CN103438877B - A kind of inertia based on SERF atomic spin effect and magnetic field integral measurement method - Google Patents

Abstract

Based on inertia and the magnetic field integral measurement method of SERF atomic spin effect, first set up the block mold of inertia/magnetic field integrated measuring; The second, make and measure sensing unit, carry out high-frequency ac and heat without magnetoelectricity; Open driving laser (z-axis) and optical pumping is carried out to sensing unit; Detection laser (x-axis) is injected in its vertical direction; 3rd, carry out active magnetic compensation by Three-Dimensional Magnetic compensating coil, offset external magnetic field; 4th, main field and driving laser are carried out alignment of orientation, and hyperpolarized nuclei spins, and realizes the strong coupling of nuclear spin-electron spin; 5th, adopt closed loop Faraday modulation detection method, extract the information of detection laser Atom Spin precession, obtain inertia angular velocity information; Finally, obtain the current value of field compensation signal, calculate current magnetic field information.The present invention has the advantages that measuring accuracy is high, independence is strong.

Description

Inertia and magnetic field integrated measurement method based on SERF atomic spin effect

Technical Field

The invention relates to an inertia and magnetic field integrated measurement method based on an SERF atomic spin effect, which can be used for researching a novel navigation system based on inertia and magnetic field combination.

Background

National defense and military require high-precision inertial navigation and guidance systems and extremely weak magnetic field measurement technologies. At present, the difficulty in improving the precision of the gyroscope becomes a key for restricting the improvement of the performance of the inertial navigation system. The existing high-precision gyroscope mainly comprises a rotor gyroscope and an optical gyroscope, but meets the technical bottleneck of further improving the precision. With the development of quantum regulation and control technology, an inertial measurement device based on SERF atomic spin effect becomes possible and is verified by principle, and becomes the development direction of next generation ultrahigh precision inertial measurement equipment. Weak magnetic field measurements require a magnetometer with ultra-high sensitivity. At present, the magnetometers widely applied mainly include a fluxgate magnetometer, a superconducting quantum interference magnetometer and an atomic spin magnetometer, wherein a magnetic field measuring device based on an atomic spin effect with a passive magnetic shielding system achieves the highest magnetic field measuring sensitivity of human beings at present. And the unshielded SERF atomic spin magnetometer technology based on the active magnetic compensation technology is also gradually developed.

The inertial measurement device and the magnetic field measurement device based on the SERF atomic spin effect have ultrahigh expected sensitivity, and experimental research work is carried out by a plurality of domestic and foreign research institutions, but a measurement technology integrating the inertial measurement device and the magnetic field measurement device is not reported.

Disclosure of Invention

The technical problem to be solved by the invention is as follows: the invention overcomes the defects of the prior art, provides an inertia and magnetic field integrated measurement method based on SERF atomic spin effect under a non-shielding magnetic field, and has the advantages of high measurement precision and strong autonomy.

The technical solution of the invention is as follows: an inertia and magnetic field integrated measurement method based on SERF atomic spin effect is characterized in that the method firstly establishes an integral model for the integrated measurement of inertia and magnetic field; secondly, manufacturing a measurement sensitive unit, and carrying out high-frequency alternating-current non-magnetoelectric heating; starting a driving laser (z axis) to perform optical pumping on the sensitive unit; emitting detection laser in the vertical direction (x axis); thirdly, performing active magnetic compensation through a three-dimensional magnetic compensation coil to offset an external magnetic field; fourthly, carrying out azimuth alignment on the main magnetic field and the driving laser to hyperpolarize nuclear spin, and realizing strong coupling of nuclear spin and electron spin; fifthly, extracting information of atomic spin precession in the detection laser by adopting a closed-loop Faraday modulation detection method to obtain inertial angular velocity information; and finally, acquiring the current value of the magnetic field compensation signal, and calculating to obtain the current magnetic field information. The method comprises the following specific steps:

1. establishing an integral model of the inertia/magnetic field integral measuring device, wherein the integral model comprises an inertia angular velocity measuring model based on an SERF atomic spin effect and a current feedback magnetic field measuring model based on an active magnetic compensation technology;

(1) the inertial angular velocity measurement model based on the SERF atomic spin effect comprises an SERF state atomic spin dynamics model and an atomic spin precession detection model;

under the influence of an external magnetic field and a rotation angular velocity, the polarizability of electron spin and nuclear spin can be described as follows by using a Bloch equation system:

$\frac{\∂\stackrel{\→}{P}}{\mathrm{dt}}=\mathrm{\γ}\stackrel{\→}{B}\×\stackrel{\→}{P}-\stackrel{\→}{\mathrm{\Ω}}\×\stackrel{\→}{P}$

comprehensively considering relaxation of electron spin of alkali metal atom and nuclear inertia gas nuclear spinAnd mutual polarizationAnd driving and detecting the laser optical pumping action R_P、R_dAnd the slowing factor Q (P) of nuclear spin to electron spin generation^e) A complete electron spin dynamics model can be obtained:

$\frac{\∂{\stackrel{\→}{P}}^e}{\∂t}=\frac{{\mathrm{\γ}}_e}{Q\left(P^e\right)}(\stackrel{\→}{B}+{\stackrel{\→}{B}}^n+\stackrel{\→}{L})\×{\stackrel{\→}{P}}^e-\stackrel{\→}{\mathrm{\Ω}}\×{\stackrel{\→}{P}}^e+\frac{(R_P\·{\stackrel{\→}{s}}_P+R_d\·{\stackrel{\→}{s}}_d+R_{\mathrm{se}}^{\mathrm{en}}\·{\stackrel{\→}{P}}^n-R_{\mathrm{tot}}^e\·{\stackrel{\→}{P}}^e)}{Q\left(P^e\right)}$

nuclear spin kinetic model:

$\frac{\∂{\stackrel{\→}{P}}^n}{\∂t}={\mathrm{\γ}}_n(\stackrel{\→}{B}+{\stackrel{\→}{B}}^e)\×{\stackrel{\→}{P}}^n-\stackrel{\→}{\mathrm{\Ω}}\×{\stackrel{\→}{P}}^n+R_{\mathrm{se}}^{\mathrm{ne}}\·{\stackrel{\→}{P}}^e-R_{\mathrm{tot}}^n\·{\stackrel{\→}{P}}^n$

wherein,

the electron spin polarizability of the alkali metal atom;

nuclear spin polarizability of noble gas atoms;

γ_e: the electron spin gyromagnetic ratio of alkali metal atoms;

γ_n: nuclear spin gyromagnetic ratio of inert gas atoms;

Q(P^e): a slowing factor;

an ambient magnetic field;

a magnetic field generated by nuclear spin sensed by electron spin;

a magnetic field generated by electron spin sensed by nuclear spin;

the optical displacement sensed by the electron spin of the alkali metal atom is equivalent to a magnetic field;

the rotation angular velocity of the carrier relative to the inertial system;

R_P: the optical pumping rate to drive the laser;

driving photon angular momentum transfer orientation of the laser;

R_d: detecting the optical pumping rate of the laser;

detecting the photon angular momentum transfer direction of the laser;

nuclear spin pumping rate;

electron spin pumping rate;

the total relaxation rate of the electron spin of the alkali metal atom;

total relaxation rate of noble gas nuclear spins;

after active magnetic compensation, the remanence is only in the z-axis direction. Longitudinal componentAndis less affected by the lateral component and,andall pointing in the z-axis direction. Order toOnly when angular velocity is input in a direction perpendicular to the z-axis,andthe steady state value of (a) is not affected by it, and is:

$P_z^e=\frac{R^P}{R_{\mathrm{tot}}^e-\frac{R_{\mathrm{se}}^{\mathrm{en}}{\·R}_{\mathrm{se}}^{\mathrm{ne}}}{R_{\mathrm{tot}}^n}}\≈\frac{R_p}{R_{\mathrm{tot}}^e}$

$P_z^n=\frac{R_p\·R_{\mathrm{se}}^{\mathrm{ne}}}{R_{\mathrm{tot}}^e{\·R}_{\mathrm{tot}}^n-R_{\mathrm{se}}^{\mathrm{en}}{\·R}_{\mathrm{se}}^{\mathrm{ne}}}=P_z^e\frac{R_{\mathrm{se}}^{\mathrm{ne}}}{R_{\mathrm{tot}}^n}$

detection by pointing detection laser to x axisOrder toWhen the measured rotation angular velocity is small, the steady state solution obtained after the high-order term is omitted is as follows:

$P_x^e=\frac{P_z^e{\·\mathrm{\γ}}_e\·R_{\mathrm{tot}}^e}{{R_{\mathrm{tot}}^e}^2+{\mathrm{\γ}}_e{(\mathrm{\Δ}{B}_z+L_z)}^2}.$

$\{\frac{{\mathrm{\Ω}}_y}{{\mathrm{\γ}}_n}+L_y+\frac{R_d}{{\mathrm{\γ}}_e{\·P}_z^e}+\frac{{\mathrm{\γ}}_e}{R_{\mathrm{tot}}^e}{L}_x{\·L}_z+$

$\mathrm{\Δ}{B}_z[\frac{B_y}{B_c}+\frac{{\mathrm{\γ}}_e\·(\mathrm{\Δ}{B}_z+L_z)B_x}{R_{\mathrm{tot}}^e\·B_c}+\frac{{\mathrm{\γ}}_e}{R_{\mathrm{tot}}^e}(\frac{{\mathrm{\Ω}}_x}{{\mathrm{\γ}}_n}+L_x)]\}$

control of Delta B_zIs zero, the drive and detection lasers are further controlled such that L_x、L_y、L_z、R_dAre all zero, the above formula is further simplified as:

$P_x^e=\frac{P_z^e{\·\mathrm{\γ}}_e\·}{R_{\mathrm{tot}}^e}\·\frac{{\mathrm{\Ω}}_y}{{\mathrm{\γ}}_n}$

supplementing a beam of detection laser in the y-axis directionCarrying out measurement; according to and solvingIn the same way, the user can select the different types of the different,the method is simplified as follows:

$P_y^e=-\frac{P_z^e\·{\mathrm{\γ}}_e}{R_{\mathrm{tot}}^e}\·\frac{{\mathrm{\Ω}}_x}{{\mathrm{\γ}}_n}$

the measurement of the angular velocity in the y-axis direction and the x-axis direction can be realized through the two formulas.

(2) Atomic spin detection modeling: atomic spin precession detection is mapped to the detection of the polarization plane rotation angle of linearly polarized laser light.

$\mathrm{\θ}=\frac{\mathrm{\πvl}}{c}[n_{+}\left(v\right)-n_{-}\left(v\right)]$

Where θ is the rotation angle of the polarization plane, v is the frequency of the detection laser, l is the length of the sensing unit through which the detection light passes, c is the speed of light, n is₊(v)、n_-(v) For alkali metal vapour to different polarized light sigma⁺、σ^-Refractive index n of₊(v)、n_-(v) The refractive index of the alkali metal vapor is expressed as:

$n\left(v\right)=1+\left(\frac{n{r}_e{c}^{2}f}{4v}\right)\mathrm{Im}\left[v(v-v_0)\right]$

wherein n is the atomic density, r_eThe classical electron radius, f the resonance intensity, and the other parameters have the same physical meaning.

For the alkali metal D1 wire,

$\left\{\begin{array}{c}{n}_{-}\left(v\right)=1+2\mathrm{\ρ}(+1/2)\left(\frac{n{r}_e{c}^2{f}_{D1}}{4v}\right)\mathrm{Im}\left[v(v-v_{D1})\right]\\ n_{+}\left(v\right)=1+2\mathrm{\ρ}(-1/2)\left(\frac{n{r}_e{c}^2{f}_{D1}}{4v}\right)\mathrm{Im}\left[v(v-v_{D1})\right]\end{array}\right.$

wherein rho (-1/2) and rho (+1/2) are atomic numbers of different ground state population, and v_D1Corresponding to the center wavelength of the D1 line.

For the line D2,

$\left\{\begin{array}{c}{n}_{-}\left(v\right)=1+2\left(\frac{3}{4}\mathrm{\ρ}(-1/2)+\frac{1}{4}\mathrm{\ρ}(+1/2)\right)\left(\frac{n{r}_e{c}^2{f}_{D1}}{4v}\right)\mathrm{Im}\left[v(v-v_{D1})\right]\\ n_{+}\left(v\right)=1+2(\frac{1}{4}\mathrm{\ρ}(-1/2)+\frac{3}{4}\mathrm{\ρ}(+1/2))\left(\frac{n{r}_e{c}^2{f}_{D1}}{4v}\right)\mathrm{Im}\left[v(v-v_{D1})\right]\end{array}\right.$

wherein v is_D2Corresponding to the center wavelength of the D2 line.

When ρ (-1/2) ≠ ρ (+1/2), the atom has birefringence. Polarizability P_xρ (+1/2) - ρ (-1/2). N is to be₊(v)、n_-(v) Substituting the expression of (a) into the formula theta to obtain an atomic spin precession detection model:

$\mathrm{\θ}\left(v\right)=\frac{\mathrm{\π}}{6}{P}_x^e\·\ln r_{e}c\·\left\{\mathrm{Im}\right[V(v-v_{D2})]-\mathrm{Im}[V(v-v_{D1})\left]\right\}$

and (3) adopting a closed-loop Faraday modulation method, wherein the light intensity detected by the photoelectric detector is as follows:

I＝I₀sin²(θ+A·cosωt)

where a · cos ω t is a high-frequency modulation signal, and θ is a polarization plane rotation angle.

The result after phase-lock amplification is:

I_ω＝2I₀·A·θ

according to the output of the lock-in amplifier_ωObtaining the deflection angle theta and then obtainingAnd then angular velocity information is obtained.

(3) The active magnetic compensation model adopts a three-axis Helmholtz coil as a driver of three-dimensional magnetic compensation,

from biot savart law:

$d\stackrel{\→}{B}=\frac{\mathrm{\μId}\stackrel{\→}{s}\×\stackrel{\→}{r}}{r^3}$

wherein, I is the current intensity,in order to be the differential of the line element,is the displacement vector, μ is the permeability.

Integrating the magnetic field and substituting B ═ mu H to obtain the established current feedback magnetic field measurement model based on the active magnetic compensation technology:

the intensity of the current flowing through the linear magnetic field is I, the flowing direction of the current is consistent with the direction of the line element ds, r is a displacement vector, and H is the required magnetic field.

2. Manufacturing a measurement sensitive unit, carrying out high-frequency alternating-current non-magnetoelectric heating, placing a driving laser in the z-axis direction, adjusting a D1 line with the frequency of alkali metal atoms, carrying out optical pumping on the sensitive unit, injecting a detection laser in the x-axis direction, and adjusting a D2 line with the frequency of alkali metal atoms;

3. placing the sensitive unit manufactured in the step 2 in the center of a triaxial Helmholtz coil, and performing active magnetic compensation by adopting a three-dimensional magnetic field in-situ active magnetic compensation method based on optical pumping to offset the magnetic field of the sensitive unit;

the circularly polarized light is incident into the alkali metal gas chamber, so that the driving laser is transmitted through the laser of the alkali metal gas chamber in the z-axis direction and is absorbed by the photoelectric detector to obtain P_transAndproportional, defining a positive coefficient k_PDAnd satisfies the following conditions:

$P_{\mathrm{trans}}=k_{\mathrm{PD}}\·P_z^e$

will P_transTo B_xAnd (3) calculating a partial derivative to obtain:

$\frac{{\∂P}_{\mathrm{trans}}}{\∂B_x}=-\frac{2k_{\mathrm{PD}}{R}_p{{\mathrm{\γ}}_e}^2{R}_2({B_z}^2{{\mathrm{\γ}}_e}^2+R_2^2)}{({B_x}^2+{B_y}^2){{\mathrm{\γ}}_e}^2{R}_2+{B_z}^2{{\mathrm{\γ}}_e}^2{R}_1+R_2^2{R}_1}=k_{B_x}\·B_x$

R₁、R₂the longitudinal relaxation rate and the transverse relaxation rate are respectively, and other physical quantities have the same meanings as above.

When B is present_xWhen going to 0, P_transHas been increasing. Thus, the maximum P is obtained by adjusting the magnitude of the compensation field of the x-coil_trans. The compensation of the z-axis magnetic field is slightly different from the x-and y-axes. When B is present_zWhen going to 0, P_transAre decreasing. Magnetic field scanning is respectively carried out on the x coil, the y coil and the z coil, and a compensation point is found to counteract the environmental magnetic field.

The method comprises the following specific steps:

(1) circularly polarized light is incident into the alkali metal gas chamber in the z-axis direction, and laser penetrating through the alkali metal gas chamber is absorbed by the photoelectric detector;

(2) attempting to generate two compensating magnetic fields B by means of an x-coil_cx1And B_cx2Comparing the outputs P of the two magnetic fields_trans1And P_trans2If P is_trans1Ratio P_trans2Large, then B_cx1The residual magnetic field is made to be closer to zero, and B is reserved_cx1Generating another B_cx2And comparing, retaining better compensation magnetic field until P_trans1And P_trans2No longer resolvable, defining the error magnetic field Δ B of the magnetic compensation_x=(B_cx1-B_cx2) /2, final compensation field B_cxIs (B)_cx1+B_cx2)／2；

(3) By y-coilAttempting to generate two compensating magnetic fields B_cy1And B_cy2Comparing the outputs P of the two magnetic fields_trans1And P_trans2If P is_trans1Ratio P_trans2Large, then B_cy1The residual magnetic field is made to be closer to zero, and B is reserved_cy1Generating another B_cy2And comparing, retaining better compensation magnetic field until P_trans1And P_trans2No longer resolvable, defining the error magnetic field Δ B of the magnetic compensation_y=(B_cy1-B_cy2) /2, final compensation field B_cyIs (B)_cy1+B_cy2)／2；

(4) Attempting to generate two compensating magnetic fields B by means of a z-coil_cz1And B_cz2Rapidly comparing the output P of the two magnetic fields_trans1And P_trans2If P is_trans1Ratio P_trans2Small, then B_cz1The residual magnetic field is made to be closer to zero, and B is reserved_cz1Generating another B_cz2And comparing, retaining better compensation magnetic field until P_trans1And P_trans2No longer resolvable, defining the error magnetic field Δ B of the magnetic compensation_z=(B_cz1-B_cz2) /2, final compensation field B_czIs (B)_cz1+B_cz2)／2。

(5) And (4) repeating the steps (2) to (4) to find a compensation point under the natural environment magnetic field so as to counteract the environment magnetic field.

4. Aligning the main magnetic field in the step 3 with the driving laser in the step 2 by taking the z-axis as the main magnetic field direction:

p received by the photoelectric detector after the driving laser is aligned with the azimuth of the main magnetic field_transThe expression is as follows:

$P_{\mathrm{trans}}=k_{\mathrm{PD}}\·R_p\frac{B_z^2{\mathrm{\γ}}_e^2+R_2^2}{B_z^2{\mathrm{\γ}}_e^2{R}_1+R_2^2{R}_1}=k_{\mathrm{PD}}\·\frac{R_p}{R_1}$

wherein the physical quantities are as defined above.

Actively applying a modulating magnetic field B in the x-axis_xfsin ω t with a constant magnetic field of B_x0When the modulation magnetic field is low, the signal P received by the photoelectric detector_transComprises the following steps:

$P_{\mathrm{trans}}=k_{\mathrm{PD}}\·R_p\frac{B_z^2{\mathrm{\γ}}_e^2+R_2^2}{(B_{x0}^2+B_{\mathrm{xf}}^2{\sin }^2\mathrm{\ωt}+2B_{x0}{B}_{\mathrm{xf}}\sin \mathrm{\ωt}){\mathrm{\γ}}_e^2{R}_2+B_y^2{\mathrm{\γ}}_e^2{R}_2+B_z^2{\mathrm{\γ}}_e^2{R}_1+R_2^2{R}_1}$

adjustment ofSize until the output no longer contains the term with frequency ω.

(1) B is actively magnetically compensated by three-dimensional magnetic field_x、B_y、B_zAdjusted to zero as much as possible; actively generating a B_zBecoming the main magnetic field;

(2) applying a modulated magnetic field B in the x-axis_xfsin ω t, adjusting the azimuthal projection of the drive laser in the x-axis until P_transNo longer contains a term of frequency ω;

(3) applying a modulated magnetic field B in the y-axis_yfsin ω t, adjusting the azimuthal projection of the drive laser in the y-axis until P_transNo longer contains a term of frequency ω;

(4) generating different main magnetic field strengths, and respectively applying modulated magnetic fields B on the x-axis_xfsin ω t, application of a modulating magnetic field B on the y-axis_yfsin ω t, test P_transWhether the output of (a) contains a term with frequency omega, if not, the alignment is completed; otherwise, repeating the steps (1) to (4).

5. After the main magnetic field is aligned with the driving laser in azimuth in step 4, the magnetic fields of the x axis and the y axis approach zero, the driving laser is operated to enable alkali metal atoms to enter an SERF state, and then a main magnetic field B is actively added_zCarrying out nuclear spin hyperpolarization to realize strong nuclear spin-electron spin coupling;

6. inputting an angular velocity, extracting information of atomic spin precession in the detection laser by adopting a closed-loop Faraday modulation detection method according to the inertial angular velocity measurement model based on the SERF atomic spin effect established in the step 1, and further obtaining the inertial angular velocity; and (3) obtaining a magnetic field measurement value under the current carrier coordinate system according to the current feedback magnetic field measurement model based on the active magnetic compensation technology established in the step (1).

The principle of the invention is as follows: the nuclear spin of inert gas is coupled with the electron spin of alkali metal atoms, the nuclear spin of the inert gas automatically tracks and compensates the change of an external magnetic field, and the influence of the magnetic field on the electron spin shafting property of the alkali metal atoms is isolated; the method comprises the following steps of optically pumping atoms by driving laser fixedly connected with a carrier to force atomic spin to precess to the direction of the driving laser, wherein the atomic spin finally deviates from the driving laser to generate an included angle due to the axial fixity of an inertia space; the change of the spin direction of the atom is detected by the detection laser, so that the measurement of the angular velocity is realized.

Because the spin of the atom has angular momentum and magnetic moment, the response of the spin magnetic moment of the atom to the magnetic field can be utilized to realize the measurement of the magnetic field. The basic principle is as follows: under the action of a weak magnetic field, atom spin generates Larmor precession; on the other hand, under the action of the driving laser, the driving laser forces the atomic spins back to the direction of the driving laser. Therefore, under the combined action of a weak magnetic field and driving laser, the atomic spin pointing direction reaches an equilibrium state, the pointing direction finally deviates from the original direction of the driving laser, the deviation degree is related to the pumping efficiency of the driving laser and the strength of the magnetic field, the deviation angle can be detected by the detection laser, the magnetic field of the magnetic compensation coil is indicated to be offset from the external magnetic field by adjusting the current of the three-dimensional magnetic compensation coil by utilizing the angle, and the size of the compensation magnetic field can be calculated by reading the size of the current loaded on the three-dimensional coil, so that the measurement of the three-dimensional magnetic field is realized.

Compared with the prior art, the invention has the advantages that: the invention integrates inertia and magnetic field measurement technology based on SERF atomic spin effect, namely, the three-dimensional active magnetic compensation technology is adopted to realize SERF state atomic spin under an unshielded magnetic field, so as to carry out inertia angular velocity measurement and magnetic field measurement, provide a model for inertia and magnetic field measurement, provide a measurement scheme, integrate inertia measurement and magnetic field measurement into a whole, and have the advantages of high measurement precision and strong autonomy.

Drawings

FIG. 1 is a flow chart of an integrated inertial and magnetic field measurement scheme of the present invention;

fig. 2 is a schematic diagram of a hardware structure of the three-dimensional active magnetic compensation system.

Detailed Description

As shown in fig. 1 and 2, the specific method of the present invention is as follows:

1. establishing an integral model of an inertia/magnetic field integrated measuring device, wherein the integral model comprises an inertia angular velocity measuring model based on SERF atomic spin effect and a current feedback magnetic field measuring model based on active magnetic compensation technology;

(1) the inertial angular velocity measurement model based on the SERF atomic spin effect comprises an SERF state atomic spin dynamics model and an atomic spin precession detection model;

the polarizability of electron spin and nuclear spin under the influence of external magnetic field and rotation angular velocity can be described as follows by using Bloch equation system

$\frac{\∂\stackrel{\→}{P}}{\mathrm{dt}}=\mathrm{\γ}\stackrel{\→}{B}\×\stackrel{\→}{P}-\stackrel{\→}{\mathrm{\Ω}}\×\stackrel{\→}{P}---\left(1\right)$

Comprehensively considering relaxation of electron spin of alkali metal atom and nuclear inertia gas nuclear spinAnd mutual polarizationAnd driving and detecting the laser optical pumping action R_P、R_dAnd the slowing factor Q (P) of nuclear spin to electron spin generation^e) A complete electron spin dynamics model can be obtained:

$\frac{\∂{\stackrel{\→}{P}}^e}{\∂t}\text{=}\frac{{\mathrm{\γ}}_e}{Q\left(P^e\right)}(\stackrel{\→}{B}+{\stackrel{\→}{B}}^n+\stackrel{\→}{L})\×{\stackrel{\→}{P}}^e-\stackrel{\→}{\mathrm{\Ω}}\×{\stackrel{\→}{P}}^e+\frac{(R_P\·{\stackrel{\→}{s}}_P+R_d\·{\stackrel{\→}{s}}_d+R_{\mathrm{se}}^{\mathrm{en}}\·{\stackrel{\→}{P}}^n-R_{\mathrm{tot}}^e\·{\stackrel{\→}{P}}^e)}{Q\left(P^e\right)}---\left(2\right)$

and nuclear spin dynamics model:

$\frac{\∂{\stackrel{\→}{P}}^n}{\∂t}={\mathrm{\γ}}_n(\stackrel{\→}{B}+{\stackrel{\→}{B}}^e)\×{\stackrel{\→}{P}}^n-\stackrel{\→}{\mathrm{\Ω}}\×{\stackrel{\→}{P}}^n+R_{\mathrm{se}}^{\mathrm{ne}}\·{\stackrel{\→}{P}}^e-R_{\mathrm{tot}}^n\·{\stackrel{\→}{P}}^n---\left(3\right)$

wherein,

the electron spin polarizability of the alkali metal atom;

nuclear spin polarizability of noble gas atoms;

γ_e: of alkali metal atomsSpin-spin ratio of electrons;

γ_n: nuclear spin gyromagnetic ratio of inert gas atoms;

Q(P^e): a slowing factor;

an ambient magnetic field;

a magnetic field generated by nuclear spin sensed by electron spin;

a magnetic field generated by electron spin sensed by nuclear spin;

the optical displacement sensed by the electron spin of the alkali metal atom is equivalent to a magnetic field;

the rotation angular velocity of the carrier relative to the inertial system;

R_P: the optical pumping rate to drive the laser;

driving photon angular momentum transfer orientation of the laser;

R_d: detecting the optical pumping rate of the laser;

detecting the photon angular momentum transfer direction of the laser;

nuclear spin pumping rate;

electron spin pumping rate;

the total relaxation rate of the electron spin of the alkali metal atom;

total relaxation rate of noble gas nuclear spins;

after magnetic compensation, the remanence is only in the z-axis direction. Longitudinal componentAndis less affected by the lateral component and,andall pointing in the z-axis direction. Order toOnly when the angular velocity is input in the z-axis perpendicular direction,andthe steady state value of (a) is not affected by it, and is:

$P_z^e=\frac{R^P}{R_{\mathrm{tot}}^e-\frac{R_{\mathrm{se}}^{\mathrm{en}}{\·R}_{\mathrm{se}}^{\mathrm{ne}}}{R_{\mathrm{tot}}^n}}\≈\frac{R_p}{R_{\mathrm{tot}}^e}---\left(4\right)$ )

$P_z^n=\frac{R_p\·R_{\mathrm{se}}^{\mathrm{ne}}}{R_{\mathrm{tot}}^e\·R_{\mathrm{tot}}^n-R_{\mathrm{se}}^{\mathrm{en}}{\·R}_{\mathrm{se}}^{\mathrm{ne}}}=P_z^e\frac{R_{\mathrm{se}}^{\mathrm{ne}}}{R_{\mathrm{tot}}^n}$

detection by pointing detection laser to x axisOrder toWhen the measured rotation angular velocity is small, the steady state solution obtained after the high-order term is omitted is as follows:

$P_x^e=\frac{P_z^e\·{\mathrm{\γ}}_e\·R_{\mathrm{tot}}^e}{{R_{\mathrm{tot}}^e}^2+{\mathrm{\γ}}_e{({\mathrm{\ΔB}}_z+L_z)}^2}.$

$\{\frac{{\mathrm{\Ω}}_y}{{\mathrm{\γ}}_n}+L_y+\frac{R_d}{{\mathrm{\γ}}_e\·P_z^e}+\frac{{\mathrm{\γ}}_e}{R_{\mathrm{tot}}^e}{L}_x\·L_z+---\left(5\right)$

${\mathrm{\ΔB}}_z[\frac{B_y}{B_c}+\frac{{\mathrm{\γ}}_e\·({\mathrm{\ΔB}}_z+L_z)B_x}{R_{\mathrm{tot}}^e\·B_c}+\frac{{\mathrm{\γ}}_e}{R_{\mathrm{tot}}^e}(\frac{{\mathrm{\Ω}}_x}{{\mathrm{\γ}}_n}+L_x)]\}$

control of Delta B_zIs zero, the drive and detection lasers are further controlled such that L_x、L_y、L_z、R_dAre all zero, the above formula is further simplified as:

$P_x^e=\frac{P_z^e{\·\mathrm{\γ}}_e\·}{R_{\mathrm{tot}}^e}\·\frac{{\mathrm{\Ω}}_y}{{\mathrm{\γ}}_n}---\left(6\right)$

supplementing a beam of detection laser in the y-axis direction, andcarrying out measurement; according to and solvingIn the same way, the user can select the different types of the different,the method is simplified as follows:

$P_y^e=-\frac{P_z^e\·{\mathrm{\γ}}_e}{R_{\mathrm{tot}}^e}\·\frac{{\mathrm{\Ω}}_x}{{\mathrm{\γ}}_n}---\left(7\right)$

the measurement of the angular velocity in the y-axis direction and the x-axis direction can be realized through the two formulas.

(2) Atomic spin detection modeling: atomic spin precession detection is mapped to the detection of the polarization plane rotation angle of linearly polarized laser light.

$\mathrm{\θ}=\frac{\mathrm{\πvl}}{c}[n_{+}\left(v\right)-n_{-}\left(v\right)]---\left(8\right)$

Where θ is the rotation angle of the polarization plane, v is the frequency of the detection laser, l is the length of the sensing unit through which the detection light passes, c is the speed of light, n is₊(v)、n_-(v) For alkali metal vapour to different polarized light sigma⁺、σ^-Refractive index n of₊(v)、n_-(v) The refractive index of the alkali metal vapor is expressed as:

$n\left(v\right)=1+\left(\frac{{\mathrm{nr}}_e{c}^{2}f}{4v}\right)\mathrm{Im}\left[v(v-v_0)\right]---\left(9\right)$

wherein n is the atomic density, r_eThe classical electron radius, f the resonance intensity, and the other parameters have the same physical meaning.

For the alkali metal D1 wire,

$\left\{\begin{array}{c}{n}_{-}\left(v\right)=1+2\mathrm{\ρ}(+1/2)\left(\frac{{\mathrm{nr}}_e{c}^2{f}_{D1}}{4v}\right)\mathrm{Im}\left[v(v-v_{D1})\right]\\ n_{+}\left(v\right)=1+2\mathrm{\ρ}(-1/2)\left(\frac{{\mathrm{nr}}_e{c}^2{f}_{D1}}{4v}\right)\mathrm{Im}\left[v(v-v_{D1})\right]\end{array}\right.---\left(10\right)$

wherein rho (-1/2) and rho (+1/2) are atomic numbers of different ground state population, and v_D1Corresponding to the center wavelength of the D1 line.

For the line D2,

$\left\{\begin{array}{c}{n}_{-}\left(v\right)=1+2(\frac{3}{4}\mathrm{\ρ}(-1/2)+\frac{1}{4}\mathrm{\ρ}(+1/2))\left(\frac{{\mathrm{nr}}_e{c}^2{f}_{D1}}{4v}\right)\mathrm{Im}\left[v(v-v_{D1})\right]\\ n_{+}\left(v\right)=1+2(\frac{1}{4}\mathrm{\ρ}(-1/2)+\frac{3}{4}\mathrm{\ρ}(+1/2))\left(\frac{{\mathrm{nr}}_e{c}^2{f}_{D1}}{4v}\right)\mathrm{Im}\left[v(v-v_{D1})\right]\end{array}\right.---\left(11\right)$

wherein v is_D2Corresponding to the center wavelength of the D2 line.

When ρ (-1/2) ≠ ρ (+1/2), the atom has birefringence. Polarizability P_x(= ρ (+1/2) — ρ (-1/2). N is to be₊(v)、n_-(v) Substituting the expression of (a) into the formula theta to obtain an atomic spin precession detection model:

$\mathrm{\θ}\left(v\right)=\frac{\mathrm{\π}}{6}{P}_x^e\·\ln r_{e}c\·\left\{\mathrm{Im}\right[V(v-v_{D2})]-\mathrm{Im}[V(v-v_{D1})\left]\right\}---\left(12\right)$

and (3) adopting a closed-loop Faraday modulation method, wherein the light intensity detected by the photoelectric detector is as follows:

I＝I₀sin²(θ+A·cosωt)(13)

where a · cos ω t is a high-frequency modulation signal, and θ is a polarization plane rotation angle.

The result after phase-lock amplification is:

I_ω＝2I₀·A·θ(14)

according to the output of the lock-in amplifier_ωObtaining the deflection angle theta and then obtainingAnd then angular velocity information is obtained.

(3) The active magnetic compensation model adopts a three-axis Helmholtz coil as a driver of three-dimensional magnetic compensation,

from Biao-Saval law there are

$d\stackrel{\→}{B}=\frac{\mathrm{\μId}\stackrel{\→}{s}\×\stackrel{\→}{r}}{r^3}---\left(15\right)$

Wherein, I is the current intensity,in order to be the differential of the line element,is the displacement vector, μ is the permeability. Integrating the magnetic field and substituting B ═ mu H to obtain the established current feedback magnetic field measurement model based on the active magnetic compensation technology:

the intensity of the current flowing through the linear magnetic field is I, the flowing direction of the current is consistent with the direction of the line element ds, r is a displacement vector, and H is the required magnetic field.

2. A sensing unit (containing 20 Torr) was charged with an appropriate alkali-inert gas ratio¹²⁹Xe, 100Torr N₂One drop of Cs) is heated to about 110 ℃ by adopting 200KHz high-frequency alternating current without magnetism; placing a driving laser in the z-axis direction, adjusting a D1 line with the frequency of alkali metal atoms, and optically pumping the sensitive unit with the power of 1W; while the detection laser is launched in the x-axis, with the frequency chosen as the D2 line for Cs.

3. Placing the sensitive unit manufactured in the step 2 in the center of a triaxial Helmholtz coil, and performing active magnetic compensation by adopting a three-dimensional magnetic field in-situ active magnetic compensation method based on optical pumping to offset the magnetic field of the sensitive unit;

the schematic diagram of the hardware structure of the three-dimensional active magnetic compensation system is shown in fig. 2, wherein 1 is a driving laser, 2 is a beam expander, 3 is a polarizer, 4 is an 1/4 wave plate, 5 is a three-dimensional magnetic compensation coil, 6 is an alkali metal gas chamber, 7 is a lens, 8 is a photodetector, 9 is a feedback coil, and 10, 11 and 12 are coils of z, x and y axes respectively.

The drive laser passes through 1/4 wave plates after expanding and polarizing. The atoms in the alkali metal gas chamber are pumped, and the laser penetrating through the gas chamber is converged by the lens and then detected by the photoelectric detector.

Based on the hardware structure given in FIG. 2, the kinetic process of electron spin in the alkali metal gas chamber is described by adopting a Bloch equation set,

$\left(\begin{array}{c}{{\stackrel{\·}{P}}_x}^e\\ {{\stackrel{\·}{P}}_y}^e\\ {{\stackrel{\·}{P}}_z}^e\end{array}\right)={\mathrm{\γ}}_e\·\left(\begin{array}{c}{B}_x\\ B_y\\ B_z\end{array}\right)\×\left(\begin{array}{c}{P_x}^e\\ {P_y}^e\\ {P_z}^e\end{array}\right)+\left(\begin{array}{c}0\\ 0\\ R_p\end{array}\right)-\left(\begin{array}{c}{R}_2{P_x}^e\\ R_2{P_y}^e\\ R_1{P_z}^e\end{array}\right)---\left(17\right)$

in the formula, R₁、R₂Longitudinal relaxation rate and transverse relaxation rate, respectively. The first term on the right in the equation is the larmor precession of the electron spin under the magnetic field, the second term is the pumping action that drives the laser, and the third term is the various relaxation actions. Solving the steady state solution of the equation to obtain:

$\left\{\begin{array}{c}{P_x}^e=R_p{\mathrm{\γ}}_e\frac{B_y{B}_2+B_x{B}_z{\mathrm{\γ}}_e}{({B_x}^2+{B_y}^2){{\mathrm{\γ}}_e}^2{R}_2+{B_z}^2{{\mathrm{\γ}}_e}^2{R}_1+R_2^2{R}_1}\\ {P_y}^e=R_p{\mathrm{\γ}}_e\frac{-B_x{R}_2+B_y{B}_z{\mathrm{\γ}}_e}{({B_x}^2+{B_y}^2){{\mathrm{\γ}}_e}^2{R}_2+{B_z}^2{{\mathrm{\γ}}_e}^2{R}_1+R_2^2{R}_1}\\ {P_z}^e=R_p=\frac{{B_z}^e{{\mathrm{\γ}}_e}^2+R_2^2}{({B_x}^2+{B_y}^2){{\mathrm{\γ}}_e}^2{R}_2+{B_z}^2{{\mathrm{\γ}}_e}^2{R}_1+R_2^2{R}_1}\end{array}\right.----\left(18\right)$

the circularly polarized light is incident into the alkali metal gas chamber, so that the driving laser is transmitted through the laser of the alkali metal gas chamber in the z-axis direction and is absorbed by the photoelectric detector to obtain P_transAndis in direct proportion. Due to P_transAndif both values are positive, a positive coefficient k can be defined_PDAnd satisfies the following conditions:

$P_{\mathrm{trans}}=k_{\mathrm{PD}}\·P_z^e---\left(19\right)$

will P_transTo B_xCalculating a deviation to obtain

$\frac{{\∂P}_{\mathrm{trans}}}{{\∂B}_x}=-\frac{{2k}_{\mathrm{PD}}{R}_p{{\mathrm{\γ}}_e}^2{R}_2({B_z}^2{{\mathrm{\γ}}_e}^2+R_2^2)}{{[({B_x}^2+{B_y}^2){{\mathrm{\γ}}_e}^2{R}_2+{B_z}^2{{\mathrm{\γ}}_e}^2{R}_1+R_2^2{R}_1]}^2}{B}_x={k_B}_x\·B_x---\left(20\right)$

When B is present_xWhen going to 0, P_transHas been increasing. Maximum P is obtained by adjusting the compensating magnetic field of the x coil_transIs compensating for B_xOne basis for (1). In the same way, the basis for compensating the y-axis magnetic field can be obtained. The compensation of the z-axis magnetic field is slightly different from the x-and y-axes. When B is present_zWhen going to 0, P_transAre decreasing. Magnetic field scanning is respectively carried out on the x coil, the y coil and the z coil, and a compensation point is found to counteract the environmental magnetic field.

The method comprises the following specific steps:

(1) circularly polarized light is incident into the alkali metal gas chamber in the z-axis direction, and laser penetrating through the alkali metal gas chamber is absorbed by the photoelectric detector;

(2) attempting to generate two compensating magnetic fields B by means of an x-coil_cx1And B_cx2Rapidly comparing the output P of the two magnetic fields_trans1And P_trans2If P is_trans1Ratio P_trans2Large, then B_cx1The residual magnetic field is made to be closer to zero, and B is reserved_cx1Generating another B_cx2And comparing, retaining better compensation magnetic field until P_trans1And P_trans2No longer resolvable, defining the error magnetic field Δ B of the magnetic compensation_x＝(B_cx1-B_cx2) /2, final compensation field B_cxIs (B)_cx1+B_cx2)/2. The y axis is the same;

(3) attempting to generate two compensating magnetic fields B by means of a y-coil_cy1And B_cy2Comparing the outputs P of the two magnetic fields_trans1And P_trans2If P is_trans1Ratio P_trans2Large, then B_cy1The residual magnetic field is made to be closer to zero, and B is reserved_cy1Generating another B_cy2And comparing, retaining better compensation magnetic field until P_trans1And P_trans2Indistinguishable, magnetically compensated error field △ B_y＝(B_cy1-B_cy2) /2, final compensation field B_cyIs (B)_cy1+B_cy2)/2；

(4) Attempting to generate two compensating magnetic fields B by means of a z-coil_cz1And B_cz2Rapidly comparing the output P of the two magnetic fields_trans1And P_trans2If P is_trans1Ratio P_trans2Small, then B_cz1Make the residual magnetic field closer to zero and ensureLeave B_cz1Generating another B_cz2And comparing, retaining better compensation magnetic field until P_trans1And P_trans2No longer resolvable, defining the error magnetic field Δ B of the magnetic compensation_z＝(B_cz1-B_cz2) /2, final compensation field B_czIs (B)_cz1+B_cz2)/2；

(5) And (4) repeating the steps (2) to (4) to find a compensation point under the natural environment magnetic field so as to counteract the environment magnetic field.

4. Aligning the main magnetic field in the step 3 with the driving laser in the step 2 by taking the z-axis as the main magnetic field direction:

actively applying a modulating magnetic field B in the x-axis_xfsin ω t with a constant magnetic field of B_x0When the modulation magnetic field is low, the signal P received by the photoelectric detector_transComprises the following steps:

$P_{\mathrm{trans}}=k_{\mathrm{PD}}\·R_p\frac{B_z^2{\mathrm{\γ}}_e^2+R_2^2}{(B_{x0}^2+B_{\mathrm{xf}}^2{\sin }^2\mathrm{\ωt}+{2B}_{x0}{B}_{\mathrm{xf}}\sin \mathrm{\ωt}){\mathrm{\γ}}_e^2{R}_2+B_y^2{\mathrm{\γ}}_e^2{R}_2+B_z^2{\mathrm{\γ}}_e^2{R}_1+R_2^2{R}_1}---\left(21\right)$

adjustment ofSize until the output no longer contains the term with frequency ω.

The method comprises the following specific steps:

(1) b is actively magnetically compensated by three-dimensional magnetic field_x、B_y、B_zAdjusted to zero as much as possible(ii) a Actively generating a B_zBecoming the main magnetic field;

(2) applying a modulated magnetic field B in the x-axis_xfsin ω t, adjusting the azimuthal projection of the drive laser in the x-axis until P_transNo longer contains a term of frequency ω;

(3) applying a modulated magnetic field B in the y-axis_yfsin ω t, adjusting the azimuthal projection of the drive laser in the y-axis until P_transNo longer contains a term of frequency ω;

(4) generating different main magnetic field strengths, and respectively applying modulated magnetic fields B on the x-axis_xfsin ω t, application of a modulating magnetic field B on the y-axis_yfsin ω t, test P_transWhether the output of (a) contains a term with frequency omega, if not, the alignment is completed; otherwise, repeating the steps (1) to (4).

5. After the main magnetic field is aligned with the driving laser in azimuth in step 4, the magnetic fields of the x axis and the y axis approach zero, the driving laser is operated to enable alkali metal atoms to enter an SERF state, and then a main magnetic field B is actively added_zAnd carrying out nuclear spin hyperpolarization to realize strong nuclear spin-electron spin coupling.

6. Inputting a smaller angular velocity in the y-axis direction, detecting the pointing direction of the laser to the x-axis, andand (6) detecting.

Firstly, according to the light intensity I modulated by closed loop Faraday and amplified by phase lock_ωCalculating the rotation angle theta of the linear polarization plane by the formula (14); then according to the formula (12), the calculation is carried out to obtainAnd (6) is substituted to obtain the angular velocity in the y-axis direction.

7. And (3) obtaining a magnetic field measurement value under the current carrier coordinate system according to the current feedback magnetic field measurement model based on the active magnetic compensation technology established in the step (1).

Those skilled in the art will appreciate that the invention may be practiced without these specific details.

Claims (5)

1. An inertia and magnetic field integrated measurement method based on SERF atomic spin effect is characterized by comprising the following steps:

(1) establishing an integral model for integrated measurement of inertia and a magnetic field, wherein the integral model comprises an inertial angular velocity measurement model based on an SERF (spin exchange filter) atomic spin effect and a current feedback magnetic field measurement model based on an active magnetic compensation technology;

(2) making a measurement sensitive unit, heating with high-frequency AC non-magnetoelectricity, placing driving laser in z-axis direction, and adjusting D1 wire with frequency of alkali metal atom to make measurement sensitiveThe sensing unit performs optical pumping, emits detection laser in an x axis, and adjusts the frequency to be a D2 line of alkali metal atoms; the measurement sensitive unit is an alkali metal-inert gas sensitive unit containing 20Torr¹²⁹Xe, 100Torr N₂Except for a drop of Cs;

(3) placing the measurement sensitive unit manufactured in the step (2) in the center of a three-axis Helmholtz coil, and performing active magnetic compensation by adopting a three-dimensional magnetic field in-situ active magnetic compensation method based on optical pumping to offset the magnetic field of the sensitive unit;

(4) taking the z axis as the direction of a main magnetic field, and aligning the main magnetic field in the step (3) with the driving laser in the step (2) in an azimuth manner;

(5) after the main magnetic field is aligned with the driving laser azimuth in the step (4), the magnetic fields of the x axis and the y axis approach zero, the driving laser is operated, and a main magnetic field B is actively added_zCarrying out nuclear spin hyperpolarization to realize strong nuclear spin-electron spin coupling;

(6) inputting angular velocity, and extracting information of atomic spin precession in the detection laser by adopting a closed-loop Faraday modulation detection method according to the inertial angular velocity measurement model based on the SERF atomic spin effect established in the step (1) so as to obtain the inertial angular velocity; and (2) obtaining a magnetic field measurement value under the current carrier coordinate system according to the current feedback magnetic field measurement model based on the active magnetic compensation technology established in the step (1).

2. The integrated inertia and magnetic field measurement method based on the SERF atomic spin effect as claimed in claim 1, wherein: the inertial angular velocity measurement model based on the SERF atomic spin effect in the step (1) comprises an SERF state atomic spin dynamics model and an atomic spin precession detection model:

(1) SERF state atomic spin dynamics model:

under the influence of an external magnetic field and a rotation angular velocity, the polarizability of electron spin and nuclear spin is described by using a Bloch equation set as follows:

comprehensively considering relaxation of electron spin of alkali metal atom and nuclear inertia gas nuclear spinAndand driving and detecting the laser optical pumping action R_P、R_dAnd the slowing factor Q (P) of nuclear spin to electron spin generation^e) Obtaining a complete electron spin dynamics model:

$\frac{\∂{\stackrel{\→}{P}}^e}{\∂t}=\frac{{\mathrm{\γ}}_e}{Q\left(P^e\right)}\left(\stackrel{\→}{B}+{\stackrel{\→}{B}}^n+\stackrel{\→}{L}\right)\×{\stackrel{\→}{P}}^e-\stackrel{\→}{\mathrm{\Ω}}\×{\stackrel{\→}{P}}^e+\frac{\left(R_P\·{\stackrel{\→}{s}}_P+R_d\·{\stackrel{\→}{s}}_d+R_{se}^{en}\·{\stackrel{\→}{P}}^n-R_{tot}^e\·{\stackrel{\→}{P}}^e\right)}{Q\left(P^e\right)}$

and nuclear spin dynamics model:

$\frac{\∂{\stackrel{\→}{P}}^n}{\∂t}={\mathrm{\γ}}_n\left(\stackrel{\→}{B}+{\stackrel{\→}{B}}^e\right)\×{\stackrel{\→}{P}}^n-\stackrel{\→}{\mathrm{\Ω}}\×{\stackrel{\→}{P}}^n+R_{se}^{ne}\·{\stackrel{\→}{P}}^e-R_{tot}^n\·{\stackrel{\→}{P}}^n$

wherein,

the electron spin polarizability of the alkali metal atom;

nuclear spin polarizability of noble gas atoms;

γ_e: the electron spin gyromagnetic ratio of alkali metal atoms;

γ_n: nuclear spin gyromagnetic ratio of inert gas atoms;

Q(P^e): a slowing factor;

an ambient magnetic field;

a magnetic field generated by nuclear spin sensed by electron spin;

a magnetic field generated by electron spin sensed by nuclear spin;

the optical displacement sensed by the electron spin of the alkali metal atom is equivalent to a magnetic field;

the rotation angular velocity of the carrier relative to the inertial system;

R_P: the optical pumping rate to drive the laser;

driving photon angular momentum transfer orientation of the laser;

R_d: for detecting laser lightAn optical pumping power;

detecting the photon angular momentum transfer direction of the laser;

nuclear spin pumping rate;

electron spin pumping rate;

the total relaxation rate of the electron spin of the alkali metal atom;

total relaxation rate of noble gas nuclear spins;

after active magnetic compensation, the remanence is only in the direction of z-axis and the longitudinal componentAndis less affected by the lateral component and,andall of the steady state values point to the z-axis direction, so thatInputting angular velocity in the direction perpendicular to the z-axis onlyWhen the temperature of the water is higher than the set temperature,andthe steady state value of (a) is not affected by it, and is:

$P_z^e=\frac{R^P}{R_{tot}^e-\frac{R_{se}^{en}.R_{se}^{ne}}{R_{tot}^n}}\≈\frac{R_p}{R_{tot}^e}$

$P_z^n=\frac{R_p.R_{se}^{ne}}{R_{tot}^e.R_{tot}^n-R_{se}^{en}.R_{se}^{ne}}=P_z^e\frac{R_{se}^{ne}}{R_{tot}^n}$

detection by pointing detection laser to x axisOrder toWhen the measured rotation angular velocity is small, the steady state solution obtained after the high-order term is omitted is as follows:

$P_x^e=\frac{P_z^e.{\mathrm{\γ}}_e.R_{tot}^e}{{R_{tot}^e}^2+{\mathrm{\γ}}_e{({\mathrm{\ΔB}}_z+L_z)}^2}.$

$\{\frac{{\mathrm{\Ω}}_y}{{\mathrm{\γ}}_n}+L_y+\frac{R_d}{{\mathrm{\γ}}_e.P_z^e}+\frac{{\mathrm{\γ}}_e}{R_{tot}^e}{L}_x.L_z+$

${\mathrm{\ΔB}}_z\[\frac{B_y}{B_c}+\frac{{\mathrm{\γ}}_e.({\mathrm{\ΔB}}_z+L_z)B_x}{R_{tot}^e.B_c}+\frac{{\mathrm{\γ}}_e}{R_{tot}^e}(\frac{{\mathrm{\Ω}}_x}{{\mathrm{\γ}}_n}+L_x)\]\}$

control △ B_zIs zero, the drive and detection lasers are further controlled such that L_x、L_y、L_z、R_dAre all zero, the above formula is further simplified as:

$P_x^e=\frac{P_z^e.{\mathrm{\γ}}_e.}{R_{tot}^e}.\frac{{\mathrm{\Ω}}_y}{{\mathrm{\γ}}_n}$

supplementing a beam of detection laser in the y-axis direction, andcarrying out measurement; finally, the product is processedThe method is simplified as follows:

$P_y^e=-\frac{P_z^e.{\mathrm{\γ}}_e}{R_{tot}^e}.\frac{{\mathrm{\Ω}}_x}{{\mathrm{\γ}}_n}$

the angular velocity in the directions of the x axis and the y axis can be measured through the two formulas;

(2) atomic spin precession detection model:

$\mathrm{\θ}=\frac{\mathrm{\π}vl}{c}\[n_{+}\left(v\right)-n_{-}\left(v\right)\]$

where θ is the rotation angle of the polarization plane, v is the frequency of the detection laser, l is the length of the sensing unit through which the detection laser passes, c is the speed of light, n is₊(v)、n_-(v) For alkali metal vapour to different polarized light sigma⁺、σ^-Refractive index n of₊(v)、n_-(v) The refractive index of the alkali metal vapor is expressed as:

$n\left(v\right)=1+\left(\frac{{\mathrm{nr}}_e{c}^{2}f}{4v}\right)\mathrm{Im}\[V(v-v_0)\]$

wherein n is the atomic density, r_eIs the classical electron radius, and f is the resonance intensity;

for the alkali metal D1 wire,

$\left\{\begin{array}{c}{n}_{-}\left(v\right)=1+2\mathrm{\ρ}(+1/2)\left(\frac{{\mathrm{nr}}_e{c}^2{f}_{D1}}{4v}\right)\mathrm{Im}\[V(v-v_{D1})\]\\ n_{+}\left(v\right)=1+2\mathrm{\ρ}(-1/2)\left(\frac{{\mathrm{nr}}_e{c}^2{f}_{D1}}{4v}\right)\mathrm{Im}\[V(v-v_{D1})\]\end{array}\right.$

wherein rho (-1/2) and rho (+1/2) are atomic numbers of different ground state population, and nu_D1Center wavelength corresponding to line D1;

for the line D2,

$\left\{\begin{array}{c}{n}_{-}\left(v\right)=1+2\left(\frac{3}{4}\mathrm{\ρ}\right(-1/2)+\frac{1}{4}\mathrm{\ρ}(+1/2\left)\right)\left(\frac{{\mathrm{nr}}_e{c}^2{f}_{D1}}{4v}\right)\mathrm{Im}\[V(v-v_{D1})\]\\ n_{+}\left(v\right)=1+2\left(\frac{1}{4}\mathrm{\ρ}\right(-1/2)+\frac{3}{4}\mathrm{\ρ}(+1/2\left)\right)\left(\frac{{\mathrm{nr}}_e{c}^2{f}_{D1}}{4v}\right)\mathrm{Im}\[V(v-v_{D1})\]\end{array}\right.$

wherein, v_D2Center wavelength corresponding to line D2;

when ρ (-1/2) ≠ ρ (+1/2), the atom has birefringence; polarizability P_xP (+1/2) -p (-1/2), and mixing n₊(v)、n_-(v) Substituting the expression of (a) into the formula theta to obtain an atomic spin precession detection model:

$\mathrm{\θ}\left(\mathrm{\ν}\right)=\frac{\mathrm{\π}}{6}{P}_x^e\·{\mathrm{lnr}}_{e}c\·\{\mathrm{Im}\[V(\mathrm{\ν}-{\mathrm{\ν}}_{D2})\]-\mathrm{Im}\[V(\mathrm{\ν}-{\mathrm{\ν}}_{D1})\]\}.$

3. the integrated inertia and magnetic field measurement method based on the SERF atomic spin effect as claimed in claim 1, wherein: the current feedback magnetic field measurement model based on the active magnetic compensation technology in the step (1) is as follows:

a triaxial Helmholtz coil is used as a three-dimensional magnetic compensation driver, and the three-dimensional magnetic compensation driver has the following characteristics according to the Biot-Saval law:

$d\stackrel{\→}{B}=\frac{\mathrm{\μ}Id\stackrel{\→}{s}\×\stackrel{\→}{r}}{r^3}$

wherein, I is the current intensity,in order to be the differential of the line element,is a displacement vector, mu is magnetic conductivity; integrating the current and substituting B ═ mu H to obtain the current feedback magnet based on the active magnetic compensation technologyA field measurement model:

the intensity of the current flowing through the linear magnetic field is I, the flowing direction of the current is consistent with the direction of the line element ds, r is a displacement vector, and H is the required magnetic field.

4. The method for integrated measurement of inertia and magnetic field based on SERF atomic spin effect as claimed in claim 1, wherein the three-dimensional magnetic field in-situ active magnetic compensation process in step (3) is as follows:

(31) circularly polarized light is incident into the alkali metal gas chamber in the z-axis direction, and laser penetrating through the alkali metal gas chamber is absorbed by the photoelectric detector;

(32) attempting to generate two compensating magnetic fields B by means of an x-coil_cx1And B_cx2Comparing the outputs P of the two magnetic fields_trans1And P_trans2If P is_trans1Ratio P_trans2Large, then B_cx1The residual magnetic field is made to be closer to zero, and B is reserved_cx1Generating another B_cx2And comparing, retaining better compensation magnetic field until P_trans1And P_trans2Indistinguishable, magnetically compensated error field △ B_x＝(B_cx1-B_cx2) /2, final compensation field B_cxIs (B)_cx1+B_cx2)/2；

(33) Attempting to generate two compensating magnetic fields B by means of a y-coil_cy1And B_cy2Comparing the outputs P of the two magnetic fields_trans1And P_trans2If P is_trans1Ratio P_trans2Large, then B_cy1The residual magnetic field is made to be closer to zero, and B is reserved_cy1Generating another B_cy2And comparing, retaining better compensation magnetic field until P_trans1And P_trans2Indistinguishable, magnetically compensated error field △ B_y＝(B_cy1-B_cy2) /2, final compensation field B_cyIs (B)_cy1+B_cy2)/2；

(34) Attempting to generate two compensating magnetic fields B by means of a z-coil_cz1And B_cz2Comparing the outputs P of the two magnetic fields_trans1And P_trans2If P is_trans1Ratio P_trans2Small, then B_cz1The residual magnetic field is made to be closer to zero, and B is reserved_cz1Generating another B_cz2And comparing, retaining better compensation magnetic field until P_trans1And P_trans2Indistinguishable, magnetically compensated error field △ B_z＝(B_cz1-B_cz2) /2, final compensation field B_czIs (B)_cz1+B_cz2)/2；

(35) And (6) repeating the steps (32) to (34) to find a compensation point under the natural environment magnetic field so as to counteract the environment magnetic field.

5. The integrated inertia and magnetic field measurement method based on the SERF atomic spin effect as claimed in claim 1, wherein: the method for performing azimuth alignment in the step (4) is realized as follows:

(41) b is actively magnetically compensated by three-dimensional magnetic field_x、B_y、B_zAdjusted to zero as much as possible; actively generating a B_zBecoming the main magnetic field;

(42) applying a modulated magnetic field B in the x-axis_xfsin ω t, adjusting the azimuthal projection of the drive laser in the x-axis until P_transNo longer contains a term of frequency ω;

(43) applying a modulated magnetic field B in the y-axis_yfsin ω t, adjusting the azimuthal projection of the drive laser in the y-axis until P_transNo longer contains a term of frequency ω;

(44) generating different main magnetic field strengths, and respectively applying modulated magnetic fields B on the x-axis_xfsin ω t, application of a modulating magnetic field B on the y-axis_yfsin ω t, test P_transWhether the output of (a) contains a term with frequency omega, if not, the alignment is completed; otherwise, repeating the steps (41) to (44).