration magnetic field when measuring the sensitivity. The magnetic field cross-modulation compensation is achieved by driving the three-dimensional magnetic field coil with a signal generator. First, use the X-direction coil to apply a sinusoidal magnetic field modulation with a fundamental frequency in the X direction. Change the driving voltage of the X-direction magnetic field coil until the output signal of the magnetometer becomes a second harmonic frequency, that is, find the X-direction magnetic field compensation point. The same method applies to the other two axes;

[0087] (2) Apply a sinusoidal modulation magnetic field of 1 kHz on the x-axis, and use a photodetector to detect the information of the light passing through the gas cell. After converting the optical signal into an electrical signal, it is amplified 100,000 times by a transimpedance amplifier. Then, the first harmonic of the output signal is demodulated by a lock-in amplifier, and the demodulated signal is input into the signal processing system to obtain the relevant information of the atomic magnetometer. At this time, an additional scanning magnetic field of -60 nT to +60 nT is applied on the x-axis to obtain the dispersion curve of the magnetometer;

[0088] (3) Use the relationship between the full width at half maximum (magnetic linewidth) of the dispersion curve and the relaxation of the magnetometer to obtain the total relaxation rate of the magnetometer in the current state. Then change the incident optical power density and obtain the current total relaxation rate again. Since only the optical pumping rate in the relaxation rate is affected by the optical power density, continuously change the incident optical power density (more than 10 times and without repetition, the more optical power density points, the higher the accuracy) to fit the relationship between the total relaxation rate and the optical power density, and obtain the relationship between the optical pumping rate and other relaxation rates;

[0089] (4) Use the formula of the polarizability, substitute the optical pumping rate and other relaxation rates to obtain the change of the polarizability with the optical power density, and repeat multiple times to take the average value and error bars. The selected optical power densities cover a very wide range. At a relatively large optical power density, the optical absorption of atoms will saturate, and its relaxation rate will also saturate. Therefore, the polarizability will first increase and then change little;

[0090] (5) Change the temperature and repeat the above process to obtain the relationship between the polarizability and the temperature. At this time, the relationship between the polarizability and the optical power density and temperature is obtained, which is beneficial to further experimental research.

[0091] (6) The core of the measurement scheme involved is: apply a scanning magnetic field to the magnetometer to obtain the dispersion curve of its output signal, and perform modeling analysis on the output signal of the magnetometer. Finally, use the relationship between the full width at half maximum (magnetic linewidth) of the dispersion curve and the relaxation of the magnetometer to obtain the total relaxation rate of the magnetometer in the current state. Then continuously change the incident optical power density to obtain the relationship between the optical pumping rate and other relaxation rates. Use the formula of the polarizability to obtain the change of the polarizability with the optical power density, and repeat multiple times to take the average value and error bars. At the same time, the application of a wide range of optical power densities covers the saturation region of the relaxation rate, which greatly improves the accuracy of polarizability measurement.

[0092] (7) It can be carried out simultaneously during the daily optimization of the atomic magnetometer without the need for any additional equipment. The high-precision polarization rate measurement method ensures the efficient and accurate parameter optimization and performance analysis, which is of great significance for improving the sensitivity and stability of the magnetic field measurement system. The higher the polarization rate, the better the system stability, the larger the scale factor and output signal intensity, and the better the signal-to-noise ratio. Ensuring the increase of the polarization rate also guarantees the improvement of the magnetic measurement sensitivity, further promoting the application of the atomic magnetometer in the measurement of cardiac and brain magnetism.

[0093] The polarization rate is an important parameter of the atomic magnetometer, and the high-efficiency and high-stability electron polarization determine the performance of the atomic magnetometer. To ensure the high-accuracy and high-precision operation of the atomic magnetometer, various optimizations need to be carried out on the magnetometer, and the polarization rate is the most effective index among them. Therefore, the accurate measurement of the polarization rate determines the efficiency of the working parameter optimization of the magnetometer.

[0094] The circularly polarized light polarization technology and the magnetic field cross-modulation compensation technology are adopted. By measuring the total relaxation rate at different light power densities and fitting it, the light pumping rate and the magnitudes of other relaxation rates are obtained respectively, and then the polarization rate is obtained.

[0095] A scanning magnetic field is applied to the magnetometer to obtain the dispersion curve of its output signal, and the output signal of the magnetometer is modeled and analyzed. Finally, the total relaxation rate of the magnetometer in the current state is obtained by using the relationship between the full width at half maximum (magnetic line width) of the dispersion curve and the relaxation of the magnetometer.

[0096] This method can be carried out simultaneously during the daily optimization of the atomic magnetometer without the need for any additional equipment. At the same time, due to the consideration of the saturated part of the relaxation rate, the measurement accuracy of the polarization rate is very high. The high-precision polarization rate measurement method ensures the efficient and accurate parameter optimization and performance analysis, which is of great significance for improving the system sensitivity and stability. And it can be extended to the biaxial or even triaxial atomic measurement system, with strong application prospects.

[0097] The content not described in detail in the specification of the present invention belongs to the prior art well-known to those skilled in the art. It is hereby pointed out that the above description helps those skilled in the art to understand the present invention, but does not limit the protection scope of the present invention. Any implementation that is an equivalent replacement, modification, improvement, and / or simplification of the above description without departing from the essential content of the present invention falls within the protection scope of the present invention.

Claims

1. A method for measuring the polarization rate of a relaxation-based atomic magnetometer, characterized in that, It includes the following steps: Step 1: Start the atomic magnetometer polarizability measurement experimental system. Heat the alkali metal gas cell to 150 °C using a non-magnetic electric heating system, and make the atomic magnetometer work in the "near-zero magnetic state" using multi-layer magnetic shielding and magnetic field cross-modulation compensation technology; Step 2: Apply a 1 kHz sinusoidal modulation magnetic field on the x-axis. Detect the information of the light passing through the alkali metal gas cell using a photodetector to obtain the output signal, and demodulate the first harmonic of the output signal using a lock-in amplifier; Step 3: Based on applying a 1 kHz sinusoidal modulation magnetic field on the x-axis, apply a scanning magnetic field from -60 nT to +60 nT to obtain the dispersion curve of the magnetometer. Use the relationship between the magnetic linewidth of the dispersion curve and the relaxation of the magnetometer to obtain the total relaxation rate of the magnetometer in the current state; Step 4: Change the incident light power density multiple times, fit the relationship between the total relaxation rate and the incident light power density to obtain the relationship between the optical pumping rate and other relaxation rates. The other relaxation rate is equal to the total relaxation rate minus the optical pumping rate. Thus, obtain the variation relationship of the polarizability with the incident light power density, repeat multiple times and take the average value and error bars; Step 5: The selected incident light power density includes the saturation region of the relaxation rate. Obtain the variation relationship of the polarizability with temperature by changing the temperature.

2. The method for measuring the polarization rate of a relaxation-based atomic magnetometer according to claim 1, characterized in that, In step 1, the outer diameter of the alkali metal gas cell is 4 mm, the inner diameter is 3 mm. The alkali metal gas cell contains rubidium and nitrogen. Use circularly polarized laser with a 2.7 mm spot of rubidium atom D1 line to pump and polarize the atoms in the cell. Use a three-axis magnetic field coil with a known coil constant to perform magnetic field cross-modulation compensation. The multi-layer magnetic shielding shields the geomagnetic field to the nT level.

3. The method for measuring the polarization rate of a relaxation-based atomic magnetometer according to claim 1, characterized in that, In step 2, it includes converting the optical signal into an electrical signal and then amplifying it 100,000 times using a transimpedance amplifier, and then demodulating the first harmonic of the output signal using a lock-in amplifier.

4. The method for measuring the polarization rate of a relaxation-based atomic magnetometer according to claim 1, characterized in that, In step 4, it includes changing the incident light power density ≥ 10 times and without repetition. The more light power density points, the higher the accuracy.

5. The method for measuring the polarization rate of a relaxation-based atomic magnetometer according to claim 1, characterized in that, It includes the following relationships: where P0 is the polarizability, Rop is the optical pumping rate, and Rrel is the other relaxation rate; where R tot is the total relaxation rate, is the spin-exchange collision relaxation rate, proportional to its spin-exchange rate, R SD is the spin-destruction collision relaxation rate, R wall is the bubble-wall collision relaxation rate, R trap is the spin-trapping relaxation rate; where ρ(-1 / 2) is the atomic number density of the bright state energy level in the saturation region of the relaxation rate, ρ(+1 / 2) is the atomic number density of the dark state energy level in the saturation region of the relaxation rate, a is the optical pumping efficiency, and the optical pumping efficiency refers to the probability of being excited from the m J =-1 / 2 sublevel and decaying to the m J =+1 / 2 sublevel, or is expressed as the average angular momentum increase per photon absorbed by the atom. m J =-1 / 2 and m J =+1 / 2 are the two Zeeman sublevels of the ground state, representing the bright state and the dark state respectively, and t is the time.

6. The method for measuring the polarization rate of a relaxation-based atomic magnetometer according to claim 1, characterized in that, The pumping light is emitted by a distributed feedback laser with a blue detuning of 20 GHz. Couple the pumping light to the prototype through a polarization-maintaining fiber. The output end of the fiber is equipped with a collimator, and the diameter of the collimated output spot is 2.7 mm. Then, successively pass through an adjusted linear polarizer and a λ / 4 wave plate to convert the linearly polarized light into circularly polarized light and then input it into the gas cell to polarize the atoms. The three-dimensional magnetic field coil is composed of an X-direction magnetic field coil, a Y-direction magnetic field coil, and a Z-direction magnetic field coil. The driving voltage in the coil is controlled by a signal generator. One set of three-dimensional magnetic field coils is used for magnetic field cross-modulation compensation, and another set of magnetic field coils is used to apply a calibration magnetic field when measuring the sensitivity. The magnetic field cross-modulation compensation is achieved by driving the three-dimensional magnetic field coil with a signal generator. First, use the X-direction coil to apply a sinusoidal magnetic field modulation with a fundamental frequency in the X direction. Change the driving voltage of the X-direction magnetic field coil until the output signal of the magnetometer becomes a second harmonic frequency, that is, find the X-direction magnetic field compensation point. The same principle applies to the other two axes.

7. The method for measuring the polarization rate of a relaxation-based atomic magnetometer according to claim 1, characterized in that, In the atomic magnetometer polarizability measurement experimental system in step 1, it includes a distributed feedback laser, and the distributed feedback laser is successively connected to a lock-in amplifier through a polarization-maintaining optical fiber, an optical fiber collimator, a linear polarizer, a λ / 4 wave plate, an alkali metal gas cell, a photodetector and a transimpedance amplifier. The lock-in amplifier is respectively connected to a waveform generator and a data processing system. The waveform generator is connected to a magnetic field coil. The alkali metal gas cell is located in an oven, the oven is located in the magnetic field coil, and the magnetic field coil is located in a multi-layer magnetic shielding barrel.

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