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arXiv:1811.05404

Polarization and fundamental sensitivity of $^{\text{39}}$K ($^{\text{133}}$Cs)-$^{\text{85}}$Rb-$^{\text{21}}$Ne co-magnetometers

Jianhua Liu, Dong-Yang Jing, Lin Zhuang, Wei Quan, Jiancheng Fang, Wu‐Ming Liu

Published Nov 5, 2018• 0 citations
arXivHTMLPDF

Abstract

The hybrid optical pumping spin exchange relaxation free (HOPSERF) atomic co-magnetometers make ultrahigh sensitivity measurement of inertia achievable. The wall relaxation rate has a big effect on the polarization and fundamental sensitivity for the co-magnetometer, but it is often neglected in the experiments. However, there is almost no work about the systematic analysis of the influence factors on the polarization and the fundamental sensitivity of the HOPSERF co-magnetometers. Here, we systematically study the polarization and the fundamental sensitivity of 39K-85Rb-21Ne and 133Cs-85Rb-21Ne HOPSERF co-magnetometers with low polarization limit and the wall relaxation rate. The 21Ne number density, the power density and wavelength of pump beam will affect the polarization greatly by affecting the pumping rate of pump beam. We obtain a general formula on the fundamental sensitivity of the HOPSERF co-magnetometers due to shot-noise and the fundamental sensitivity changes with multiple systemic parameters, where the suitable number density of buffer gas and quench gas make the fundamental sensitivity highest. The fundamental sensitivity $7.5355\times10^{-11}$ $\rm rad/s/Hz^{1/2}$ of 133Cs-85Rb-21Ne co-magnetometer is higher than the ultimate theoretical sensitivity $2\times10^{-10}$ $\rm rad/s/Hz^{1/2}$ of K-21Ne co-magnetometer.

DOI
10.48550/arxiv.1811.05404

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Polarization and fundamental sensitivity of 39K (133Cs)–85Rb–21Ne co-magnetometers*

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The hybrid optical pumping spin exchange relaxation free (HOPSERF) atomic co-magnetometers make ultrahigh sensitivity measurement of inertia achievable. The wall relaxation rate has a big effect on the polarization and fundamental sensitivity for the co-magnetometer, but it is often neglected in the experiments. However, there is almost no work about the systematic analysis of the influence factors on the polarization and the fundamental sensitivity of the HOPSERF co-magnetometers. Here we systematically study the polarization and the fundamental sensitivity of 39K–85Rb–21Ne and 133Cs–85Rb–21Ne HOPSERF co-magnetometers with low polarization limit and the wall relaxation rate. The 21Ne number density, the power density and wavelength of pump beam will affect the polarization greatly by affecting the pumping rate of the pump beam. We obtain a general formula on the fundamental sensitivity of the HOPSERF co-magnetometers due to shot-noise and the fundamental sensitivity changes with multiple systemic parameters, where the suitable number density of buffer gas and quench gas make the fundamental sensitivity highest. The fundamental sensitivity 7.5355×10–11 rad·s–1·Hz–1/2 of 133Cs–85Rb–21Ne co-magnetometer is higher than the ultimate theoretical sensitivity 2×10–10 rad·s–1·Hz–1/2 of K–21Ne co-magnetometer.

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The polarization and the fundamental sensitivity of $^{39}$K ($^{133}$Cs)-$^{85}$Rb-$^{21}$Ne co-magnetometer

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We have studied the polarization of the 85Rb and the fundamental sensitivity of two types of hybrid optical pumping spin exchange relaxation free (SERF) co-magnetometers based on 39K-85Rb-21Ne and 133Cs-85Rb-21Ne with taking the wall relaxation rate into account,which has a big effect on the polarization and fundamental sensitivity,but it is often neglected in the experiments,respectively.The polarization of the 85Rb varies with the thirteen systemic parameters: the number density of buffer gas 21Ne and quench gas N2,frequency rate of pump beam,cell temperature,the photon number flux,mole fraction of 85Rb,cell effective radius,pump beam spot radius,power density of pump beam,input rotation velocity in the x and y direction,external magnetic field in the y and z direction,respectively.The number density of the 21Ne,photon number flux,pump beam spot radius and frequency rate will affect the polarization of the 85Rb greatly by affecting the the pumping rate of pump beam,a magnetic field produced by 85Rb atom spins and experienced by the 21Ne spins.We obtain a general formula on the fundamental sensitivity of the hybrid optical pumping SERF co-magnetometers due to shot-noise,where the fundamental sensitivity varies with the twelve systemic parameters: the number density of buffer gas and quench gas,frequency rate of pump beam,photon number flux,mole fraction of 85Rb,cell effective radius,pump beam spot radius,power density of pump beam,external magnetic field,measurement volume,cell temperature and measurement time.The highest fundamental sensitivity $7.5878\times10^{-11}$ $rad/s/Hz^{1/2}$ of 133Cs-85Rb-21Ne co-magnetometer is higher than the ultimate theoretical sensitivity $2\times10^{-10}$ $rad/s/Hz^{1/2}$ of K-21Ne co-magnetometer.The fundamental sensitivity limit of the hybrid optical pumping SERF co-magnetometers is superior to $3.7334\times10^{-12}$ $rad/s/Hz^{1/2}$.

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Abstract The hybrid optical pumping spin exchange relaxation free (SERF) atomic magnetometers can realize ultrahigh sensitivity measurement of magnetic field and inertia. We have studied the 85 Rb polarization of two types of hybrid optical pumping SERF magnetometers based on 39 K- 85 Rb- 4 He and 133 Cs- 85 Rb- 4 He respectively. Then we found that 85 Rb polarization varies with the number density of buffer gas 4 He and quench gas N 2 , pumping rate of pump beam and cell temperature respectively, which will provide an experimental guide for the design of the magnetometer. We obtain a general formula on the fundamental sensitivity of the hybrid optical pumping SERF magnetometer due to shot-noise. The formula describes that the fundamental sensitivity of the magnetometer varies with the number density of buffer gas and quench gas, the pumping rate of pump beam, external magnetic field, cell effective radius, measurement volume, cell temperature and measurement time. We obtain a highest fundamental sensitivity of 1.5073 aT / Hz 1/2 (1 aT = 10 −18 T ) with 39 K- 85 Rb- 4 He magnetometer between above two types of magnetometers when 85 Rb polarization is 0.1116. We estimate the fundamental sensitivity limit of the hybrid optical pumping SERF magnetometer to be superior to 1.8359 × 10 −2 aT / Hz 1/2 , which is higher than the shot-noise-limited sensitivity of 1 aT / Hz 1/2 of K SERF atomic magnetometer.

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Probe beam influence on spin polarization in spin-exchange relaxation-free co-magnetometers

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Abstract Spin-exchange relaxation-free (SERF) co-magnetometers have promising applications in both inertial navigation and fundamental physics experiments. However, the fluctuation in the spin polarization caused by the probe beam has a non-negligible influence on the co-magnetometer signal. In this paper, a theoretical model containing three parameters of the probe beam is established by extending the coupled Bloch equation. Based on this model, the influence of probe power density on the transient and steady-state response of the SERF co-magnetometer is analyzed. According to the transient response model, a new measurement method for transverse optical pumping of the probe beam is proposed. Then, for the steady-state response model, a steady-state error suppression method is suggested by adjusting the degree of circular polarization of the probe beam. Eventually, the suppression method is used to refine the SERF co-magnetometer, achieving a suppression rate of 70.31% in transverse electron spin polarization fluctuations, thus improving the co-magnetometer to a stability of 0.0079∘ h−1. To our knowledge, this is better than what has been reported so far.

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The hybrid optical pumping atomic magnetometers have not realized its theoretical sensitivity, the optimization is critical for optimal performance. The optimizations proposed in this paper are suitable for hybrid optical pumping atomic magnetometer, which contains two alkali species. To optimize the parameters, the dynamic equations of spin evolution with two alkali species were solved, whose steady-state solution is used to optimize the parameters. The demand of the power of the pump beam is large for hybrid optical pumping. Moreover, the sensitivity of the hybrid optical pumping magnetometer increases with the increase of the power density of the pump beam. The density ratio between the two alkali species is especially important for hybrid optical pumping magnetometer. A simple expression for optimizing the density ratio is proposed in this paper, which can help to determine the mole faction of the alkali atoms in fabricating the hybrid cell before the cell is sealed. The spin-exchange rate between the two alkali species is proportional to the saturated density of the alkali vapor, which is highly dependent on the temperature of the cell. Consequently, the sensitivity of the hybrid optical pumping magnetometer is dependent on the temperature of the cell. We proposed the thermal optimization of the hybrid cell for a hybrid optical pumping magnetometer, which can improve the sensitivity especially when the power of the pump beam is low. With these optimizations, a sensitivity of approximately 5 fT/Hz(1/2) is achieved with gradiometer arrangement.

Review of Scientific Instruments•Dec 1, 2014•38 citations
Polarization and fundamental sensitivity of 39^{\text{39}}39K (133^{\text{133}}133Cs)-85^{\text{85}}85Rb-21^{\text{21}}21Ne co-magnetometers
The hybrid optical pumping spin exchange relaxation free (HOPSERF) atomic co-magnetometers make ultrahigh sensitivity measurement of inertia achievable. The wall relaxation rate has a big effect on the polarization and fundamental sensitivity for the co-magnetometer, but it is often neglected in the experiments. However, there is almost no work about the systematic analysis of the influence factors on the polarization and the fundamental sensitivity of the HOPSERF co-magnetometers. Here, we systematically study the polarization and the fundamental sensitivity of 39K-85Rb-21Ne and 133Cs-85Rb-21Ne HOPSERF co-magnetometers with low polarization limit and the wall relaxation rate. The 21Ne number density, the power density and wavelength of pump beam will affect the polarization greatly by affecting the pumping rate of pump beam. We obtain a general formula on the fundamental sensitivity of the HOPSERF co-magnetometers due to shot-noise and the fundamental sensitivity changes with multiple systemic parameters, where the suitable number density of buffer gas and quench gas make the fundamental sensitivity highest. The fundamental sensitivity 7.5355×10−117.5355\times10^{-11}7.5355×10−11 rad/s/Hz1/2\rm rad/s/Hz^{1/2}rad/s/Hz1/2 of 133Cs-85Rb-21Ne co-magnetometer is higher than the ultimate theoretical sensitivity 2×10−102\times10^{-10}2×10−10 rad/s/Hz1/2\rm rad/s/Hz^{1/2}rad/s/Hz1/2 of K-21Ne co-magnetometer.
The hybrid optical pumping spin exchange relaxation free (HOPSERF) atomic co-magnetometers make ultrahigh sensitivity measurement of inertia achievable. The wall relaxation rate has a big effect on the polarization and fundamental sensitivity for the co-magnetometer, but it is often neglected in the experiments. However, there is almost no work about the systematic analysis of the influence factors on the polarization and the fundamental sensitivity of the HOPSERF co-magnetometers. Here we systematically study the polarization and the fundamental sensitivity of 39K–85Rb–21Ne and 133Cs–85Rb–21Ne HOPSERF co-magnetometers with low polarization limit and the wall relaxation rate. The 21Ne number density, the power density and wavelength of pump beam will affect the polarization greatly by affecting the pumping rate of the pump beam. We obtain a general formula on the fundamental sensitivity of the HOPSERF co-magnetometers due to shot-noise and the fundamental sensitivity changes with multiple systemic parameters, where the suitable number density of buffer gas and quench gas make the fundamental sensitivity highest. The fundamental sensitivity 7.5355×10–11 rad·s–1·Hz–1/2 of 133Cs–85Rb–21Ne co-magnetometer is higher than the ultimate theoretical sensitivity 2×10–10 rad·s–1·Hz–1/2 of K–21Ne co-magnetometer.
The polarization and the fundamental sensitivity of 39^{39}39K (133^{133}133Cs)-85^{85}85Rb-21^{21}21Ne co-magnetometer
We have studied the polarization of the 85Rb and the fundamental sensitivity of two types of hybrid optical pumping spin exchange relaxation free (SERF) co-magnetometers based on 39K-85Rb-21Ne and 133Cs-85Rb-21Ne with taking the wall relaxation rate into account,which has a big effect on the polarization and fundamental sensitivity,but it is often neglected in the experiments,respectively.The polarization of the 85Rb varies with the thirteen systemic parameters: the number density of buffer gas 21Ne and quench gas N2,frequency rate of pump beam,cell temperature,the photon number flux,mole fraction of 85Rb,cell effective radius,pump beam spot radius,power density of pump beam,input rotation velocity in the x and y direction,external magnetic field in the y and z direction,respectively.The number density of the 21Ne,photon number flux,pump beam spot radius and frequency rate will affect the polarization of the 85Rb greatly by affecting the the pumping rate of pump beam,a magnetic field produced by 85Rb atom spins and experienced by the 21Ne spins.We obtain a general formula on the fundamental sensitivity of the hybrid optical pumping SERF co-magnetometers due to shot-noise,where the fundamental sensitivity varies with the twelve systemic parameters: the number density of buffer gas and quench gas,frequency rate of pump beam,photon number flux,mole fraction of 85Rb,cell effective radius,pump beam spot radius,power density of pump beam,external magnetic field,measurement volume,cell temperature and measurement time.The highest fundamental sensitivity 7.5878×10−117.5878\times10^{-11}7.5878×10−11 rad/s/Hz1/2rad/s/Hz^{1/2}rad/s/Hz1/2 of 133Cs-85Rb-21Ne co-magnetometer is higher than the ultimate theoretical sensitivity 2×10−102\times10^{-10}2×10−10 rad/s/Hz1/2rad/s/Hz^{1/2}rad/s/Hz1/2 of K-21Ne co-magnetometer.The fundamental sensitivity limit of the hybrid optical pumping SERF co-magnetometers is superior to 3.7334×10−123.7334\times10^{-12}3.7334×10−12 rad/s/Hz1/2rad/s/Hz^{1/2}rad/s/Hz1/2.
Abstract The hybrid optical pumping spin exchange relaxation free (SERF) atomic magnetometers can realize ultrahigh sensitivity measurement of magnetic field and inertia. We have studied the 85 Rb polarization of two types of hybrid optical pumping SERF magnetometers based on 39 K- 85 Rb- 4 He and 133 Cs- 85 Rb- 4 He respectively. Then we found that 85 Rb polarization varies with the number density of buffer gas 4 He and quench gas N 2 , pumping rate of pump beam and cell temperature respectively, which will provide an experimental guide for the design of the magnetometer. We obtain a general formula on the fundamental sensitivity of the hybrid optical pumping SERF magnetometer due to shot-noise. The formula describes that the fundamental sensitivity of the magnetometer varies with the number density of buffer gas and quench gas, the pumping rate of pump beam, external magnetic field, cell effective radius, measurement volume, cell temperature and measurement time. We obtain a highest fundamental sensitivity of 1.5073 aT / Hz 1/2 (1 aT = 10 −18 T ) with 39 K- 85 Rb- 4 He magnetometer between above two types of magnetometers when 85 Rb polarization is 0.1116. We estimate the fundamental sensitivity limit of the hybrid optical pumping SERF magnetometer to be superior to 1.8359 × 10 −2 aT / Hz 1/2 , which is higher than the shot-noise-limited sensitivity of 1 aT / Hz 1/2 of K SERF atomic magnetometer.
An optically pumped atomic magnetometer using a hybrid cell of potassium and rubidium atoms was demonstrated to yield high sensitivity to magnetic fields. We operated the magnetometer with the four possible combinations of optically pumped and optically probed atoms and found that the combination of optically pumped potassium and optically probed rubidium showed the highest sensitivity among the four combinations because the rubidium atoms were denser than those of potassium. Furthermore, we investigated the dependence of the sensitivity on the power densities of the pump and probe beams and the wavelength of the probe beam. The magnetometer using the hybrid cell required higher pump-beam power and had narrower magnetic linewidth than those of the single alkali-metal cell. However, the magnetic linewidth was larger than the theoretical value, ignoring the spin relaxation caused by the spin-exchange collisions. By adjusting the laser conditions, the highest sensitivity approached 30 fTrms/Hz1/2.
Abstract Spin-exchange relaxation-free (SERF) co-magnetometers have promising applications in both inertial navigation and fundamental physics experiments. However, the fluctuation in the spin polarization caused by the probe beam has a non-negligible influence on the co-magnetometer signal. In this paper, a theoretical model containing three parameters of the probe beam is established by extending the coupled Bloch equation. Based on this model, the influence of probe power density on the transient and steady-state response of the SERF co-magnetometer is analyzed. According to the transient response model, a new measurement method for transverse optical pumping of the probe beam is proposed. Then, for the steady-state response model, a steady-state error suppression method is suggested by adjusting the degree of circular polarization of the probe beam. Eventually, the suppression method is used to refine the SERF co-magnetometer, achieving a suppression rate of 70.31% in transverse electron spin polarization fluctuations, thus improving the co-magnetometer to a stability of 0.0079∘ h−1. To our knowledge, this is better than what has been reported so far.
The hybrid optical pumping atomic magnetometers have not realized its theoretical sensitivity, the optimization is critical for optimal performance. The optimizations proposed in this paper are suitable for hybrid optical pumping atomic magnetometer, which contains two alkali species. To optimize the parameters, the dynamic equations of spin evolution with two alkali species were solved, whose steady-state solution is used to optimize the parameters. The demand of the power of the pump beam is large for hybrid optical pumping. Moreover, the sensitivity of the hybrid optical pumping magnetometer increases with the increase of the power density of the pump beam. The density ratio between the two alkali species is especially important for hybrid optical pumping magnetometer. A simple expression for optimizing the density ratio is proposed in this paper, which can help to determine the mole faction of the alkali atoms in fabricating the hybrid cell before the cell is sealed. The spin-exchange rate between the two alkali species is proportional to the saturated density of the alkali vapor, which is highly dependent on the temperature of the cell. Consequently, the sensitivity of the hybrid optical pumping magnetometer is dependent on the temperature of the cell. We proposed the thermal optimization of the hybrid cell for a hybrid optical pumping magnetometer, which can improve the sensitivity especially when the power of the pump beam is low. With these optimizations, a sensitivity of approximately 5 fT/Hz(1/2) is achieved with gradiometer arrangement.