CN104833690B - A kind of atom magnetic resonance gyroscope alkali metal atom polarizability method for real-time measurement - Google Patents

Abstract

The present invention proposes a kind of atom magnetic resonance gyroscope alkali metal atom polarizability method for real-time measurement, belongs to Atomic Physics field.The present invention passes through to measure atom pond alkali metal atom density at different temperatures, measure again and the intert-gas atoms nuclear magnetic resonance frequency excursion leading to is polarized it becomes possible to obtain the polarizability of alkali metal atom in atom pond on the premise of not changing atom magnetic resonance gyroscope light channel structure and magnetic field environment due to alkali metal atom；Then set up the threedimensional model with temperature and the change of alkali metal atom polarizability for the atom pool gas inert atom nuclear magnetic resonance frequency excursion, in atom magnetic resonance gyroscope normal work, measure intert-gas atoms nuclear magnetic resonance, NMR (NMR) frequency displacement under arbitrary temperature spot it is possible to be calculated the polarizability of alkali metal atom in atom pond in real time.Measuring method proposed by the present invention is simple, does not affect magnetic resonance gyroscope light channel structure, significant to the performance improving atom magnetic resonance gyroscope.

Description

A kind of atom magnetic resonance gyroscope alkali metal atom polarizability method for real-time measurement

Technical field

The present invention relates to a kind of atom magnetic resonance gyroscope (Nuclear Magnetic Resonance Gyro, or NMRG) the method for alkali metal polarizability measurement, the method is passed through to measure in atom magnetic resonance gyroscope atom pond by static steady Magnetic field and alkali metal atom spin polarization coefficient intert-gas atoms nmr frequency, obtain alkali metal atom in real time Polarizability, belong to Atomic Physics field.

Background technology

In recent years, with the development of quantum theory, atom manipulation, micro-processing technology and contemporary optics, atomic sensor Modern science and technology are increasingly widely applied, from the research (NMR (Nuclear Magnetic Resonance)-imaging) to human brain to fortune The navigation level accurate measurement (atom magnetic resonance gyroscope) of animal body can find their figure.Increasing machine both at home and abroad Structure also carries out the research to sensors such as atom accelerometer, atom magnetometer, atom magnetic resonance gyroscopes in succession.Former at these In sub- device, atom pond is their core component.

Usually, alkali metal atom, intert-gas atoms and buffer gas atoms are comprised in atom pond, should according to different With requiring, some sensors are to polarize alkali metal atom directly as sensitive atom by optical pumping, such as atomic clock and nonmagnetic atom Power instrument etc.；Some sensors are then by optical pumping polarization alkali metal atom, then act on through overspin collision exchange, and alkali metal is former The polarization of son passes to intert-gas atoms, obtains carrier rotation angle speed by the Larmor precession frequency displacement of intert-gas atoms Degree, such as atom magnetic resonance gyroscope etc..

The ultimate principle of atom magnetic resonance gyroscope is：

In static steady magnetic field magnetic fieldUnder effect, there is nonzero spin angular momentumAtom produce around magnetostatic field direction Precession, its Larmor precession frequency:

Wherein γ is the gyromagnetic ratio of atom,For Larmor precession frequency.When system is around magnetostatic fieldWith angular velocity During rotation, actual observation to precession frequency be：

Due to Larmor precession frequencyIt is the amount determining when magnetostatic field is stablized, system be can be obtained by by formula (2) Rotational angular velocity

In order that a large amount of atoms have macroscopic magnetization vector in atom pondGenerally adopt optical pumping (Optical Pumping) technology, using alkali metal transition spectral line (such as⁸⁷The corresponding optical maser wavelength of the D1 line of Rb is 795nm) laser of respective frequencies Irradiated atoms pond, makes alkali metal atom produce polarization after absorbing photon, then will by spin-exchange (Spin Exchange) effect Polarization passes to noble gases (such as¹²⁹Xe and¹³¹Xe) atom, by intert-gas atoms Lai sensitive the external world rotational angular velocity, with On be exactly atom magnetic resonance gyroscope work ultimate principle.

Improve the detection accuracy of atom magnetic resonance gyroscope and job stability it is necessary to ensure noble gases in atom pond Atom has higher polarizability and stable precession frequency, but when atom magnetic resonance gyroscope works, detects light and pumping The power of light, and the change of atom pond temperature and atom pond inwall condition all can affect the spin of alkali metal atom in atom pond Polarizability, thus affecting precession frequency and the polarizability of intert-gas atoms, so when atom magnetic resonance gyroscope works, Realize the real-time measurement to alkali metal atom polarizability, thus provide for atom nuclear magnetic resonance, NMR close loop mode control system controlling letter Number accurate feedback, be very important.

In atom pond, the polarizability P of alkali metal atom can be expressed as：

In formula, R_pIt is pumping rate, R_rexIt is alkali metal atom spin relaxation speed, R_totBe including optical pumping and atom from Total relaxation rate of rotation relaxation：

R_tot=R_p+R_rex=a I_op+R_rex(4)

In formula,For the relation between pumping rate and pump light intensities, h is planck constant, and v is pumping optical frequency Rate, I_opFor pump light light intensity, for ensureing that in atom pond, alkali metal atom has higher polarizability, pump light is sufficiently strong, power Typically arrive hundreds of milliwatt magnitude tens, σ (v) is the absorption cross-section to different pumping frequency for the alkali metal atom, can basis Different inflation ratio Theoretical Calculation in atom pond obtain.

Document [1]【Fang Jian-Cheng,Wan Shuang-Ai and Chen Yao,“Measurement of¹²⁹Xe frequency shift due to Cs–¹²⁹Xe collisions,”Chin.Phys.B Vol.23,No.6 (2014).】In by measure total relaxation rate with light intensity variation relation, and measure different pumping by force under relaxation rate, then by Formula (3) can be obtained by the polarizability of corresponding alkali metal atom.But this method not only needs to change different light intensity values, Also need to measure alkali-metal relaxation rate, so change atom magnetic resonance gyroscope work system light channel structure it is impossible to Measure when the work of atom magnetic resonance gyroscope.

Document [2]【A.R.Young,S.Appelt,A.B.Baranga,C.Erickson and W.Happer, “Three-dimensional imaging of spin polarization of alkali-metal vapor in optical pumpingcells,”Appl.Phys.Lett.70,3081(1997).】By in the direction vertical with detecting light Upper applying and rubidium atomic electrons paramagnetic resonance (Electron Paramagnetic Resonance, EPR) the corresponding radio frequency of frequency Magnetic field, the circular polarization obtaining being modulated by radio-frequency (RF) magnetic field detects light transmission rate curve, and radio-frequency (RF) magnetic field passes through rubidium atom Zeeman substate When, the ratio of the relative area of absworption peak that each substate produces is proportional to the ratio of each energy level relative energy-level population, thus obtaining Rubidium atomic pola-rizability.In atom pond, alkali-metal electron paramagnetic resonance frequency is bigger than the Larmor frequency of intert-gas atoms A lot, magnetic field when in this way needing the magnetic field applying respective frequencies to be worked with atomic spin gyro is differed greatly, and And detection light path part is also inconsistent, measures therefore nor when atom magnetic resonance gyroscope works.

Content of the invention

The present invention can not measure in its atom pond in atom magnetic resonance gyroscope normal work in real time for prior art The defect of alkali metal atom polarizability, proposes intert-gas atoms core in a kind of atom magnetic resonance gyroscope atom pond by measurement The method that magnetic resonance frequency to measure alkali metal atom polarizability in real time.

The method is based on following principle：Due to intert-gas atoms nuclear magnetic resonance, NMR frequency in atom magnetic resonance gyroscope atom pond Shifting is proportional to alkali metal atom number density and polarizability, by measuring atom pond alkali metal atom density at different temperatures, Change left-handed (dextrorotation) polarization state of pumping circularly polarized light again thus obtaining the noble gases leading to due to alkali metal atom polarization Atom nuclear magnetic resonance frequency excursion is it becomes possible to obtain on the premise of not changing atom magnetic resonance gyroscope light channel structure and magnetic field environment The polarizability of alkali metal atom in atom pond；Then, by measuring alkali metal atom density with temperature in the atom pond obtaining Variation relation, calculates when temperature and alkali metal atom polarizability change, produces magnetic field by alkali metal atom polarization and led to Atom pond in intert-gas atoms nuclear magnetic resonance frequency excursion, thus setting up intert-gas atoms nuclear magnetic resonance frequency excursion in atom pond Threedimensional model with temperature and the change of alkali metal atom polarizability；Finally, in atom magnetic resonance gyroscope normal work, pass through Measure the intert-gas atoms nmr frequency at arbitrary temperature it is possible to be calculated alkali metal atom in atom pond in real time Polarizability.

The technical solution used in the present invention is：A kind of atom magnetic resonance gyroscope alkali metal atom polarizability side of measurement in real time Method, the method comprises the following steps：

S1：Density N (T) of alkali metal atom in measurement atom magnetic resonance gyroscope atom pond：

Alkali metal atom density in atom pond can be estimated by saturated vapor pressure empirical equation, but due to atom pond The absorption to alkali metal atom for the inwall, in atom pond during real work, the density of alkali metal atom is less than by saturated vapor pressure warp Test the calculated value of formula, so needing the alkali metal atom number density at different temperatures first to atom pond to survey Amount.During using laser illumination atom pond corresponding with alkali metal atom jump frequency, according to Lambert-Bill law, thoroughly Penetrate light intensity I_outWith detection light intensity I_inRelation be：

I_out=I_ine^-N(T)σ(v)L(5)

In formula, N (T) is the density of alkali metal atom in atom pond, raises with atom pond temperature and is gradually increased；σ (v) is alkali The absorption cross-section of metallic atom, can be calculated by the buffer gas being filled with atom pond, and L is the light path in atom pond, Determined by the shape in atom pond, size.

Alkali metal atom density N (T) transmission spectrum curve at different temperatures is first calculated by (5) formula, then with reality Transmission spectrum curve contrast under the different temperatures of border measurement, using least square fitting it is possible to obtain under different temperatures Alkali metal atom number density value N (T) in atom pond.

S2：Intert-gas atoms nuclear magnetic resonance frequency excursion in measurement atom magnetic resonance gyroscope atom pond：

When atom magnetic resonance gyroscope works, the noble gases nmr frequency being actually detected be steady magnetic field, The magnetic field that alkali metal polarization produces and system rotate coefficient result.In atom pond, the alkali metal atom of spin polarization can be led The nmr frequency causing intert-gas atoms is moved, and this frequency displacement leads to because fermi level interacts：

In formulaIt is the nuclear spin of intert-gas atoms,It is the electron spin of alkali metal atom, " → " represent this thing Reason amount is vector, do not have " → " representing the corresponding scalar value of this physical quantity, coupling constant α can be written as：

| ψ (R) | in formula²It is the alkali metal valency electron wave function square near intert-gas atoms core, g_sIt is Lande factor, μ_BIt is Bohr magneton,It is the nuclear magnetic moment of intert-gas atoms, under the downfield environment of atom magnetic resonance gyroscope work, The nuclear magnetic resonance frequency excursion of the intert-gas atoms being led to by alkali metal atom polarization can be written as：

In formula, h is Planck's constant, k₀It is enhancer, N (T) is alkali metal atom number density,<S_z>It is alkali metal valency electricity The polarization of son.Formula (8) can be written as further：

In formulaThe gyromagnetic ratio of intert-gas atoms, P is that in atom magnetic resonance gyroscope atom pond, alkali metal is former The polarizability of son, g_IFor the corresponding g-factor of intert-gas atoms,For reduced Planck constant, therefore by fermi level The resonance frequency shift of the intert-gas atoms that interaction leads to, can be described as by alkali metal atom polarization generation in atom pond The resonant frequency shift that magnetic field leads to, this magnetic field size is：

The direction in alkali metal atom polarization generation magnetic field and alkali metal electron spin orientation are related, therefore change pumping circle partially Shake the polarization state of light, thus it is possible to vary the orientation of alkali metal electron spin, thus changing the side that alkali metal atom polarization produces magnetic field To.When being respectively adopted left-handed and right-hand circular polarization optical pumping atom pond, the intert-gas atoms nmr frequency observing It is respectively：

Intert-gas atoms nmr frequency ω when contrast is respectively adopted left-handed and right-hand circular polarization optical pumping atom pond₁ And ω₂It is possible to obtain the intert-gas atoms nuclear magnetic resonance frequency excursion Δ ω being led to by alkali metal atom polarization in atom pond：

S3：Calculate the polarizability of alkali metal atom in magnetic resonance gyroscope atom pond：

This process is in two steps：

S3.1：The intert-gas atoms nuclear-magnetism being led to by alkali metal atom polarization in atom pond is obtained altogether according to formula (13) Shake frequency displacement Δ ω, calculates the magnetic field being produced by alkali metal atom polarization in atom pond：

Formula (10) can be written as further：

In formula it isIt is proportionality coefficient, be by the thing of intert-gas atoms and alkali metal atom in atom pond Reason characteristic determines, when determining alkali metal atom and intert-gas atoms species in atom pond,Value for a determination.

S3.2：Density N (T) according to alkali metal atom in atom pond calculated in step S1 and step S3.1 are fallen into a trap The proportionality coefficient obtainingIt is calculated the polarizability P of alkali metal atom in atom magnetic resonance gyroscope atom pond：

Therefore, by change pumping circularly polarized light left-handed or dextropolarization state it is possible to according to measurement noble gases Atom nuclear magnetic resonance frequency excursion Δ ω, is calculated the polarizability P of alkali metal atom in atom pond.

S4：Set up intert-gas atoms nmr frequency in atom magnetic resonance gyroscope atom pond golden with temperature T and alkali Belong to the threedimensional model of atomic polarizability P change：

In atom magnetic resonance gyroscope atom pond, alkali metal atom density N (T) with the empirical equation that temperature T changes is：

In formula, V amasss for atom cell body, and R is gas constant, is obtained in atom pond under different temperatures according to measurement in step S1 Density N (T) of alkali metal atom, carries out least square fitting to empirical equation (17), obtains alkali metal atom in atom pond The variation relation of density with temperature.Alkali metal atom polarization in atom pond can be obtained further according to formula (15) and produce magnetic fieldWith Alkali metal atom polarizability P and the change of atom pond temperature T：

Therefore, under optical pumping state, static steady magnetic field isWhen, it is lazy that atom magnetic resonance gyroscope is actually detected Property gas atom nmr frequency (Left-hand circular polarization optical pumping) is：

With atom pond temperature T and alkali metal atom polarizability P as coordinate axess, an atom nuclear-magnetism is set up according to (19) formula Resonance gyro intert-gas atoms nuclear magnetic resonance frequency excursion is with the three-dimensional mould of atom pond temperature and the change of alkali metal atom polarizability Type, when atomic nucleus magneto gyrocompass works, according to the intert-gas atoms nmr frequency ω that obtains of detection₁It is possible to according to This threedimensional model obtains the alkali metal atom polarizability P under corresponding temperature T.

Compared with prior art, the device have the advantages that being：

1. the present invention passes through to change the polarization state of pumping circularly polarized light, and in measurement atom pond, the nuclear-magnetism of intert-gas atoms is common Shake frequency displacement, thus being calculated the polarizability of alkali metal atom in atom pond, measuring method is simple, does not affect magnetic resonance gyroscope Light channel structure；

2. the intert-gas atoms nuclear magnetic resonance frequency excursion leading to alkali metal atom polarization is added to by static steady magnetic field In the Larmor precession frequency producing, thus it is golden with temperature and alkali to set up intert-gas atoms nmr frequency in atom pond Belong to atomic polarizability change threedimensional model, only need the nmr frequency of real-time monitoring intert-gas atoms it is possible to according to This threedimensional model obtains the alkali metal atom polarizability under corresponding temperature, realizes atom magnetic resonance gyroscope alkali metal polarizability Measure in real time, significant to the performance improving atom magnetic resonance gyroscope.

Brief description

Fig. 1 is atom magnetic resonance gyroscope device for measuring polarizability；

In figure：1. detecting laser, 2. beam-expanding collimation lens, 3. detection light beam, 4. steady magnetic field, 5. magnetic shielding cover, 6. Field coil, 7. incubation chamber, 8. atom pond, 9. lens, 10.Wave plate, 11. wollaston prisms, 12. balance photodetections Device, 13. computers, 14. pump lasers, 15.Wave plate, 16. reflecting mirrors, 17. pump beams.

Fig. 2 is atom magnetic resonance gyroscope polarizability method for real-time measurement flow chart；

Fig. 3 is atom magnetic resonance gyroscope intert-gas atoms nmr frequency with atom pond temperature and alkali metal atom Some threedimensional model schematic diagram that polarizability changes；

Specific embodiment

The present invention is further illustrated below in conjunction with the accompanying drawings, but should not therefore limit the scope of the invention.

As shown in figure 1, the atom magnetic resonance gyroscope device for measuring polarizability using the method for the invention is sharp by detecting Photonic system I, pumping laser subsystem II, temperature and magnetic field control subsystem III and Signal acquiring and processing subsystem IV tetra- Individual part composition；The function of described exploring laser light subsystem I is the density of alkali metal atom and indifferent gas in Measurement atom pond The nmr frequency of body atom, this subsystem is made up of detecting laser 1, beam-expanding collimation lens group 2, wherein detecting laser Alkali metal atom transition absorption curve can be obtained by rate of scanning in alkali metal atom density measure, detect intert-gas atoms During nmr frequency, frequency stable is at alkali metal atom transition absorption center of curve；Described pumping laser subsystem II is by pump Pu laser instrument 14,Wave plate 15 and beam-expanding collimation lens group 2 form, and wherein pump laser 14 is used for the alkali gold of output high-power Belong to the line polarized light of atomic transition absworption peak respective frequencies, pass throughWave plate 15 is changed into circularly polarized light, more saturating through beam-expanding collimation Microscope group 2 and reflecting mirror 16 are irradiated on atom pond 8, and then the alkali metal atom that polarizes；Described temperature and magnetic field control subsystem III Be made up of magnetic shielding cover 5, field coil 6, incubation chamber 7, atom pond 8, wherein magnetic shielding cover 5 be used for shield extraneous earth's magnetic field and its The interference in his magnetic field, shields precision 10^-9T, field coil 6 is used for producing the steady magnetic required for the work of atom magnetic resonance gyroscope Field and alternating magnetic field, incubation chamber 7 is used for heating the temperature in simultaneously stability contorting atom pond 8；Described Signal acquiring and processing subsystem System IV by lens 9,Wave plate 10, wollaston prism 11, balance photodetector 12, computer 13 form, and wherein lens 9 are used Emergent light is converged on balance photodetector 12,Wave plate 10 and wollaston prism 11 are used for separating the two of emergent light Individual quadrature component, processes the nmr frequency calculating intert-gas atoms in atom pond by computer 13.

The flow chart of measuring method of the present invention is as shown in Fig. 2 comprising the following steps that of the method：

1st, it is filled with a small amount of alkali metal in atom pond 8, this embodiment adopts rubidium, atom pond 8 is the pros of length of side 1cm Body, is filled with the N of 100torr in atom pond 8₂As buffer gas, and it is filled with 2torr's¹²⁹Xe is as the extraneous angle of rotation of detection The intert-gas atoms of speed.Atom pond 8 is put in incubation chamber 7, using no magnetic electrically heated mode, atom pond 8 is heated simultaneously Make its temperature stabilization in 80-120 degree.

2nd, measure the density of rubidium atom in atom magnetic resonance gyroscope atom pond 8, concretely comprise the following steps：

Adjusting detecting laser 1 makes output laser swept frequency range through alkali metal atom transition center frequency, by balance Photodetector 12 collects the absorption curve that transmitted light intensity changes with frequency, according to I_out=I_ine^-N(T)σ(v)LTheoretical Calculation is not With the absorption curve of rubidium atom under density, the curve obtaining with experiment measurement carries out least square fitting it is possible to calculate To in atom pond 8, rubidium atom number density is 2.31 × 10 when 90 degree¹²cm^-3.Adjust heating box 7 temperature control burtons so that it may To obtain atom pond rubidium atomic density value in atom pond at different temperatures.

3rd, in measurement atom magnetic resonance gyroscope atom pond 8¹²⁹Xe atom nuclear magnetic resonance frequency excursion：

Driving magnetic field coil 6 produces longitudinal magnetostatic field that size is 10.27uTIt is applied across intert-gas atoms simultaneously The lateral magnetic field of Larmor precession frequency carries out frequency sweep, the signal obtaining is carried out Fourier transformation, obtains¹²⁹Xe atom Actual precession frequency is：

WillWave plate 15 rotates 90 degree, makes the polarization reversal of rubidium atom in atom pond 8, then apply lateral magnetic field to carry out Frequency sweep, obtains¹²⁹The actual precession frequency of Xe atom is：

Can obtain being led to by the polarization of rubidium atom in atom pond 8¹²⁹The nuclear magnetic resonance frequency excursion of Xe atom is：

Wherein：γ_Xe=2 π × 11.86Hz/ μ T,

The rubidium atomic density 2.31 × 10 when 90 degree being obtained according to measurement¹²cm^-3, now atom pond can be calculated Interior rubidium atomic pola-rizability is P_Rb=2<S_z>=69.2%.

4th, set up intert-gas atoms nmr frequency in atom magnetic resonance gyroscope atom pond 8 golden with temperature and alkali Belong to the threedimensional model of atomic polarizability change：

According to measuring relation N that in the atom pond obtaining, rubidium atom varies with temperature in step 2_Rb(T), can be with Theoretical Calculation The relation being changed with atom pond 8 temperature and rubidium atomic polarizability due to the magnetic field that the polarization of rubidium atom produces：

And then can be according to formula：It is calculated¹²⁹Xe atom nuclear-magnetism Resonant frequency is with the value of atom pond temperature and the change of rubidium atomic polarizability.With atom pond temperature and alkali metal atom polarizability it is Coordinate axess, as shown in figure 3, set up an atom magnetic resonance gyroscope intert-gas atoms nuclear magnetic resonance frequency excursion with atom pond temperature And the threedimensional model of alkali metal atom polarizability change, while atom magnetic resonance gyroscope works, obtained according to detection Intert-gas atoms nmr frequency it is possible to obtain the alkali metal atom polarizability under corresponding temperature according to model.Example As when temperature be 90 degree when, if detect obtain intert-gas atoms nmr frequency be 121.882Hz it is possible to according to The polarizability that this model obtains alkali metal atom in atom pond is 35%.

Claims (1)

1. a kind of atom magnetic resonance gyroscope alkali metal atom polarizability method for real-time measurement it is characterised in that the method include with Lower step：

S1：Density N (T) of alkali metal atom in measurement atom magnetic resonance gyroscope atom pond：

During using laser illumination atom pond corresponding with alkali metal atom jump frequency, according to Lambert-Bill law, thoroughly Penetrate light intensity I_outWith detection light intensity I_inRelation be：

I_out=I_ine^-N(T)σ(v)L(1)

In formula, N (T) is the density of alkali metal atom in atom pond, raises with atom pond temperature and is gradually increased；σ (v) is alkali metal The absorption cross-section of atom, can be calculated by the buffer gas being filled with atom pond, L is the light path in atom pond, by former The shapes and sizes of subpool determine；

Alkali metal atom density N (T) transmission spectrum curve at different temperatures is first calculated by (1) formula, then surveys with actual Transmission spectrum curve contrast under the different temperatures of amount, using least square fitting it is possible to obtain atom under different temperatures Alkali metal atom number density value N (T) in pond；

S2：Intert-gas atoms nuclear magnetic resonance frequency excursion in measurement atom magnetic resonance gyroscope atom pond：

In atom pond, the alkali metal atom of spin polarization can lead to the nmr frequency of intert-gas atoms to be moved, this frequency Shifting leads to because fermi level interacts：

$\mathrm{\&alpha;}\stackrel{\&RightArrow;}{K}\&CenterDot;\stackrel{\&RightArrow;}{S}---\left(2\right)$

In formulaIt is the nuclear spin of intert-gas atoms,It is the electron spin of alkali metal atom, " → " represent that this physical quantity is Vector, do not have " → " representing the corresponding scalar value of this physical quantity, coupling constant α can be written as：

$\mathrm{\&alpha;}=\frac{8\mathrm{\&pi;}}{3}{g}_s{\mathrm{\&mu;}}_B\frac{{\mathrm{\&mu;}}_K}{K}|\mathrm{\&psi;}\left(R\right){|}^2---\left(3\right)$

| ψ (R) | in formula²It is the alkali metal valency electron wave function square near intert-gas atoms core, g_sIt is Lande factor, μ_BIt is Bohr magneton,It is the nuclear magnetic moment of intert-gas atoms, under the downfield environment of atom magnetic resonance gyroscope work, by alkali The nuclear magnetic resonance frequency excursion of the intert-gas atoms that metallic atom polarization leads to can be written as：

$\mathrm{\&Delta;}\mathrm{\&omega;}=-\frac{1}{h}\frac{\left|{\mathrm{\&mu;}}_K\right|}{K}\frac{8\mathrm{\&pi;}}{3}{\mathrm{\&mu;}}_B{g}_s{k}_{0}N\left(T\right)<S_z>---\left(4\right)$

In formula, h is Planck's constant, k₀It is enhancer, N (T) is the density of alkali metal atom,<S_z>It is alkali metal valency electron Polarization；Formula (4) can be written as further：

In formulaFor the gyromagnetic ratio of intert-gas atoms, P is alkali metal atom in atom magnetic resonance gyroscope atom pond Polarizability, g_IFor the corresponding g-factor of intert-gas atoms,For reduced Planck constant, therefore mutual by fermi level Act on the resonance frequency shift of the intert-gas atoms leading to, the magnetic field being produced by alkali metal atom polarization in atom pond can be described as The resonant frequency shift leading to, this magnetic field size is：

$\stackrel{\&RightArrow;}{B}=\frac{4}{3}{k}_0{g}_s{\stackrel{\&RightArrow;}{\mathrm{\&mu;}}}_{B}N\left(T\right)P---\left(6\right)$

Alkali metal atom polarization produces the direction in magnetic field and alkali metal electron spin is orientated related, therefore change pumping circularly polarized light Polarization state, thus it is possible to vary the orientation of alkali metal electron spin, thus change alkali metal atom polarization produce magnetic field direction；When When being respectively adopted left-handed and right-hand circular polarization optical pumping atom pond, the intert-gas atoms nmr frequency observing is respectively For：

${\mathrm{\&omega;}}_1=\mathrm{\&gamma;}({\stackrel{\&RightArrow;}{B}}_0+\stackrel{\&RightArrow;}{B})---\left(7\right)$

${\mathrm{\&omega;}}_2=\mathrm{\&gamma;}({\stackrel{\&RightArrow;}{B}}_0-\stackrel{\&RightArrow;}{B})---\left(8\right)$

Intert-gas atoms nmr frequency ω when contrast is respectively adopted left-handed and right-hand circular polarization optical pumping atom pond₁With ω₂It is possible to obtain the intert-gas atoms nuclear magnetic resonance frequency excursion Δ ω being led to by alkali metal atom polarization in atom pond：

$\mathrm{\&Delta;}\mathrm{\&omega;}=\mathrm{\&gamma;}\stackrel{\&RightArrow;}{B}=\frac{1}{2}({\mathrm{\&omega;}}_1-{\mathrm{\&omega;}}_2)---\left(9\right)$

S3：Calculate the polarizability of alkali metal atom in magnetic resonance gyroscope atom pond：

This process is in two steps：

S3.1：Obtain the intert-gas atoms nuclear magnetic resonance, NMR frequency being led to by alkali metal atom polarization in atom pond according to formula (9) Move Δ ω, calculate the magnetic field being produced by alkali metal atom polarization in atom pond：

$\stackrel{\&RightArrow;}{B}=\frac{\mathrm{\&Delta;}\mathrm{\&omega;}}{\mathrm{\&gamma;}}---\left(10\right)$

Formula (6) can be written as further：

$\stackrel{\&RightArrow;}{B}=\frac{4}{3}{k}_0{g}_s{\stackrel{\&RightArrow;}{\mathrm{\&mu;}}}_{B}N\left(T\right)P=\stackrel{\&RightArrow;}{k}\&CenterDot;N\left(T\right)\&CenterDot;P---\left(11\right)$

In formula it isIt is proportionality coefficient, be by the physical characteristics of intert-gas atoms and alkali metal atom in atom pond Determine, when determining alkali metal atom and intert-gas atoms species in atom pond,Value for a determination；

S3.2：Calculate in density N (T) according to alkali metal atom in atom pond calculated in step S1 and step S3.1 The proportionality coefficient arrivingIt is calculated the polarizability P of alkali metal atom in atom magnetic resonance gyroscope atom pond：

$P=\frac{\stackrel{\&RightArrow;}{B}}{\stackrel{\&RightArrow;}{k}\&CenterDot;N\left(T\right)}---\left(12\right)$

Therefore, by change pumping circularly polarized light left-handed or dextropolarization state it is possible to according to measurement intert-gas atoms Nuclear magnetic resonance frequency excursion Δ ω, is calculated the polarizability P of alkali metal atom in atom pond；

S4：Set up intert-gas atoms nmr frequency in atom magnetic resonance gyroscope atom pond former with temperature T and alkali metal The threedimensional model of muon polarization rate P change：

In atom magnetic resonance gyroscope atom pond, alkali metal atom density N (T) with the empirical equation that temperature T changes is：

${\log }_{10}\left(N\right(T)RT/V)=15.88253-\frac{4529.635}{T}+0.00058663T-2.99138{\log }_{10}T---\left(13\right)$

In formula, V amasss for atom cell body, and R is gas constant, obtains alkali gold in atom pond under different temperatures according to measurement in step S1 Belong to density N (T) of atom, least square fitting is carried out to empirical equation (13), obtains alkali metal atom density in atom pond Variation with temperature relation；Alkali metal atom polarization in atom pond can be obtained further according to formula (11) and produce magnetic fieldWith alkali gold Belong to the change of atomic polarizability P and atom pond temperature T：

$\stackrel{\&RightArrow;}{B}=\frac{4}{3}{k}_0{g}_s{\stackrel{\&RightArrow;}{\mathrm{\&mu;}}}_{B}N\left(T\right)P=\stackrel{\&RightArrow;}{B}(T,P)---\left(14\right)$

Therefore, under optical pumping state, static steady magnetic field isWhen, atom magnetic resonance gyroscope be actually detected left-handed Under circularly polarized light pumping condition, intert-gas atoms nmr frequency is：

${\mathrm{\&omega;}}_1=\mathrm{\&gamma;}({\stackrel{\&RightArrow;}{B}}_0+\stackrel{\&RightArrow;}{B})=A+\mathrm{\&gamma;}\stackrel{\&RightArrow;}{B}(T,P)---\left(15\right)$

With atom pond temperature T and alkali metal atom polarizability P as coordinate axess, an atom nuclear magnetic resonance, NMR is set up according to (15) formula The threedimensional model that gyro intert-gas atoms nuclear magnetic resonance frequency excursion changes with atom pond temperature and alkali metal atom polarizability, During the work of atomic nucleus magneto gyrocompass, the intert-gas atoms nmr frequency ω being obtained according to detection₁It is possible to according to this three-dimensional Model obtains the alkali metal atom polarizability P under corresponding temperature T.