Effects of pump laser power and vapor cell temperature on SERF gyroscope

SHI Meng,LIU Yuan-xing,WANG Xue-feng,WANG Wei

(Beijing Institute of Aerospace Control Devices,Beijing100854,China)

The SERF gyroscope,utilizing alkali-metal atomic spin and noble gas atomic spin coupling,is applied to verify the physics beyond standard model[1-3],and it can also be used to the high precision gyroscope because of its high sensitive to rotation[4-5].The SERF gyroscope works in the spin-exchange relaxation free(SERF)regime,where the Larmor processing frequency of electronic spin is much less than the collision rate with other electrons.The polarization of electronic spin is kept unchangeable due to the rapid collisions,and the relaxation from the spin exchange is suppressed[6].SERF phenomenon was firstly proposed by Happer in Columbia University in the1970s[7-8].In2002,the research group in Princeton University applied the SERF effect with noble gas scenario to the SERF gyroscope[9].After then the SERF gyroscope has been largely developed[10-15].

In the SERF regime,the electronic spin relaxation rate is much smaller than that in normal condition,and it is more sensitive to rotation or variation of the magnetic field.When the SERF gyroscope reaches the SERF condition,the external magnetic field fluctuation is automatically compensated by the nuclear spin magnetic field.The compensation process is the key point to realize the gyroscope or search the anomy fields,whilethe external magnetic field effect is suppressed only when the nuclear spin magnetic field is firstly cancelled by the coil’s magnetic field in the polarization direction.The compensation point of the nuclear magnetic field is affected by the laser power and the cell temperature.Until now,there are not many researches proceeding on compensation point influenced by the vapor cell tempe-rature and the pump laser power.In this paper,the rela-tion between compensation fields with the pump laser power and the cell temperature is investigated based on the coupling equation between electronic spin and nuclear spin.The experimental results show that the pump laser power has larger effect on the compensation field than that of the cell temperature.

1 Theory and simulation

1.1 Coupling Equation

In the SERF regime,electronic spin will strongly couple with nuclear spin.The polarizations of electronic spin and nuclear spin affect each other by the following coupling equation[3,9]:

where Peand Pnare the polarization of electronic spin and nuclear spin respectively, Beand Bnare the indu-cing magnetic field of electronic spin and nuclear spin respectively, Rteotand Rtnotare the total relaxation rate of electronic spin and nuclear spin respectively, Pze0and Pn0are the initial polarization of electronic spin and

z nuclear spin respectively,and Qis the slowing down factor of electron.

The initial polarization of the electronic spin is decided by the laser pumping rate Rpand the total relaxation Rteot,

where

RPis proportional to the pump laser power,andis the relaxation rate of electronic spin from other sources,such as the spin-exchange relaxation rate by collision with other electrons,collision with the cell wall,etc.In SERF regime,the spin-exchange relaxation rate of elec-trons becomes very tiny,which leads to small.

The polarization of nuclear spin is realized by the spin-exchange with electronic spin,and it is proportional to the initial polarization of the electronic spin.It is also affected by the exchange rateand its total relaxa-tion.The polarization of nuclear spin is

The pump rate is proportional to the laser power.There-fore,as the laser power rises,the initial polarization rate of electronic spin and nuclear spin will become larger.

The inducing magnetic fields of electronic spin and nuclear spin are proportional to their initial polarization rates,respectively,

whereκ1andκ2are the scattering factors of electron and nucleus, Meand Mnare the total magnetic moments of electron and nucleus,μeandμnare the magnetic moments of electron and nucleus,ρeandρnare the densities of electrons and nuclei,and Vis the volume of the vapor cell.

Since polarization has three orientations,Eq.(1)is a three-dimensional equation.In the experiment,only the electronic polarization is detected by a probe laser.The probe laser has one orientation,which is defined as the x direction.Therefore,only the x-axis polarization projec-tion of electronic spin in the Eq.(1)is considered,and the solution is

The first two terms in Eq.(6)are damping terms,which decay quickly.In the steady state,only the last term is left,

It can be seen when nuclear inducing magnetic field is canceled by the magnetic field of the coils,the polari-zation of electronic spin in the x-axis is zero.It meansthat the polarization of electronic spin is kept in the initial direction,along the z axis,even whenxB andyB are not zero.The low frequency fluctuation of the external magnetic field will not affect the electronic spin due to the nuclear spin magnetic field compensation process.

The signal is sensed by electronic spin(refer to87Rb),which is polarized by the pump laser.Nuclear spin(refer to129Xe)is polarized by the spin exchange process from electronic spin.When the probe light goes through the cell with polarized electronic spin,the output of PBS(pola-rization beam splitter prism)balanced polarimetry is[16]

whereθ is the angular change of the plane of the probe light,0I is the intensity of the probe light,eN is the alkali density,lis the optical path length,c is light speed，er is the classical radius of the electron,fis the coupling constant,output is proportional to the electronic spin polarization in the x-axis.

When the system is in the steady state,and the external magnetic in x direction is compensated,the output of the signal is

It can be seen that the signal is proportional to By,and it is affected by B,where the sign of B + Bndecides the signalSbeing weather in phase of Byor in the opposite phase ofBy.

The compensation magnetic field is mostly depen-dent on the nuclear spin magnetic field Bn,meanwhile the electronic spin magnetic field is negligible for much lower density. The nuclear spin magnetic field Bnis proportional to the nuclei spin magnetic moment.

whereκis the fermi-contact constant,Mn=μn0NnPnis the magnetic moment of the nuclei spin,μn0is the nuclear magnetic moment,Nnis the number of the nuclear,andis the polarization rate of the nuclear spin.

The polarization rate of the nuclear spin is linear,which is dependent on the polarization rate of the elec-tronic spin,and indirectly dependent on the pumping rate[2].

whereexR is the spin exchanging rate between nuclei and electrons,relR is the spin relaxation rate of the nuclear spin,Peis the polarization rate of the electronic spin,is the spin relaxation rate of the electronic spin,and RPis the pumping rate.The pumping rate is propor-tional to the pump laser power.Therefore,it can be concluded that the compensation magnetic field is pro-portional to the pump laser power.

The relation between the compensation magnetic field and the cell temperature is unambiguous in theory because the cell temperature not only affects the density of the alkali atoms but also influences the relaxation rate of the nuclear and electronic spin.However the experi-mental result can offer guidance for further investigation on the compensation magnetic field.

2.2 Simulation

It can be seen from Eq.(9)that when B =- Bn,the

z steady signal will not be affected by Bxand By.Define the change of the magnetic field in y direction asΔByand the output of the signal asΔS.Generate a square magnetic field in y direction,and|Δ By|= 2 0nTwhich is a fixed value,thenΔSchanges as a dispersive curve with the variation of Bzbecause of the square term in the denominator of Eq.(9).The width of the dispersive is determined by the total relaxation rate of electronic spin Rteot,and the center value,called compensation point,is determined by the inducing magnetic field of nuclear spin Bn.

To verify the dispersive curve,we make a simula-tion on it.Define:Rp=fpI,where I is the pump laser power,and fpis the pumping coefficient.The simulation parameters are chosen withγe=2.8×1010Hz/T,Q=4.5,Be=0.1nT,Bc=25nT,ΔBy=20nT,fp=50mW-1⋅s-1.The output signalΔSis decided by the amplification circuit,which has arbitrary scale.The dispersive curve ofΔS changed with Bzis shown in Fig.1, where different values of pump laser power are chosen.

Fig.1 Dispersive curve simulation of the signal with zB

In Fig.1,the width refers to the curve with the pump laser power Ip=100mW.The simulation result shows that as the pump laser power rises,the width of the dispersive becomes larger.The center value of the curve(eg.the compensation point)moves left.

3 Experiment and analysis

3.1 Experimental setup

The experimental setup of the SERF gyroscope is shown in Fig.2.There are a few drops of87Rb,20Torr of129Xe and600Torr of N2as the quenching gas filled in a vapor cell.The cell is heated to120℃by a heating plate with a high-frequency AC current.The cell is placed in the center of a three-dimensional coil which is used to cancel the external magnetic field as well as generate the needed magnetic field.The outer of the coil is a four-layer magnetic shield,which is used to shield the effects from the geomagnetic field.

A light from the pump laser is adjusted by a colli-mating lens,and then it is changed to a circular polarized light by going through a quarter-wave plate.The light is used to polarize the Rb atoms along the z-axis.Another light from the probe laser is also adjusted by a collimating lens,and its polarization is adjusted by a half-wave plate.It goes through the cell in x-axis,and it is divided into two lights by a PBS after that,and then collected by detectors.

Fig.2 The setup of the SERF gyroscope

3.2 Experimental result

When the system is steady,generate a10nT,100mHz,square-wave magnetic field in y direction,as shown in Fig.3.The signal has different outputs with the varia-tion of Bzin different regions.When Bz=-Bn,the signal is steady,which is unaffected by the input magnetic field,and the nuclear spin magnetic field compensates the change of the magnetic field.The vibrations near the sudden change ofyB are described by the damping terms in Eq.(6).

Fig.3 SignalS(black line)responds to yB(red line)

3.2.1 Effects of pump laser power on nuclear magnetic field

The pumping rate is determined by the laser power.When the pump laser power rises,the pumping rate goes larger.As the consequence,the total relaxation ratethe initial polarization rate Pze0and the magnetic field Bnalso go larger.To cancel the nuclear spin magnetic field,the external compensation field should become larger as well.As shown in the left subfigure of Fig.4,the compensation point moves to leftward as the laser power rising,and the width of the dispersive curve becomes wider,which is accordance with the simulation result of Fig.1in Section2.When the pump laser powerchanges from9.7 mW to105.6 mW,the compensation magnetic field is varied from-1.0nT to-9.9nT.The inducing magnetic fieldnB is proportional to the polari-zation of the nuclear spin0nP ,which is proportional to the pumping ratePR shown in Eq.(4).It means that the compensation field is proportional to the pump laser power,which is shown in the right subfigure of Fig.4.

Fig.4 Effect of the pump laser power on the compensation field

3.2.2 Effects of cell temperature on nuclear magnetic filed

As the vapor cell temperature rising,the density of Rb atoms becomes larger.In the meantime,the collisions among electrons become more frequent.The spin-exchange relaxation rate of electrons goes smaller,and therefore the total relaxation rategoes smaller.The temperature also affects the relaxation rate of the nuclear spin and its spin-exchange with electronic spin.As a result,the polarization of the nuclei changes little and also leads to little change of the inducing magnetic field Bn.As shown in the left subfigure of Fig.5,when the cell temperature rises,the compensation point moves to the left and then moves back to the right,which changes in a small range.As the cell temperature goes down,goes smaller,which leads to smaller width of the dispersive curve shown in the left subfigure of Figure5.In the right subfigure of Fig.5,the compensation field shows no disciplinary with the cell temperature.When the cell temperature changes from107.5℃to149.3℃,the compensation magnetic field is varied from-3.2nT to-5.5nT and then goes back to-1.0nT.It is shown that the compensation magnetic field is less sensitive to the cell temperature than to the pump laser power.

Fig.5 Effect of the cell temperature on the compensation field

4 Conclusion

The SERF gyroscope works in the SERF Regime,where the nuclear magnetic field compensates the exter-nal magnetic field and keeps electronic spin unchanging.It is an advantage for the gyroscope or new physical research,since it has very high sensitivity.However the compensation field is affected by the pump laser power and the cell temperature.

The experimental result shows that when the pump laser power changes from 9.7 mW to 105.6 mW, the compensation magnetic field is varied by 8.9 nT, which is proportional to the pump laser power. When the cell temperature changes from 107.5℃ to 149.3℃, the compensation magnetic field is varied by 4.5 nT, and it has no obvious relevance with the cell temperature. The compensation field is more sensitive to the pump laser power than the cell temperature.

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