Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Optics Express

Analysis of effects of magnetic field gradient on atomic spin polarization and relaxation in optically pumped atomic magnetometers

Xiujie Fang, Kai Wei, Yueyang Zhai, Tian Zhao, Xu Chen, Mingti Zhou, Ying Liu, Danyue Ma, Zhisong Xiao

Published Jan 14, 2022• 61 citations
Publisher

Abstract

The magnetic field gradient within optical pumping magnetometers (OPMs) suppresses sensitivity improvement. We investigated the effects of the magnetic field gradient along the x-, y-, and z-axes on the limiting factors of magnetometers under extremely low magnetic field conditions. We modified the magnetic field gradient relaxation model such that it can be applied to atoms in the spin exchange relaxation free (SERF) regime. The gradient relaxation time and spin polarizations, combined with fast spin-exchange interaction, were determined simultaneously using the oscillating cosine magnetic field excitation and amplitude spectrum analysis method. During the experiments, we eliminated the errors caused by the temperature and pumping power, and considered different isotope spin exchange collisions in naturally abundant Rb during the data analysis to improve the fitting accuracy. The experimental results agreed well with those of theoretical calculations and confirmed the accuracy of the improved model. The contribution of the transverse magnetic field gradient to the relaxation of the magnetic field gradient cannot be ignored in the case of small static magnetic fields. Our study provides a theoretical and experimental basis for eliminating magnetic gradient relaxation in atomic sensors in the SERF region.

DOI
10.1364/oe.447041

Related papers

Comprehensive analysis of the influence of magnetic field gradients on single-beam SERF atomic magnetometer

Jiajie Li, Ying Liu, Renjie Li +3 more

Magnetic field gradients interfere with the coherence of the atomic ensemble and degrade the performance of the spin-exchange relaxation-free (SERF) atomic magnetometer. In this paper, the influence of magnetic field gradients is incorporated into the response model of single-beam atomic magnetometer, and the theoretical models of transverse relaxation rate, spin polarization and scale factor are established. Based on this model,we find that magnetic field gradients in different directions can cause varying degrees of degradation in the performance parameters of the magnetometer. The magnetic linewidths under different light power and magnetic field gradients are measured using the designed dedicated magnetic field gradients coils, and the spin polarization and magnetic field gradients relaxation rate are obtained through fitting. An unevenness and deviation of the curve are also observed in the experiments, indicating the presence of the magnetic field gradient of approximately 2 nT/cm in the magnetic shields. Furthermore, in a magnetic field gradient environment of 20 nT/cm, the mean of the long-term sensitivity decreased by 3.5 times and the standard deviation increased by 11 times. It shows that the magnetic field gradients will not only affect the signal-to-noise ratio, but also make the magnetometer more vulnerable to external interference when working. The sensitivity and stability of magnetometer will be greatly reduced. The research in this article provides a theoretical and experimental basis for eliminating the influence of magnetic field gradients and improving the accuracy of magnetic field measurements.

Results in Physics•Nov 30, 2023•11 citations

Precise Determination of Magnetic Gradient Relaxation of Coupled Atomic Spin Ensemble in Spin-Exchange Relaxation-Free Co-Magnetometer

Xiujie Fang, Kai Wei, Wenfeng Fan +5 more

Inside a spin-exchange relaxation-free (SERF) co-magnetometer with a high-pressure buffer gas atomic cell, the magnetic field gradient causes the decoherence of atomic spins to produce magnetic-field gradient relaxation. This paper presents a new method for the accurate measurement of magnetic field gradient relaxation of alkali metal atoms and inert atoms of strongly coupled spin systems under triaxial magnetic field gradients in the K-Rb-21Ne co-magnetometer. The magnetic field gradient relaxation of alkali metal atoms is measured using a step magnetic field modulation method, and the magnetic field gradient relaxation of inert atoms is measured using a combined free induction decay and spin growth method. The method does not require the use of large background magnetic fields and RF fields to maintain the atoms in the SERF state, does not require additional optics, and is not affected by the pumping or detecting of optical power. A kinetic model that considers a large electron-equivalent magnetic field was designed and a gradient relaxation model was developed. The quadratic coefficients of the experimentally measured gradient relaxation curves fit the theoretical model well over the range of the applied magnetic field gradients, confirming the validity of the proposed method.

Photonics•Apr 3, 2023•3 citations

Magnetic Field Compensation for An Optically Pumped Magnetometer Without Iteration

Yaqiong Niu, Chaofeng Ye

The most efficient way to improve the sensitivity of an optically pumped magnetometer (OPM) is to maximize the spin-polarization lifetime of the atoms. The spin exchange relaxation-free (SERF) OPM that operates in zero field environment is one of the most sensitive magnetic sensors. This paper proposes a new three-axis magnetic field compensation method for the single-beam OPM, which zeroes the magnetic field around the sensor to make it work in SERF regime. The method simultaneously employs two modulation magnetic fields and two low-frequency sweeping magnetic fields along two directions perpendicular to the laser beam during the compensation process. The output signal of the photodiode is demodulated at different frequencies, resulting in two outputs that reflect the three components of the magnetic field. This method does not require iterate to tune the three-axis field, which increases the speed of the compensation process significantly. The magnetic field resolutions of the method for the x-axis, y-axis and z-axis are 0.6 pT, 0.6 pT and 5 pt, respectively. A compact OPM with noise density about 20 fT / Hz1/2@10 Hz is developed and tested, demonstrating the feasibility of the method.

Proceedings of IEEE Sensors/Proceedings of IEEE Sensors ...•Oct 29, 2023•1 citation

Analysis of Polarization Parameters of Co-Magnetometers Based on Elliptically Polarized Light Absorption Model

Lele Ma, Z X Liu, Xinhui Liu +3 more

The spin-exchange relaxation-free (SERF) comagnetometers, owing to their ultra-high sensitivity, are widely applied in fields such as inertial and magnetic field measurements, frontier physics research, etc. This technology relies on pump light to achieve the spin polarization of alkali metal atoms. During this process, the pump light is absorbed and thus attenuated by the alkali metal atoms. In this study, an absorption decay model for elliptically polarized light was solved by the fourth-order Runge-Kutta method, breaking through the applicability limitations of conventional analytical solutions for arbitrary polarized light. The effects of pump light polarization states and power on optical pumping rate, electron polarization, and measurement sensitivity were further investigated. It was found that there is a contradiction in achieving low polarization gradient and high scale coefficient by adjusting light intensity, increasing the pump light intensity can reduce the polarization gradient but will decrease the scale coefficient. Elliptically polarized light can realize low polarization gradient while enhancing the magnetic field response. This research establishes a theoretical foundation for optimizing the selection of pump light parameters in quantum sensors.

IEEE International Conference on Electronic Measurement & Instruments•Aug 22, 2025•0 citations

Analysis and Suppression of the Cross-Axis Coupling Effect for Dual-Beam SERF Atomic Magnetometer

Fei Lu, Shuying Wang, Nuozhou Xu +3 more

Spin-exchange relaxation-free (SERF) atomic magnetometers operated under a near-zero magnetic field are used for vector magnetic field measurements with high sensitivity. Previously, the cross-axis coupling error evoked by a nonzero background magnetic field has been verified to be adverse in modulated single-beam magnetometers. Here, in a dual-beam unmodulated SERF magnetometer, we propose a somewhat different solution model for the cross-axis coupling effect where the field of interest couples with the interference field. Considering two cases where the transverse or longitudinal background field exists, the cross-axis coupling effect dependence on multiple factors is investigated here based on the dynamic response under a background magnetic field within ±5 nT. The theoretical and experimental investigation suggests that it has an adverse impact on the output response amplitude and phase and tilts the sensitive axis by several degrees, causing a measurement error on the dual-beam magnetometer. To suppress this effect, the background magnetic field is compensated through the PI closed-loop control. The coupling effect is effectively suppressed by 1.5 times at the 10–40 Hz low-frequency band and the sensitivity reaches 2.4 fT/Hz1/2.

Photonics•Oct 25, 2022•7 citations

Comprehensive analysis of the impact of optical magnetic misalignment on the performance of the SERF co-magnetometer

Ze Yu Cai, Lihong Duan, Shimiao Fan +2 more

The ultra-sensitive atomic co-magnetometer based on the spin-exchange relaxation-free (SERF) regime is a valuable tool for inertial measurements and fundamental physics research. However, the optical magnetic misalignment effect is a significant source of error in SERF co-magnetometers, limiting their magnetic field suppression ability and long-term stability. This paper establishes a response model of angular velocity and magnetic field for the SERF co-magnetometer. The impact of optical magnetic misalignment on the scale factor, magnetic field amplitude-frequency response, and angular velocity errors caused by magnetic noise is systematically investigated. The results indicate that the scale factor and magnetic field suppression ability decrease as the optical magnetic misalignment angle increases, while the angular velocity errors caused by magnetic noise increase as the misalignment angle increases. Finally, experimental results demonstrate that the optical-magnetic misalignment effect significantly compromises the long-term stability of SERF co-magnetometers, underscoring its substantial influence on the overall performance. This work contributes to understanding the mechanism of optical magnetic misalignment effects on the SERF co-magnetometer and enhances its performance.

Optics Express•Apr 10, 2025•4 citations
The magnetic field gradient within optical pumping magnetometers (OPMs) suppresses sensitivity improvement. We investigated the effects of the magnetic field gradient along the x-, y-, and z-axes on the limiting factors of magnetometers under extremely low magnetic field conditions. We modified the magnetic field gradient relaxation model such that it can be applied to atoms in the spin exchange relaxation free (SERF) regime. The gradient relaxation time and spin polarizations, combined with fast spin-exchange interaction, were determined simultaneously using the oscillating cosine magnetic field excitation and amplitude spectrum analysis method. During the experiments, we eliminated the errors caused by the temperature and pumping power, and considered different isotope spin exchange collisions in naturally abundant Rb during the data analysis to improve the fitting accuracy. The experimental results agreed well with those of theoretical calculations and confirmed the accuracy of the improved model. The contribution of the transverse magnetic field gradient to the relaxation of the magnetic field gradient cannot be ignored in the case of small static magnetic fields. Our study provides a theoretical and experimental basis for eliminating magnetic gradient relaxation in atomic sensors in the SERF region.
Magnetic field gradients interfere with the coherence of the atomic ensemble and degrade the performance of the spin-exchange relaxation-free (SERF) atomic magnetometer. In this paper, the influence of magnetic field gradients is incorporated into the response model of single-beam atomic magnetometer, and the theoretical models of transverse relaxation rate, spin polarization and scale factor are established. Based on this model,we find that magnetic field gradients in different directions can cause varying degrees of degradation in the performance parameters of the magnetometer. The magnetic linewidths under different light power and magnetic field gradients are measured using the designed dedicated magnetic field gradients coils, and the spin polarization and magnetic field gradients relaxation rate are obtained through fitting. An unevenness and deviation of the curve are also observed in the experiments, indicating the presence of the magnetic field gradient of approximately 2 nT/cm in the magnetic shields. Furthermore, in a magnetic field gradient environment of 20 nT/cm, the mean of the long-term sensitivity decreased by 3.5 times and the standard deviation increased by 11 times. It shows that the magnetic field gradients will not only affect the signal-to-noise ratio, but also make the magnetometer more vulnerable to external interference when working. The sensitivity and stability of magnetometer will be greatly reduced. The research in this article provides a theoretical and experimental basis for eliminating the influence of magnetic field gradients and improving the accuracy of magnetic field measurements.
Inside a spin-exchange relaxation-free (SERF) co-magnetometer with a high-pressure buffer gas atomic cell, the magnetic field gradient causes the decoherence of atomic spins to produce magnetic-field gradient relaxation. This paper presents a new method for the accurate measurement of magnetic field gradient relaxation of alkali metal atoms and inert atoms of strongly coupled spin systems under triaxial magnetic field gradients in the K-Rb-21Ne co-magnetometer. The magnetic field gradient relaxation of alkali metal atoms is measured using a step magnetic field modulation method, and the magnetic field gradient relaxation of inert atoms is measured using a combined free induction decay and spin growth method. The method does not require the use of large background magnetic fields and RF fields to maintain the atoms in the SERF state, does not require additional optics, and is not affected by the pumping or detecting of optical power. A kinetic model that considers a large electron-equivalent magnetic field was designed and a gradient relaxation model was developed. The quadratic coefficients of the experimentally measured gradient relaxation curves fit the theoretical model well over the range of the applied magnetic field gradients, confirming the validity of the proposed method.
The most efficient way to improve the sensitivity of an optically pumped magnetometer (OPM) is to maximize the spin-polarization lifetime of the atoms. The spin exchange relaxation-free (SERF) OPM that operates in zero field environment is one of the most sensitive magnetic sensors. This paper proposes a new three-axis magnetic field compensation method for the single-beam OPM, which zeroes the magnetic field around the sensor to make it work in SERF regime. The method simultaneously employs two modulation magnetic fields and two low-frequency sweeping magnetic fields along two directions perpendicular to the laser beam during the compensation process. The output signal of the photodiode is demodulated at different frequencies, resulting in two outputs that reflect the three components of the magnetic field. This method does not require iterate to tune the three-axis field, which increases the speed of the compensation process significantly. The magnetic field resolutions of the method for the x-axis, y-axis and z-axis are 0.6 pT, 0.6 pT and 5 pt, respectively. A compact OPM with noise density about 20 fT / Hz1/2@10 Hz is developed and tested, demonstrating the feasibility of the method.
The spin-exchange relaxation-free (SERF) comagnetometers, owing to their ultra-high sensitivity, are widely applied in fields such as inertial and magnetic field measurements, frontier physics research, etc. This technology relies on pump light to achieve the spin polarization of alkali metal atoms. During this process, the pump light is absorbed and thus attenuated by the alkali metal atoms. In this study, an absorption decay model for elliptically polarized light was solved by the fourth-order Runge-Kutta method, breaking through the applicability limitations of conventional analytical solutions for arbitrary polarized light. The effects of pump light polarization states and power on optical pumping rate, electron polarization, and measurement sensitivity were further investigated. It was found that there is a contradiction in achieving low polarization gradient and high scale coefficient by adjusting light intensity, increasing the pump light intensity can reduce the polarization gradient but will decrease the scale coefficient. Elliptically polarized light can realize low polarization gradient while enhancing the magnetic field response. This research establishes a theoretical foundation for optimizing the selection of pump light parameters in quantum sensors.
Spin-exchange relaxation-free (SERF) atomic magnetometers operated under a near-zero magnetic field are used for vector magnetic field measurements with high sensitivity. Previously, the cross-axis coupling error evoked by a nonzero background magnetic field has been verified to be adverse in modulated single-beam magnetometers. Here, in a dual-beam unmodulated SERF magnetometer, we propose a somewhat different solution model for the cross-axis coupling effect where the field of interest couples with the interference field. Considering two cases where the transverse or longitudinal background field exists, the cross-axis coupling effect dependence on multiple factors is investigated here based on the dynamic response under a background magnetic field within ±5 nT. The theoretical and experimental investigation suggests that it has an adverse impact on the output response amplitude and phase and tilts the sensitive axis by several degrees, causing a measurement error on the dual-beam magnetometer. To suppress this effect, the background magnetic field is compensated through the PI closed-loop control. The coupling effect is effectively suppressed by 1.5 times at the 10–40 Hz low-frequency band and the sensitivity reaches 2.4 fT/Hz1/2.
The ultra-sensitive atomic co-magnetometer based on the spin-exchange relaxation-free (SERF) regime is a valuable tool for inertial measurements and fundamental physics research. However, the optical magnetic misalignment effect is a significant source of error in SERF co-magnetometers, limiting their magnetic field suppression ability and long-term stability. This paper establishes a response model of angular velocity and magnetic field for the SERF co-magnetometer. The impact of optical magnetic misalignment on the scale factor, magnetic field amplitude-frequency response, and angular velocity errors caused by magnetic noise is systematically investigated. The results indicate that the scale factor and magnetic field suppression ability decrease as the optical magnetic misalignment angle increases, while the angular velocity errors caused by magnetic noise increase as the misalignment angle increases. Finally, experimental results demonstrate that the optical-magnetic misalignment effect significantly compromises the long-term stability of SERF co-magnetometers, underscoring its substantial influence on the overall performance. This work contributes to understanding the mechanism of optical magnetic misalignment effects on the SERF co-magnetometer and enhances its performance.