CN104833690A - Method for measuring alkali metal atomic polarizability of nuclear magnetic resonance gyro in real time - Google Patents

Abstract

The invention provides a method for measuring alkali metal atomic polarizability of a nuclear magnetic resonance gyro in real time and belongs to the field of atomic physics. The method includes: measuring alkali metal atomic densities of an atomic pool at different temperatures, measuring atomic nuclear magnetic resonance frequency of inert gas caused by polarization of alkali metal atoms, and thus acquiring polarizability of the alkali metal atoms in the atomic pool without changing the optical path structure of the nuclear magnetic resonance gyro and the magnetic field environment; building a three-dimensional model of changes in nuclear magnetic resonance frequency of the inert gas in the atomic pool along with temperature and the alkali metal atomic polarizability, measuring the frequency shift of atomic NMR (nuclear magnetic resonance) of the inert gas at any temperature point while the nuclear magnetic resonance frequency normally runs, and thus calculating the polarizability of the alkali metal atoms in the atomic pool in real time. The method has the advantages that the method is simple, no influence is caused to the optical path structure of the nuclear magnetic resonance gyro and the method is of great significance to improving the performance of the nuclear magnetic resonance gyro.

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) alkaline metal polarizability measure method, the method is by measuring in atom magnetic resonance gyroscope atom pond by static steady magnetic field and the coefficient intert-gas atoms nmr frequency of alkali metal atom spin polarization, obtain the polarizability of alkali metal atom in real time, belong to atomic physics field.

Background technology

In recent years, along with the development of quantum theory, atom manipulation, micro-processing technology and contemporary optics, atomic sensor obtains applying more and more widely in modern science and technology, accurately measures the figure that (atom magnetic resonance gyroscope) can find them from the research (Magnetic resonance imaging) to human brain to the navigation level of moving object.Increasing mechanism also carries out the research to sensors such as atom adding velograph, atom magnetometer, atom magnetic resonance gyroscopes in succession both at home and abroad.In these atom devices, atom pond is their core component.

Usually, comprise alkali metal atom, intert-gas atoms and buffer gas atoms in atom pond, according to different application requirements, some sensors are by optical pumping polarization alkali metal atom directly as sensitive atom, as atomic clock and atom magnetometer etc.; Some sensors then to be polarized alkali metal atom by optical pumping, again through the effect of overspin collision exchange, the polarization of alkali metal atom is passed to intert-gas atoms, obtains carrier rotation angular velocity, as atom magnetic resonance gyroscope etc. by the Larmor precession frequency displacement of intert-gas atoms.

The ultimate principle of atom magnetic resonance gyroscope is:

In static steady magnetic field magnetic field under effect, there is nonzero spin angular momentum atom around static magnetic field direction produce precession, its Larmor precession frequency:

$\stackrel{\→}{{\mathrm{\ω}}_L}=\mathrm{\γ}\stackrel{\→}{B_0}---\left(1\right)$

Wherein γ is the gyromagnetic ratio of atom, for Larmor precession frequency.When system is around static magnetic field with angular velocity during rotation, actual observation to precession frequency be:

${\stackrel{\→}{{\mathrm{\ω}}_L}}^{\′}=\mathrm{\γ}\stackrel{\→}{B_0}-\stackrel{\→}{{\mathrm{\ω}}_R}---\left(2\right)$

Due to Larmor precession frequency be the amount determined when static magnetic field is stablized, just can be obtained the rotational angular velocity of system by formula (2)

In order to make a large amount of atom in atom pond, there is macroscopic magnetization vector usual employing optical pumping (OpticalPumping) technology, use alkaline metal transition spectral line (as ⁸⁷the corresponding optical maser wavelength of the D1 line of Rb is 795nm) the laser irradiated atoms pond of respective frequencies, produce polarization after making alkali metal atom absorb photons, then by spin-exchange (SpinExchange) act on polarization passed to inert gas (as ¹²⁹xe and ¹³¹xe) atom, carrying out responsive extraneous rotational angular velocity by intert-gas atoms, is exactly more than the ultimate principle of atom magnetic resonance gyroscope work.

Improve detection accuracy and the job stability of atom magnetic resonance gyroscope, will ensure that in atom pond, intert-gas atoms has higher polarizability and stable precession frequency, but when atom magnetic resonance gyroscope works, the power of detection light and pump light, and the change of atom pond temperature and atom pond inwall condition all can affect the spin polarizability of alkali metal atom in atom pond, thus affect 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 the accurate feedback of control signal for atomic nucleus magnetic resonance close loop mode control system, very important.

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

$P=\frac{R_p}{R_p+R_{\mathrm{rex}}}=\frac{R_p}{R_{\mathrm{tot}}}---\left(3\right)$

In formula, R _ppumping rate, R _rexalkali metal atom spin relaxation speed, R _totthe total relaxation rate comprising optical pumping and atomic spin 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 pump light frequency, I _opfor pump light light intensity, for ensureing that in atom pond, alkali metal atom has higher polarizability, pump light is enough strong, power generally arrives hundreds of milliwatt magnitude tens, σ (v), for alkali metal atom is to the absorption cross section of different pumping frequency, can obtain according to the difference inflation ratio theory calculate in atom pond.

Document [1] [Fang Jian-Cheng, Wan Shuang-Ai and Chen Yao, " Measurement of ¹²⁹xefrequency shift due to Cs – ¹²⁹xe collisions; " Chin.Phys.B Vol.23, No.6 (2014) .] total in by measuring relaxation rate with the variation relation of light intensity, and measure different pumping relaxation rate lower by force, more just can be obtained the polarizability of alkali metal atom of correspondence by formula (3).But this method not only needs to change different light intensity values, also needs to measure alkali-metal relaxation rate, and then changes the light channel structure of atom magnetic resonance gyroscope work system, can not 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 applying and rubidium atomic electrons paramagnetic resonance (Electron Paramagnetic Resonance on the direction vertical with detection light, EPR) radio-frequency (RF) magnetic field that frequency is corresponding, obtain the circular polarization detection light transmission rate curve by radio-frequency (RF) magnetic field modulation, when radio-frequency (RF) magnetic field is by rubidium atom Zeeman substate, the ratio of the relative area of the absorption peak that each substate produces is proportional to the ratio of each energy level relative energy-level population, thus obtain rubidium atomic pola-rizability.In atom pond, alkali-metal electron paramagnetic resonance frequency is more much larger than the Larmor frequency of intert-gas atoms, magnetic field when in this way needing the magnetic field of applying respective frequencies and atomic spin gyro to work differs greatly, and it is also inconsistent to detect light path part, therefore can not measure when atom magnetic resonance gyroscope works.

Summary of the invention

The present invention is directed to prior art can not measure alkali metal atom polarizability in its atom pond in real time defect when atom magnetic resonance gyroscope normally works, proposing a kind ofly to measure the method for alkali metal atom polarizability in real time by measuring intert-gas atoms nmr frequency in atom magnetic resonance gyroscope atom pond.

The method is based on following principle: because in atom magnetic resonance gyroscope atom pond, intert-gas atoms nuclear magnetic resonance frequency excursion 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 obtain polarizing the intert-gas atoms nuclear magnetic resonance frequency excursion caused due to alkali metal atom, just can obtain the polarizability of alkali metal atom in atom pond under the prerequisite not changing atom magnetic resonance gyroscope light channel structure and magnetic field environment; Then, the variation relation of alkali metal atom density with temperature in the atom pond obtained by measurement, calculate when temperature and the change of alkali metal atom polarizability, the nuclear magnetic resonance frequency excursion of intert-gas atoms in the atom pond caused by alkali metal atom polarization generation magnetic field, thus set up the three-dimensional model that in atom pond, intert-gas atoms nuclear magnetic resonance frequency excursion changes with temperature and alkali metal atom polarizability; Finally, when atom magnetic resonance gyroscope normally works, by measuring the intert-gas atoms nmr frequency at arbitrary temperature, just can calculate the polarizability of alkali metal atom in atom pond in real time.

The technical solution used in the present invention is: a kind of atom magnetic resonance gyroscope alkali metal atom polarizability method for real-time measurement, and the method comprises the following steps:

S1: the density N (T) measuring alkali metal atom in atom magnetic resonance gyroscope atom pond:

Alkali metal atom density in atom pond can be estimated by saturated vapor pressure experimental formula, but because atom pond inwall is to the absorption of alkali metal atom, during real work in atom pond the density of alkali metal atom lower than the value calculated by saturated vapor pressure experimental formula, so need first to measure atom pond alkali metal atom number density at different temperatures.When adopting the laser illumination atom pond corresponding with alkali metal atom jump frequency, according to Lambert-Bill law, transmitted light intensity I _outwith detection light intensity I _inpass 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, and raising with atom pond temperature increases gradually; The absorption cross section that σ (v) is alkali metal atom, can be calculated by the buffer gas be filled with in atom pond, and L is the light path in atom pond, is 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, contrast with the transmission spectrum curve under the different temperatures of actual measurement again, adopt least square fitting, just can to obtain under different temperatures alkali metal atom number density value N (T) in atom pond.

S2: measure intert-gas atoms nuclear magnetic resonance frequency excursion in atom magnetic resonance gyroscope atom pond:

When atom magnetic resonance gyroscope works, the magnetic field that the inert gas nmr frequency be actually detected is steady magnetic field, alkaline metal polarization produces and system rotate coefficient result.The alkali metal atom of spin polarization in atom pond can cause the nmr frequency of intert-gas atoms to be moved, and this frequency displacement causes because Fermi level interacts:

$\mathrm{\α}\stackrel{\→}{K}\·\stackrel{\→}{S}---\left(6\right)$

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

$\mathrm{\α}=\frac{8\mathrm{\π}}{3}{g}_s{\mathrm{\μ}}_B\frac{{\mathrm{\μ}}_K}{K}{\left|\mathrm{\ψ}\left(R\right)\right|}^2---\left(7\right)$

In formula | ψ (R) | ²the alkaline metal valence electron wave function square near intert-gas atoms core, g _slande factor, μ _bbohr magneton, be the nuclear magnetic moment of intert-gas atoms, under the downfield environment of atom magnetic resonance gyroscope work, can be written as by the polarize nuclear magnetic resonance frequency excursion of the intert-gas atoms caused of alkali metal atom:

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

In formula, h is Planck's constant, k ₀be enhancer, N (T) is alkali metal atom number density, <S _z> is the polarization of alkaline metal valence electron.Formula (8) can be written as further:

In formula the gyromagnetic ratio of intert-gas atoms, P is the polarizability of alkali metal atom in atom magnetic resonance gyroscope atom pond, g _ifor the g factor that intert-gas atoms is corresponding, for reduced Planck constant, the resonance frequency shift of the intert-gas atoms caused that therefore interacted by Fermi level, can be described as the resonant frequency shift caused by the magnetic field of alkali metal atom polarization generation in atom pond, this magnetic field size is:

$\stackrel{\&RightArrow;}{B}=\frac{4}{3}{k}_0{g}_s{\stackrel{\&RightArrow;}{\mathrm{\&mu;}}}_{B}N\left(T\right)P---\left(10\right)$

The direction that alkali metal atom polarization produces magnetic field is relevant to alkaline metal electron spin orientation, therefore changes the polarization state of pumping circularly polarized light, can change the orientation of alkaline metal electron spin, thus changes the direction that alkali metal atom polarization produces magnetic field.When adopting left-handed and right-hand circular polarization optical pumping atom pond respectively, the intert-gas atoms nmr frequency observed is respectively:

${\mathrm{\&omega;}}_1=\mathrm{\&gamma;}({\stackrel{\&RightArrow;}{B}}_0+\stackrel{\&RightArrow;}{B})---\left(11\right)$

${\mathrm{\&omega;}}_2=\mathrm{\&gamma;}({\stackrel{\&RightArrow;}{B}}_0-\stackrel{\&RightArrow;}{B})---\left(12\right)$

Contrast intert-gas atoms nmr frequency ω when adopting left-handed and right-hand circular polarization optical pumping atom pond respectively ₁and ω ₂, just can obtain being polarized the intert-gas atoms nuclear magnetic resonance frequency excursion Δ ω caused by alkali metal atom in atom pond:

$\mathrm{\&Delta;\&omega;}=\mathrm{\&gamma;}\stackrel{\&RightArrow;}{B}=\frac{1}{2}({\mathrm{\&omega;}}_1-{\mathrm{\&omega;}}_2)---\left(13\right)$

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

This process is in two steps:

S3.1: obtain being polarized the intert-gas atoms nuclear magnetic resonance frequency excursion Δ ω caused by alkali metal atom in atom pond according to formula (13), calculates and to be polarized the magnetic field produced by alkali metal atom in atom pond:

$\stackrel{\&RightArrow;}{B}=\frac{\mathrm{\&Delta;\&omega;}}{\mathrm{\&gamma;}}---\left(14\right)$

Formula (10) can be written as further:

$\stackrel{\&RightArrow;}{B}=\frac{4}{3}{k}_0{g}_s{\stackrel{\&RightArrow;}{\mathrm{\&mu;}}}_{B}N\left(T\right)P=\stackrel{\&RightArrow;}{k}\&CenterDot;N\left(T\right)\&CenterDot;P---\left(15\right)$

In formula be being scale-up factor, is determined by the physical characteristics of intert-gas atoms and alkali metal atom in atom pond, when determining alkali metal atom and intert-gas atoms kind in atom pond, it is the value determined.

S3.2: according to the scale-up factor calculated in the density N (T) of alkali metal atom in the atom pond calculated in step S1 and step S3.1 calculate the polarizability P of alkali metal atom in atom magnetic resonance gyroscope atom pond:

$P=\frac{\stackrel{\&RightArrow;}{B}}{\stackrel{\&RightArrow;}{k}\&CenterDot;N\left(T\right)}---\left(16\right)$

Therefore, by changing the left-handed or dextropolarization state of pumping circularly polarized light, just according to the intert-gas atoms nuclear magnetic resonance frequency excursion Δ ω measured, the polarizability P of alkali metal atom in atom pond can be calculated.

S4: set up the three-dimensional model that in atom magnetic resonance gyroscope atom pond, intert-gas atoms nmr frequency changes with temperature T and alkali metal atom polarizability P:

The experimental formula that in atom magnetic resonance gyroscope atom pond, alkali metal atom density N (T) changes with temperature T is:

${\log }_{10}(N\left(T\right)\mathrm{RT}/V)=15.88253-\frac{4529.635}{T}+0.00058663T-2.99138\mathrm{lo}{g}_{10}T---\left(17\right)$

In formula, V is atom pond volume, R is gas law constant, according to measuring the density N (T) obtaining alkali metal atom in atom pond under different temperatures in step S1, least square fitting is carried out to experimental formula (17), obtains the variation relation of alkali metal atom density with temperature in atom pond.Alkali metal atom polarization in atom pond can be obtained according to formula (15) again and produce magnetic field change with alkali metal atom polarizability P and atom pond temperature T:

$\stackrel{\&RightArrow;}{B}=\frac{4}{3}{k}_0{g}_s{\stackrel{\&RightArrow;}{\mathrm{\&mu;}}}_{B}N\left(T\right)P=\stackrel{\&RightArrow;}{B}(T,P)---\left(18\right)$

Therefore, under optical pumping state, static steady magnetic field is time, the intert-gas atoms nmr frequency (Left-hand circular polarization optical pumping) that atom magnetic resonance gyroscope is actually detected is:

${\mathrm{\&omega;}}_1=\mathrm{\&gamma;}({\stackrel{\&RightArrow;}{B}}_0+\stackrel{\&RightArrow;}{B})=A+\mathrm{\&gamma;}\stackrel{\&RightArrow;}{B}(T,P)---\left(19\right)$

With atom pond temperature T and alkali metal atom polarizability P for coordinate axis, according to (19) formula set up an atom magnetic resonance gyroscope intert-gas atoms nuclear magnetic resonance frequency excursion with atom pond temperature and alkali metal atom polarizability change three-dimensional model, when atomic nucleus magneto gyrocompass works, according to detecting the intert-gas atoms nmr frequency ω obtained ₁, the alkali metal atom polarizability P under corresponding temperature T just can be obtained according to this three-dimensional model.

Compared with prior art, the beneficial effect that the present invention has is:

1. the present invention is by changing the polarization state of pumping circularly polarized light, measures the nuclear magnetic resonance frequency excursion of intert-gas atoms in atom pond, thus calculates the polarizability of alkali metal atom in atom pond, and measuring method is simple, does not affect magnetic resonance gyroscope light channel structure;

2. the intert-gas atoms nuclear magnetic resonance frequency excursion that causes of being polarized by alkali metal atom joins in the Larmor precession frequency that produced by static steady magnetic field, thus set up the three-dimensional model that in atom pond, intert-gas atoms nmr frequency changes with temperature and alkali metal atom polarizability, only need the nmr frequency of Real-Time Monitoring intert-gas atoms, the alkali metal atom polarizability under corresponding temperature just can be obtained according to this three-dimensional model, realize the real-time measurement of atom magnetic resonance gyroscope alkaline metal polarizability, significant to the performance improving atom magnetic resonance gyroscope.

Accompanying drawing explanation

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

In figure: 1. detecting laser, 2. beam-expanding collimation lens, 3. detecting 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 photodetectors, 13. computing machines, 14. pump lasers, 15. wave plate, 16. catoptrons, 17. pump beams.

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

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

Embodiment

Below in conjunction with accompanying drawing, the present invention is further illustrated, but should therefore not limit the scope of the invention.

As shown in Figure 1, adopt the atom magnetic resonance gyroscope device for measuring polarizability of the method for the invention by exploring laser light subsystem I, pumping laser subsystem II, temperature and Magnetic control subsystem III and Signal acquiring and processing subsystem IV tetra-part form; The function of described exploring laser light subsystem I is the density of alkali metal atom and the nmr frequency of intert-gas atoms in Measurement atom pond, this subsystem is made up of detecting laser 1, beam-expanding collimation lens combination 2, wherein detecting laser sweep frequency can obtain alkali metal atom transition absorption curve when alkali metal atom density measure, and when detecting intert-gas atoms nmr frequency, frequency is stabilized in alkali metal atom transition absorption center of curve place; Described pumping laser subsystem II by pump laser 14, wave plate 15 and beam-expanding collimation lens combination 2 form, and wherein pump laser 14 is for the linearly polarized light of the alkali metal atom transition absorption peak respective frequencies of output high-power, pass through wave plate 15 becomes circularly polarized light, then is irradiated on atom pond 8 through beam-expanding collimation lens combination 2 and catoptron 16, and then polarization alkali metal atom; Described temperature and Magnetic control subsystem III are made up of magnetic shielding cover 5, field coil 6, incubation chamber 7, atom pond 8, and wherein magnetic shielding cover 5 is used for shielding the interference in extraneous terrestrial magnetic field and other magnetic fields, shielding precision 10 ^-9t, field coil 6 is used for producing the steady magnetic field required for the work of atom magnetic resonance gyroscope and alternating magnetic field, and incubation chamber 7 is used for heating and the temperature in stability contorting atom pond 8; Described Signal acquiring and processing subsystem IV by lens 9, wave plate 10, wollaston prism 11, balance photodetector 12, computing machine 13 form, and wherein lens 9 are used for emergent light to converge on balance photodetector 12, wave plate 10 and wollaston prism 11 are used for being separated two quadrature components of emergent light, are calculated the nmr frequency of intert-gas atoms in atom pond by computing machine 13 process.

As shown in Figure 2, the concrete steps of the method are as follows for the process flow diagram of measuring method of the present invention:

1, in atom pond 8, be filled with a small amount of alkaline metal, this embodiment adopts rubidium, and atom pond 8 is the square of length of side 1cm, is filled with the N of 100torr in atom pond 8 ₂as buffer gas, and be filled with 2torr's ¹²⁹xe is as the intert-gas atoms of the extraneous rotational angular velocity of detection.Incubation chamber 7 is put in atom pond 8, adopts and without magnetic electrically heated mode atom pond 8 to be heated and to make its temperature stabilization at 80-120 degree.

2, measure the density of rubidium atom in atom magnetic resonance gyroscope atom pond 8, concrete steps are:

Regulate detecting laser 1 to make Output of laser swept frequency range through alkali metal atom transition center frequency, collect the absorption curve of transmitted light intensity with frequency change, according to I by balance photodetector 12 _out=I _ine ^{-N (T) σ (v) L}the absorption curve of rubidium atom under theory calculate different densities, the curve obtained with experiment measuring carries out least square fitting, and just can calculate rubidium atomicity density in atom pond 8 is 2.31 × 10 90 degree time ¹²cm ^-3.Regulate the temperature control burtons of heating box 7, just can obtain atom pond rubidium atomic density value in atom pond at different temperatures.

3, measure in atom magnetic resonance gyroscope atom pond 8 ¹²⁹xe atom nuclear magnetic resonance frequency excursion:

Driving magnetic field coil 6 produces longitudinal static magnetic field that size is 10.27uT frequency sweep is carried out in the lateral magnetic field being simultaneously applied across intert-gas atoms Larmor precession frequency, the signal obtained is carried out Fourier transform, obtains ¹²⁹the precession frequency of Xe atom reality is:

${\mathrm{\&omega;}}_1=\mathrm{\&gamma;}({\stackrel{\&RightArrow;}{B}}_0+{\stackrel{\&RightArrow;}{B}}_{\mathrm{Rb}})=121.756\mathrm{Hz}$

Will wave plate 15 rotates 90 degree, makes the polarization reversal of rubidium atom in atom pond 8, then applies lateral magnetic field and carry out frequency sweep, obtains ¹²⁹the precession frequency of Xe atom reality is:

${\mathrm{\&omega;}}_2=\mathrm{\&gamma;}({\stackrel{\&RightArrow;}{B}}_0-{\stackrel{\&RightArrow;}{B}}_{\mathrm{Rb}})=121.924\mathrm{Hz}$

Can obtain being caused by the polarization of rubidium atom in atom pond 8 ¹²⁹the nuclear magnetic resonance frequency excursion of Xe atom is:

$\mathrm{\&Delta;\&omega;}={\mathrm{\&gamma;}}_{\mathrm{Xe}}{\stackrel{\&RightArrow;}{B}}_{\mathrm{Rb}}=\frac{1}{2}({\mathrm{\&omega;}}_1-{\mathrm{\&omega;}}_2)=0.084\mathrm{Hz}$

Wherein: γ _xe=2 π × 11.86Hz/ μ T,

${\stackrel{\&RightArrow;}{B}}_{\mathrm{Rb}}=\frac{4}{3}{k}_0{g}_s{\stackrel{\&RightArrow;}{\mathrm{\&mu;}}}_B{N}_{\mathrm{Rb}}{P}_{\mathrm{Rb}}$

According to measuring the rubidium atomic density 2.31 × 10 90 degree time obtained ¹²cm ^-3, can calculate now in atom pond rubidium atomic pola-rizability be P _rb=2<S _z>=69.2%.

4, the three-dimensional model that in atom magnetic resonance gyroscope atom pond 8, intert-gas atoms nmr frequency changes with temperature and alkali metal atom polarizability is set up:

According to measuring the temperature variant relation N of rubidium atom in the atom pond that obtains in step 2 _rb(T), can the magnetic field that produces due to the polarization of rubidium atom of theory calculate with the relation of atom pond 8 temperature and the change of rubidium atomic polarizability:

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

And then can according to formula: ${\mathrm{\&omega;}}_1=\mathrm{\&gamma;}({\stackrel{\&RightArrow;}{B}}_0+{\stackrel{\&RightArrow;}{B}}_{\mathrm{Rb}})=A+\mathrm{\&gamma;}\stackrel{\&RightArrow;}{k}\&CenterDot;N_{\mathrm{Rb}}\left(T\right)\&CenterDot;P_{\mathrm{Rb}}$ Calculate ¹²⁹the value that Xe atomic nucleus magnetic resonance frequency changes with atom pond temperature and rubidium atomic polarizability.With atom pond temperature and alkali metal atom polarizability for coordinate axis, as shown in Figure 3, set up the three-dimensional model that an atom magnetic resonance gyroscope intert-gas atoms nuclear magnetic resonance frequency excursion changes with atom pond temperature and alkali metal atom polarizability, while the work of atom magnetic resonance gyroscope, according to detecting the intert-gas atoms nmr frequency obtained, the alkali metal atom polarizability under corresponding temperature just can be obtained according to model.Such as when temperature is 90 degree, if the nmr frequency that detection obtains intert-gas atoms is 121.882Hz, the polarizability that just can obtain alkali metal atom in atom pond according to this model is 35%.

Claims (1)

1. an atom magnetic resonance gyroscope alkali metal atom polarizability method for real-time measurement, is characterized in that the method comprises the following steps:

S1: the density N (T) measuring alkali metal atom in atom magnetic resonance gyroscope atom pond:

When adopting the laser illumination atom pond corresponding with alkali metal atom jump frequency, according to Lambert-Bill law, transmitted light intensity I _outwith detection light intensity I _inpass 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, and raising with atom pond temperature increases gradually; The absorption cross section that σ (v) is alkali metal atom, can be calculated by the buffer gas be filled with in atom pond, and L is the light path in atom pond, is 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, contrast with the transmission spectrum curve under the different temperatures of actual measurement again, adopt least square fitting, just can to obtain under different temperatures alkali metal atom number density value N (T) in atom pond;

S2: measure intert-gas atoms nuclear magnetic resonance frequency excursion in atom magnetic resonance gyroscope atom pond:

The alkali metal atom of spin polarization in atom pond can cause the nmr frequency of intert-gas atoms to be moved, and this frequency displacement causes because Fermi level interacts:

$\mathrm{\&alpha;}\stackrel{\&RightArrow;}{K}\&CenterDot;\stackrel{\&RightArrow;}{S}---\left(6\right)$

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

$\mathrm{\&alpha;}=\frac{8\mathrm{\&pi;}}{3}{g}_s{\mathrm{\&mu;}}_B\frac{{\mathrm{\&mu;}}_K}{K}|{\mathrm{\&psi;}\left(R\right)|}^2---\left(7\right)$

In formula | ψ (R) | ²the alkaline metal valence electron wave function square near intert-gas atoms core, g _slande factor, μ _bbohr magneton, be the nuclear magnetic moment of intert-gas atoms, under the downfield environment of atom magnetic resonance gyroscope work, can be written as by the polarize nuclear magnetic resonance frequency excursion of the intert-gas atoms caused of alkali metal atom:

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

In formula, h is Planck's constant, k ₀be enhancer, N (T) is alkali metal atom number density, <S _z> is the polarization of alkaline metal valence electron; Formula (8) can be written as further:

In formula for the gyromagnetic ratio of intert-gas atoms, P is the polarizability of alkali metal atom in atom magnetic resonance gyroscope atom pond, g _ifor the g factor that intert-gas atoms is corresponding, for reduced Planck constant, the resonance frequency shift of the intert-gas atoms caused that therefore interacted by Fermi level, can be described as the resonant frequency shift caused by the magnetic field of alkali metal atom polarization generation in atom pond, this magnetic field size is:

$\stackrel{\&RightArrow;}{B}=\frac{4}{3}{k}_0{g}_s{\stackrel{\&RightArrow;}{\mathrm{\&mu;}}}_{B}N\left(T\right)P---\left(10\right)$

The direction that alkali metal atom polarization produces magnetic field is relevant to alkaline metal electron spin orientation, therefore changes the polarization state of pumping circularly polarized light, can change the orientation of alkaline metal electron spin, thus changes the direction that alkali metal atom polarization produces magnetic field; When adopting left-handed and right-hand circular polarization optical pumping atom pond respectively, the intert-gas atoms nmr frequency observed is respectively:

${\mathrm{\&omega;}}_1=\mathrm{\&gamma;}({\stackrel{\&RightArrow;}{B}}_0+\stackrel{\&RightArrow;}{B})---\left(11\right)$

${\mathrm{\&omega;}}_2=\mathrm{\&gamma;}({\stackrel{\&RightArrow;}{B}}_0-\stackrel{\&RightArrow;}{B})---\left(12\right)$

Contrast intert-gas atoms nmr frequency ω when adopting left-handed and right-hand circular polarization optical pumping atom pond respectively ₁and ω ₂, just can obtain being polarized the intert-gas atoms nuclear magnetic resonance frequency excursion Δ ω caused by alkali metal atom in atom pond:

$\mathrm{\&Delta;\&omega;}=\mathrm{\&gamma;}\stackrel{\&RightArrow;}{B}=\frac{1}{2}({\mathrm{\&omega;}}_1-{\mathrm{\&omega;}}_2)---\left(13\right)$

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

This process is in two steps:

S3.1: obtain being polarized the intert-gas atoms nuclear magnetic resonance frequency excursion Δ ω caused by alkali metal atom in atom pond according to formula (13), calculates and to be polarized the magnetic field produced by alkali metal atom in atom pond:

$\stackrel{\&RightArrow;}{B}=\frac{\mathrm{\&Delta;\&omega;}}{\mathrm{\&gamma;}}---\left(14\right)$

Formula (10) can be written as further:

$\stackrel{\&RightArrow;}{B}=\frac{4}{3}{k}_0{g}_s{\stackrel{\&RightArrow;}{\mathrm{\&mu;}}}_{B}N\left(T\right)P=\stackrel{\&RightArrow;}{k}\&CenterDot;N\left(T\right)\&CenterDot;P---\left(15\right)$

In formula be being scale-up factor, is determined by the physical characteristics of intert-gas atoms and alkali metal atom in atom pond, when determining alkali metal atom and intert-gas atoms kind in atom pond, it is the value determined;

S3.2: according to the scale-up factor calculated in the density N (T) of alkali metal atom in the atom pond calculated in step S1 and step S3.1 calculate the polarizability P of alkali metal atom in atom magnetic resonance gyroscope atom pond:

$P=\frac{\stackrel{\&RightArrow;}{B}}{\stackrel{\&RightArrow;}{k}\&CenterDot;\left(T\right)}---\left(16\right)$

Therefore, by changing the left-handed or dextropolarization state of pumping circularly polarized light, just according to the intert-gas atoms nuclear magnetic resonance frequency excursion Δ ω measured, the polarizability P of alkali metal atom in atom pond can be calculated;

S4: set up the three-dimensional model that in atom magnetic resonance gyroscope atom pond, intert-gas atoms nmr frequency changes with temperature T and alkali metal atom polarizability P:

The experimental formula that in atom magnetic resonance gyroscope atom pond, alkali metal atom density N (T) changes with temperature T is:

${\log }_{10}(N\left(T\right)\mathrm{RT}/V)=15.88253-\frac{4529.635}{T}+0.00058663T-2.99138{\log }_{10}T---\left(17\right)$

In formula, V is atom pond volume, R is gas law constant, according to measuring the density N (T) obtaining alkali metal atom in atom pond under different temperatures in step S1, least square fitting is carried out to experimental formula (17), obtains the variation relation of alkali metal atom density with temperature in atom pond; Alkali metal atom polarization in atom pond can be obtained according to formula (15) again and produce magnetic field change with alkali metal atom polarizability P and atom pond temperature T:

$\stackrel{\&RightArrow;}{B}=\frac{4}{3}{k}_0{g}_s{\stackrel{\&RightArrow;}{\mathrm{\&mu;}}}_{B}N\left(T\right)P=\stackrel{\&RightArrow;}{B}(T,P)---\left(18\right)$

Therefore, under optical pumping state, static steady magnetic field is time, the intert-gas atoms nmr frequency (Left-hand circular polarization optical pumping) that atom magnetic resonance gyroscope is actually detected is:

${\mathrm{\&omega;}}_1=\mathrm{\&gamma;}({\stackrel{\&RightArrow;}{B}}_0+\stackrel{\&RightArrow;}{B})=A+\mathrm{\&gamma;}\stackrel{\&RightArrow;}{B}(T,P)---\left(19\right)$

With atom pond temperature T and alkali metal atom polarizability P for coordinate axis, according to (19) formula set up an atom magnetic resonance gyroscope intert-gas atoms nuclear magnetic resonance frequency excursion with atom pond temperature and alkali metal atom polarizability change three-dimensional model, when atomic nucleus magneto gyrocompass works, according to detecting the intert-gas atoms nmr frequency ω obtained ₁, the alkali metal atom polarizability P under corresponding temperature T just can be obtained according to this three-dimensional model.