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

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

Technical field

The present invention relates to a kind of inertia based on SERF atomic spin effect and magnetic field integral measurement method, can be used for the novel navigational system studied based on inertia and magnetic field combination.

Background technology

National defense and military needs high-precision inertial navigation and guidance system and atomic weak magnetic field measurement technology.At present, gyroscope precision is difficult to improve the key becoming restriction inertial navigation system performance and improve.Existing high accuracy gyroscope instrument mainly contains rotor gyro and optical gyroscope, but encounters the technical bottleneck that precision improves further.Along with the development of quantum regulation and control technology, inertial measuring unit based on SERF atomic spin effect become may and be able to Proof-Of Principle, become the developing direction of superhigh precision inertia measurement equipment of future generation, its gyroscopic inertia based on atomic spin and the motion of precession measured angular, have the advantages such as superhigh precision, structure is simple, volume is little.Weak magnetic fields measurement needs magnetometer to have the sensitivity of superelevation.At present, widely used magnetometer mainly contains flux-gate magnetometer, superconductive quantum interference magnetometer and atomic spin magnetometer, and the magnetic field measuring device based on atomic spin effect wherein with passive magnetic shielding system achieves mankind's magnetic-field measurement sensitivity the highest at present.And also developing gradually based on the unshielded SERF atomic spin magnetometer technology of active magnetic compensation technique.

Have the expection sensitivity of superelevation based on the inertial measuring unit of SERF atomic spin effect and magnetic field measuring device, domestic and international Duo Jia research institution has carried out experimental study work, but the two integrated measuring technique is had no report.

Summary of the invention

Technology of the present invention is dealt with problems and is: overcome the deficiencies in the prior art, and provide the inertia based on SERF atomic spin effect under a kind of unmasked magnetic field and magnetic field integral measurement method, the present invention has the advantage that measuring accuracy is high, independence is strong.

Technical solution of the present invention is: based on inertia and the magnetic field integral measurement method of SERF atomic spin effect, it is characterized in that first the method sets up the block mold of inertia and 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.Concrete steps are as follows:

1, the block mold block mold setting up inertia/magnetic field integrated measurer comprises the inertia angular velocity measurement model based on SERF atomic spin effect and the current feedback magnetic-field measurement model based on active magnetic compensation technique;

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

Under the impact of external magnetic field, angular velocity of rotation, the polarizability of electron spin and nuclear spin, can use Bloch system of equations to be described as:

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

Consider the relaxation of alkali metal atom electron spin and the nuclear spin of core inert gas and mutual polarization with driving detection laser optical pumping effect R _p, R _d, and the slowing factor Q (P that nuclear spin produces electron spin ^e) complete electron spin kinetic 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 polarization rate of alkali metal atom;

the nuclear spin polarization rate of intert-gas atoms;

γ _e: the electron spin gyromagnetic ratio of alkali metal atom;

γ _n: the nuclear spin gyromagnetic ratio of intert-gas atoms;

Q (P ^e): slowing factor;

environmental magnetic field;

the magnetic field that the nuclear spin that electron spin is experienced produces;

the magnetic field that the electron spin that nuclear spin is experienced produces;

the light displacement that the electron spin of alkali metal atom is experienced, is equivalent to a magnetic field;

the rotational angular velocity of relative inertness system of carrier system;

R _p: the optical pumping rate of driving laser;

the photon angular momentum of driving laser transmits orientation;

R _d: the optical pumping rate of detection laser;

the photon angular momentum of detection laser transmits orientation;

nuclear spin pumping rate;

electron spin pumping rate;

total relaxation rate of alkali metal atom electron spin;

total relaxation rate of intert-gas atoms nuclear spin;

After carrying out active magnetic compensation, remanent magnetism is only in z-axis direction.Longitudinal component with impact by cross stream component is little, with steady-state value all point to z-axis direction.Order only when the vertical direction input angular velocity of z-axis, with steady-state value do not affect by it, for:

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

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

Make detection laser point to x-axis detect order when tested rotational angular velocity is less, the steady state solution obtained after omitting higher order term is:

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

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

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

Control Δ B _zbe zero, control further to drive and detection laser, make L _x, L _y, L _z, R _dbe zero, above formula is reduced to further:

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

A branch of detection laser is supplemented again, then in y-axis direction measure; According to solve same thinking, be reduced to:

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

The measurement to y, x-axis directional angular velocity can be realized by above two formulas.

(2) atomic spin detects modeling: atomic spin precession detects the detection being mapped as line extreme polarisation of light face corner.

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

Wherein, θ is the rotation angle of plane of polarization, and v is the frequency of detection laser, and l is the length detecting the sensing unit that light passes through, and c is the light velocity, n ₊(v), n _-v () is for alkali metal vapour is to different polarization light σ ⁺, σ ^-refractive index n ₊(v), n _-(v), the refractive index of alkali metal vapour 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 atomic density, r _efor the electron radius of classics, f is resonant intensity, and other parameter physical significances are the same.

For alkaline metal D1 line,

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

Wherein, ρ (-1/2), ρ (+1/2) are the atomicity of different ground state population, v _d1the centre wavelength of corresponding D1 line.

To D2 line,

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

Wherein, v _d2the centre wavelength of corresponding D2 line.

When ρ (-1/2) ≠ ρ (+1/2), atom has birefringence.Polarizability P _x=ρ (+1/2)-ρ (-1/2).By n ₊(v), n _-v the expression formula of () brings θ formula into, obtain atomic spin precession detection model:

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

Adopt closed loop Faraday modulation method, then the light intensity magnitude that photodetector detects is:

I＝I ₀sin ²(θ+A·cosωt)

Wherein, Acos ω t is high-frequency modulation signal, and θ is plane of polarization corner.

Result after lock-in amplify is:

I _ω＝2I ₀·A·θ

According to the I that lock-in amplifier exports _ω, obtain deflection angle theta, then obtain and then obtain angular velocity information.

(3) active magnetic compensation model adopts the driver that three axle Helmholtz coilss compensate as Three-Dimensional Magnetic,

Had by BiotSavart's law:

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

Wherein, I is strength of current, for line element differential, for displacement vector, μ is magnetic permeability.

To its integration, and B=μ H is substituted into, obtains the set up current feedback magnetic-field measurement model based on active magnetic compensation technique:

The strength of current that it flows through is I, and the direction of current flowing is consistent with the direction of line element ds, and r is displacement vector, and H is required magnetic field.

2, making is measured sensing unit and is carried out high-frequency ac and heats without magnetoelectricity, place driving laser in z-axis direction, and adjust frequency as the D1 line of alkali metal atom, optical pumping is carried out to sensing unit, inject detection laser in x-axis, and adjust frequency as the D2 line of alkali metal atom;

3, the sensing unit that step 2 makes is placed in three axle Helmholtz coils centers, adopts the three-dimensional magnetic field original position active magnetic compensation method based on optical pumping to carry out active magnetic compensation, offset the magnetic field of sensing unit;

With the incident alkaline metal air chamber of circularly polarized light, make driving laser in z-axis direction, through the laser of alkaline metal air chamber, the P obtained after being absorbed by photodetector _transwith be directly proportional, define a positive coefficient k _pD, meet:

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

By P _transto B _xask local derviation, obtain:

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

R ₁, R ₂be respectively longitudinal relaxation rate and transverse relaxation rate, other physical quantity implications are the same.

Work as B _xwhen being tending towards 0, P _transincreasing always.Therefore, by regulating the compensating field size of x coil to obtain maximum P _trans.The compensation in z-axis magnetic field and x, y-axis are slightly distinguished.Work as B _zwhen being tending towards 0, P _transreducing always.Respectively field scan is carried out to x, y, z coil, finds compensation point to offset environmental magnetic field.

Concrete steps are:

(1) with circularly polarized light in z-axis direction incident alkaline metal air chamber, through the laser of alkaline metal air chamber, absorbed by photodetector;

(2) generation two compensating field B are attempted by x coil _cx1with B _cx2, compare the output P under these two magnetic fields _trans1with P _trans2if, P _trans1compare P _trans2greatly, then B _cx1make remnant field closer to zero, retain B _cx1, produce another B _cx2and compare, retain better compensating field, until P _trans1with P _trans2can not differentiate again, the error magnetic field Δ B of definition magnetic compensation _x=(B _cx1-B _cx2)/2, final compensating field B _cxfor (B _cx1+ B _cx2)/2;

(3) generation two compensating field B are attempted by y coil _cy1with B _cy2, compare the output P under these two magnetic fields _trans1with P _trans2if, P _trans1compare P _trans2greatly, then B _cy1make remnant field closer to zero, retain B _cy1, produce another B _cy2and compare, retain better compensating field, until P _trans1with P _trans2can not differentiate again, the error magnetic field Δ B of definition magnetic compensation _y=(B _cy1-B _cy2)/2, final compensating field B _cyfor (B _cy1+ B _cy2)/2;

(4) generation two compensating field B are attempted by z coil _cz1with B _cz2, compare the output P under these two magnetic fields fast _trans1with P _trans2if, P _trans1compare P _trans2little, then B _cz1make remnant field closer to zero, retain B _cz1, produce another B _cz2and compare, retain better compensating field, until P _trans1with P _trans2can not differentiate again, the error magnetic field Δ B of definition magnetic compensation _z=(B _cz1-B _cz2)/2, final compensating field B _czfor (B _cz1+ B _cz2)/2.

(5) step (2) ~ (4) are repeated, to find compensation point under physical environment magnetic field, to offset environmental magnetic field.

4, take z-axis as main field direction, the main field in step 3 aimed at step 2 driving laser:

After the alignment of orientation of driving laser and main field, the P of photoelectric detector _transexpression formula is:

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

Wherein physical quantity implication is the same.

A modulated magnetic field B is initiatively applied in x-axis _xfsin ω t, its constant value magnetic field is B _x0, when modulated magnetic field be ω lower time, the signal P of photoelectric detector _transfor:

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

Adjustment size, until the item no longer comprising in Output rusults that frequency is ω.

(1) by three-dimensional magnetic field active magnetic compensation method, by B _x, B _y, B _zbe adjusted to zero as much as possible; Initiatively produce a B _z, become main field;

(2) modulated magnetic field B is applied in x-axis _xfsin ω t, regulates driving laser in the azimuthal projection of x-axis, until P _transoutput no longer comprise the item that frequency is ω;

(3) modulated magnetic field B is applied in y-axis _yfsin ω t, regulates driving laser in the azimuthal projection of y-axis, until P _transoutput no longer comprise the item that frequency is ω;

(4) produce different main field strength, apply modulated magnetic field B in x-axis respectively _xfsin ω t, apply modulated magnetic field B in y-axis _yfsin ω t, inspection P _transoutput in whether comprise the item that frequency is ω, if without; would complete aligning; Otherwise repeat step (1) ~ (4).

5, after step 4 main field and driving laser alignment of orientation, x-axis and y-axis magnetic field convergence zero, handle driving laser, make alkali metal atom enter SERF state, then initiatively increase a main field B _z, carry out nuclear spin hyperpolarization, realize nuclear spin-electron spin strong coupling;

6, input angular velocity, according to the inertia angular velocity measurement model based on SERF atomic spin effect that step 1 is set up, adopts closed loop Faraday modulation detection method, extracts the information of detection laser Atom Spin precession, and then obtain inertia angular velocity; According to the current feedback magnetic-field measurement model based on active magnetic compensation technique that step 1 is set up, obtain the measured magnetic field under present carrier coordinate system.

Principle of the present invention is: adopt the nuclear spin of inert gas to be coupled with the electron spin of alkali metal atom, and the nuclear spin of inert gas is from motion tracking and compensate external magnetic field change, and isolation magnetic field is on the impact of alkali metal atom electron spin gyroscopic inertia; Carry out optical pumping with the driving laser of the carrier that is connected to atom, force atomic spin precession to the direction of driving laser, but have the gyroscopic inertia of inertial space due to it, atomic spin finally can depart from driving laser and produce an angle; Detect the change in atomic spin direction with detection laser, realize the measurement to angular velocity.

Because atomic spin also has magnetic moment while having angular momentum, atomic spin magnetic moment therefore can be utilized to realize the measurement to magnetic field to the response in magnetic field.Ultimate principle is: under Weak magentic-field effect, and atomic spin produces Larmor precession; On the other hand, under the effect of driving laser, driving laser can force atomic spin to get back to the sensing of driving laser.Therefore, under the acting in conjunction of Weak magentic-field and driving laser, atomic spin is pointed to will reach an equilibrium state, this sensing finally deviate from the direction of original driving laser, the degree departed from is relevant with the intensity in magnetic field with the pumping efficiency of driving laser, this fleet angle can be detected laser detection, by the electric current of adjustment Three-Dimensional Magnetic compensating coil, this angle is utilized to indicate the magnetic field of magnetic compensation coil and external magnetic field to offset, by reading the size of current be carried in three dimensional coils, can the size in calculation compensation magnetic field, thus realize the measurement to three-dimensional magnetic field.

The present invention's advantage is compared with prior art: the present invention combines inertia based on SERF atomic spin effect and magnetic field measurement technology, namely the SERF state atomic spin under adopting three-dimensional active magnetic compensation technique to realize unshielded magnetic field, and then carry out inertia angular velocity measurement and magnetic-field measurement, give the model of inertia, magnetic-field measurement, and give measurement scheme, inertia measurement, magnetic-field measurement are integrated in one, there is the advantage that measuring accuracy is high, independence is strong.

Accompanying drawing explanation

Fig. 1 is inertia of the present invention and magnetic field integrated measuring protocol procedures figure;

Fig. 2 is the hardware configuration schematic diagram of three-dimensional active magnetic bucking-out system.

Embodiment

As shown in Figure 1, 2, concrete grammar of the present invention is as follows:

1, set up the block mold of inertia/magnetic field integrated measurer, block mold comprises the inertia angular velocity measurement model based on SERF atomic spin effect and the current feedback magnetic-field measurement model based on active magnetic compensation technique;

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

Under the impact of external magnetic field, angular velocity of rotation, the polarizability of electron spin and nuclear spin, can use Bloch system of equations to be described as

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

Consider the relaxation of alkali metal atom electron spin and the nuclear spin of core inert gas and mutual polarization with driving detection laser optical pumping effect R _p, R _d, and the slowing factor Q (P that nuclear spin produces electron spin ^e) complete electron spin kinetic model can be obtained:

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

With nuclear spin kinetic model:

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

Wherein,

the electron-spin polarization rate of alkali metal atom;

the nuclear spin polarization rate of intert-gas atoms;

γ _e: the electron spin gyromagnetic ratio of alkali metal atom;

γ _n: the nuclear spin gyromagnetic ratio of intert-gas atoms;

Q (P ^e): slowing factor;

environmental magnetic field;

the magnetic field that the nuclear spin that electron spin is experienced produces;

the magnetic field that the electron spin that nuclear spin is experienced produces;

the light displacement that the electron spin of alkali metal atom is experienced, is equivalent to a magnetic field;

the rotational angular velocity of relative inertness system of carrier system;

R _p: the optical pumping rate of driving laser;

the photon angular momentum of driving laser transmits orientation;

R _d: the optical pumping rate of detection laser;

the photon angular momentum of detection laser transmits orientation;

nuclear spin pumping rate;

electron spin pumping rate;

total relaxation rate of alkali metal atom electron spin;

total relaxation rate of intert-gas atoms nuclear spin;

After carrying out magnetic compensation, remanent magnetism is only in z-axis direction.Longitudinal component with impact by cross stream component is little, with steady-state value all point to z-axis direction.Order only when z-axis vertical direction input angular velocity, with steady-state value do not affect by it, for:

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

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

Make detection laser point to x-axis detect order when tested rotational angular velocity is less, the steady state solution obtained after omitting higher order term is:

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

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

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

Control Δ B _zbe zero, control further to drive and detection laser, make L _x, L _y, L _z, R _dbe zero, above formula is reduced to further:

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

A branch of detection laser is supplemented again in y-axis direction, right measure; According to solve same thinking, be reduced to:

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

The measurement to y, x-axis directional angular velocity can be realized by above two formulas.

(2) atomic spin detects modeling: atomic spin precession detects the detection being mapped as line extreme polarisation of light face corner.

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

Wherein, θ is the rotation angle of plane of polarization, and v is the frequency of detection laser, and l is the length detecting the sensing unit that light passes through, and c is the light velocity, n ₊(v), n _-v () is for alkali metal vapour is to different polarization light σ ⁺, σ ^-refractive index n ₊(v), n _-(v), the refractive index of alkali metal vapour 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 atomic density, r _efor the electron radius of classics, f is resonant intensity, and other parameter physical significances are the same.

For alkaline metal D1 line,

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

Wherein, ρ (-1/2), ρ (+1/2) are the atomicity of different ground state population, v _d1the centre wavelength of corresponding D1 line.

To D2 line,

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

Wherein, v _d2the centre wavelength of corresponding D2 line.

When ρ (-1/2) ≠ ρ (+1/2), atom has birefringence.Polarizability P _x=ρ (+1/2)-ρ (-1/2).By n ₊(v), n _-v the expression formula of () brings θ formula into, obtain atomic spin precession detection model:

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

Adopt closed loop Faraday modulation method, then the light intensity magnitude that photodetector detects is:

I＝I ₀sin ²(θ+A·cosωt)(13)

Wherein, Acos ω t is high-frequency modulation signal, and θ is plane of polarization corner.

Result after lock-in amplify is:

I _ω＝2I ₀·A·θ(14)

According to the I that lock-in amplifier exports _ω, obtain deflection angle theta, then obtain and then obtain angular velocity information.

(3) active magnetic compensation model adopts the driver that three axle Helmholtz coilss compensate as Three-Dimensional Magnetic,

Had by Biot-Savart law

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

Wherein, I is strength of current, for line element differential, for displacement vector, μ is magnetic permeability.To its integration, and B=μ H is substituted into, obtains the set up current feedback magnetic-field measurement model based on active magnetic compensation technique:

The strength of current that it flows through is I, and the direction of current flowing is consistent with the direction of line element ds, and r is displacement vector, and H is required magnetic field.

2, the sensing unit of properly mixed alkaline metal-inert gas will be housed (containing 20Torr's ¹²⁹the N of Xe, 100Torr ₂, a Cs), adopt the high-frequency alternating current of 200KHz to be heated to about 110 DEG C without magnetic; Place driving laser in z-axis direction, and adjust frequency as the D1 line of alkali metal atom, with the power of 1W, optical pumping is carried out to sensing unit; Inject detection laser in x-axis, frequency elects the D2 line of Cs as simultaneously.

3, the sensing unit that step 2 makes is placed in three axle Helmholtz coils centers, adopts the three-dimensional magnetic field original position active magnetic compensation method based on optical pumping to carry out active magnetic compensation, offset the magnetic field of sensing unit;

The hardware configuration schematic diagram of three-dimensional active magnetic bucking-out system as shown in Figure 2, in figure, 1 is driving laser, 2 is beam expander, and 3 is polarizer, and 4 is quarter wave plate, 5 is Three-Dimensional Magnetic compensating coil, 6 is alkaline metal air chamber, and 7 is lens, and 8 is photodetector, 9 is tickler, 10,11,12 coils being respectively z, x, y-axis.

Driving laser is to the rear by expanding and rising, and passes through quarter wave plate.Atom in pumped alkali metal air chamber, the laser through air chamber is detected by photodetector after lens converge.

Based on the hardware configuration that Fig. 2 provides, Bloch system of equations is adopted to describe the dynamic process of electron spin in alkaline metal air chamber,

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

In formula, R ₁, R ₂be respectively longitudinal relaxation rate and transverse relaxation rate.In formula, the Section 1 on the right is the Larmor precession of electron spin under magnetic field, and Section 2 is the pumping effect of driving laser, and Section 3 is various relaxations.Ask the steady state solution of above-mentioned equation, obtain:

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

With the incident alkaline metal air chamber of circularly polarized light, make driving laser in z-axis direction, through the laser of alkaline metal air chamber, the P obtained after being absorbed by photodetector _transwith be directly proportional.Due to P _transwith be on the occasion of, then definable positive coefficient k _pD, meet:

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

By P _transto B _xask local derviation, obtain

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

Work as B _xwhen being tending towards 0, P _transincreasing always.Maximum P is obtained by regulating the compensating field size of x coil _trans, be compensate B _xa foundation.In like manner, the foundation in y-axis magnetic field can be compensated.The compensation in z-axis magnetic field and x, y-axis are slightly distinguished.Work as B _zwhen being tending towards 0, P _transreducing always.Respectively field scan is carried out to x, y, z coil, finds compensation point to offset environmental magnetic field.

Concrete steps are:

(1) with circularly polarized light in z-axis direction incident alkaline metal air chamber, through the laser of alkaline metal air chamber, absorbed by photodetector;

(2) generation two compensating field B are attempted by x coil _cx1with B _cx2, compare the output P under these two magnetic fields fast _trans1with P _trans2if, P _trans1compare P _trans2greatly, then B _cx1make remnant field closer to zero, retain B _cx1, produce another B _cx2and compare, retain better compensating field, until P _trans1with P _trans2can not differentiate again, the error magnetic field Δ B of definition magnetic compensation _x=(B _cx1-B _cx2)/2, final compensating field B _cxfor (B _cx1+ B _cx2)/2.Y-axis in like manner;

(3) generation two compensating field B are attempted by y coil _cy1with B _cy2, compare the output P under these two magnetic fields _trans1with P _trans2if, P _trans1compare P _trans2greatly, then B _cy1make remnant field closer to zero, retain B _cy1, produce another B _cy2and compare, retain better compensating field, until P _trans1with P _trans2can not differentiate again, the error magnetic field △ B of definition magnetic compensation _y=(B _cy1-B _cy2)/2, final compensating field B _cyfor (B _cy1+ B _cy2)/2;

(4) generation two compensating field B are attempted by z coil _cz1with B _cz2, compare the output P under these two magnetic fields fast _trans1with P _trans2if, P _trans1compare P _trans2little, then B _cz1make remnant field closer to zero, retain B _cz1, produce another B _cz2and compare, retain better compensating field, until P _trans1with P _trans2can not differentiate again, the error magnetic field Δ B of definition magnetic compensation _z=(B _cz1-B _cz2)/2, final compensating field B _czfor (B _cz1+ B _cz2)/2;

(5) step (2) ~ (4) are repeated, to find compensation point under physical environment magnetic field, to offset environmental magnetic field.

4, take z-axis as main field direction, the main field in step 3 aimed at step 2 driving laser:

A modulated magnetic field B is initiatively applied in x-axis _xfsin ω t, its constant value magnetic field is B _x0, when modulated magnetic field be ω lower time, the signal P of photoelectric detector _transfor:

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

Adjustment size, until the item no longer comprising in Output rusults that frequency is ω.

Concrete steps are:

(1) by three-dimensional magnetic field active magnetic compensation method, by B _x, B _y, B _zbe adjusted to zero as much as possible; Initiatively produce a B _z, become main field;

(2) modulated magnetic field B is applied in x-axis _xfsin ω t, regulates driving laser in the azimuthal projection of x-axis, until P _transoutput no longer comprise the item that frequency is ω;

(3) modulated magnetic field B is applied in y-axis _yfsin ω t, regulates driving laser in the azimuthal projection of y-axis, until P _transoutput no longer comprise the item that frequency is ω;

(4) produce different main field strength, apply modulated magnetic field B in x-axis respectively _xfsin ω t, apply modulated magnetic field B in y-axis _yfsin ω t, inspection P _transoutput in whether comprise the item that frequency is ω, if without; would complete aligning; Otherwise repeat step (1) ~ (4).

5, after step 4 main field and driving laser alignment of orientation, x-axis and y-axis magnetic field convergence zero, handle driving laser, make alkali metal atom enter SERF state, then initiatively increase a main field B _z, carry out nuclear spin hyperpolarization, realize nuclear spin-electron spin strong coupling.

6, at the angular velocity that the input of y-axis direction is less, detection laser points to x-axis, right detect.

First the light intensity I according to closed loop Faraday modulation and after lock-in amplify _ω, calculate linear polarization face rotation angle θ by (14) formula; Then according to (12) formula, calculate substitute into (6) to obtain y-axis directional angular velocity.

7, according to the current feedback magnetic-field measurement model based on active magnetic compensation technique that step 1 is set up, the measured magnetic field under present carrier coordinate system is obtained.

The content be not described in detail in instructions of the present invention belongs to the known prior art of professional and technical personnel in the field.

Claims (5)

1., based on inertia and the magnetic field integral measurement method of SERF atomic spin effect, it is characterized in that comprising the following steps:

(1) set up the block mold of inertia and magnetic field integrated measuring, described block mold comprises the inertia angular velocity measurement model based on SERF atomic spin effect and the current feedback magnetic-field measurement model based on active magnetic compensation technique;

(2) making is measured sensing unit and is carried out high-frequency ac and heats without magnetoelectricity, place driving laser in z-axis direction, and adjust frequency as the D1 line of alkali metal atom, optical pumping is carried out to measurement sensing unit, inject detection laser in x-axis, and adjust frequency as the D2 line of alkali metal atom; Described measurement sensing unit is the sensing unit of alkaline metal-inert gas, containing 20Torr's ¹²⁹the N of Xe, 100Torr ₂, except a Cs;

(3) the measurement sensing unit that step (2) makes is placed in three axle Helmholtz coils centers, adopts the three-dimensional magnetic field original position active magnetic compensation method based on optical pumping to carry out active magnetic compensation, offset the magnetic field of sensing unit;

(4) take z-axis as main field direction, the main field in step (3) and step (2) driving laser are carried out alignment of orientation;

(5) after step (4) main field and driving laser alignment of orientation, x-axis and y-axis magnetic field convergence zero, handle driving laser, initiatively increase a main field B _z, carry out nuclear spin hyperpolarization, realize nuclear spin-electron spin strong coupling;

(6) input angular velocity, according to the inertia angular velocity measurement model based on SERF atomic spin effect that step (1) is set up, adopt closed loop Faraday modulation detection method, extract the information of detection laser Atom Spin precession, and then obtain inertia angular velocity; According to the current feedback magnetic-field measurement model based on active magnetic compensation technique that step (1) is set up, obtain the measured magnetic field under present carrier coordinate system.

2. a kind of inertia based on SERF atomic spin effect according to claim 1 and magnetic field integral measurement method, is characterized in that: the inertia angular velocity measurement model based on SERF atomic spin effect in described step (1) comprises SERF state atomic spin kinetic model and atomic spin precession detection model:

(1) SERF state atomic spin kinetic model:

Under the impact of external magnetic field, angular velocity of rotation, the polarizability of electron spin and nuclear spin, uses Bloch system of equations to be described as:

Consider the relaxation of alkali metal atom electron spin and the nuclear spin of core inert gas and with driving detection laser optical pumping effect R _p, R _d, and the slowing factor Q (P that nuclear spin produces electron spin ^e) obtain complete electron spin kinetic model:

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

With nuclear spin kinetic 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 polarization rate of alkali metal atom;

the nuclear spin polarization rate of intert-gas atoms;

γ _e: the electron spin gyromagnetic ratio of alkali metal atom;

γ _n: the nuclear spin gyromagnetic ratio of intert-gas atoms;

Q (P ^e): slowing factor;

environmental magnetic field;

the magnetic field that the nuclear spin that electron spin is experienced produces;

the magnetic field that the electron spin that nuclear spin is experienced produces;

the light displacement that the electron spin of alkali metal atom is experienced, is equivalent to a magnetic field;

the rotational angular velocity of relative inertness system of carrier system;

R _p: the optical pumping rate of driving laser;

the photon angular momentum of driving laser transmits orientation;

R _d: the optical pumping rate of detection laser;

the photon angular momentum of detection laser transmits orientation;

nuclear spin pumping rate;

electron spin pumping rate;

total relaxation rate of alkali metal atom electron spin;

total relaxation rate of intert-gas atoms nuclear spin;

After carrying out active magnetic compensation, remanent magnetism only in z-axis direction, longitudinal component with impact by cross stream component is little, with steady-state value all point to z-axis direction, order only when the vertical direction input angular velocity of z-axis, with steady-state value do not affect by it, for:

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

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

Make detection laser point to x-axis detect order when tested rotational angular velocity is less, the steady state solution obtained after omitting higher order term is:

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

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

${\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 _zbe zero, control further to drive and detection laser, make L _x, L _y, L _z, R _dbe zero, above formula is reduced to further:

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

A branch of detection laser is supplemented again in y-axis direction, right measure; Finally be reduced to:

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

The measurement to x, y-axis directional angular velocity can be realized by above two formulas;

(2) atomic spin precession detection model:

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

Wherein, θ is the rotation angle of plane of polarization, and v is the frequency of detection laser, and l is the length of the sensing unit that detection laser is passed through, and c is the light velocity, n ₊(v), n _-v () is for alkali metal vapour is to different polarization light σ ⁺, σ ^-refractive index n ₊(v), n _-(v), the refractive index of alkali metal vapour 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 atomic density, r _efor the electron radius of classics, f is resonant intensity;

For alkaline metal D1 line,

$\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, ρ (-1/2), ρ (+1/2) are the atomicity of different ground state population, ν _d1the centre wavelength of corresponding D1 line;

To D2 line,

$\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, ν _d2the centre wavelength of corresponding D2 line;

When ρ (-1/2) ≠ ρ (+1/2), atom has birefringence; Polarizability P _x=ρ (+1/2)-ρ (-1/2), by n ₊(v), n _-v the expression formula of () brings θ formula into, obtain 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. a kind of inertia based on SERF atomic spin effect according to claim 1 and magnetic field integral measurement method, is characterized in that: the current feedback magnetic-field measurement model based on active magnetic compensation technique in described step (1) is as follows:

The driver adopting three axle Helmholtz coilss to compensate as Three-Dimensional Magnetic, is had by Biot-Savart law:

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

Wherein, I is strength of current, for line element differential, for displacement vector, μ is magnetic permeability; To its integration, and B=μ H is substituted into, obtains the set up current feedback magnetic-field measurement model based on active magnetic compensation technique:

The strength of current that it flows through is I, and the direction of current flowing is consistent with the direction of line element ds, and r is displacement vector, and H is required magnetic field.

4. a kind of inertia based on SERF atomic spin effect according to claim 1 and magnetic field integral measurement method, is characterized in that the three-dimensional magnetic field original position active magnetic compensation process in described step (3) is as follows:

(31) with circularly polarized light in z-axis direction incident alkaline metal air chamber, through the laser of alkaline metal air chamber, absorbed by photodetector;

(32) generation two compensating field B are attempted by x coil _cx1with B _cx2, compare the output P under these two magnetic fields _trans1with P _trans2if, P _trans1compare P _trans2greatly, then B _cx1make remnant field closer to zero, retain B _cx1, produce another B _cx2and compare, retain better compensating field, until P _trans1with P _trans2can not differentiate again, the error magnetic field △ B of definition magnetic compensation _x=(B _cx1-B _cx2)/2, final compensating field B _cxfor (B _cx1+ B _cx2)/2;

(33) generation two compensating field B are attempted by y coil _cy1with B _cy2, compare the output P under these two magnetic fields _trans1with P _trans2if, P _trans1compare P _trans2greatly, then B _cy1make remnant field closer to zero, retain B _cy1, produce another B _cy2and compare, retain better compensating field, until P _trans1with P _trans2can not differentiate again, the error magnetic field △ B of definition magnetic compensation _y=(B _cy1-B _cy2)/2, final compensating field B _cyfor (B _cy1+ B _cy2)/2;

(34) generation two compensating field B are attempted by z coil _cz1with B _cz2, compare the output P under these two magnetic fields _trans1with P _trans2if, P _trans1compare P _trans2little, then B _cz1make remnant field closer to zero, retain B _cz1, produce another B _cz2and compare, retain better compensating field, until P _trans1with P _trans2can not differentiate again, the error magnetic field △ B of definition magnetic compensation _z=(B _cz1-B _cz2)/2, final compensating field B _czfor (B _cz1+ B _cz2)/2;

(35) step (32) ~ (34) are repeated, to find compensation point under physical environment magnetic field, to offset environmental magnetic field.

5. a kind of inertia based on SERF atomic spin effect according to claim 1 and magnetic field integral measurement method, is characterized in that: the alignment of orientation method of carrying out in described step (4) realizes as follows:

(41) by three-dimensional magnetic field active magnetic compensation method, by B _x, B _y, B _zbe adjusted to zero as much as possible; Initiatively produce a B _z, become main field;

(42) modulated magnetic field B is applied in x-axis _xfsin ω t, regulates driving laser in the azimuthal projection of x-axis, until P _transoutput no longer comprise the item that frequency is ω;

(43) modulated magnetic field B is applied in y-axis _yfsin ω t, regulates driving laser in the azimuthal projection of y-axis, until P _transoutput no longer comprise the item that frequency is ω;

(44) produce different main field strength, apply modulated magnetic field B in x-axis respectively _xfsin ω t, apply modulated magnetic field B in y-axis _yfsin ω t, inspection P _transoutput in whether comprise the item that frequency is ω, if without; would complete aligning; Otherwise repeat step (41) ~ (44).