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

IEEE Transactions on Instrumentation and Measurement

In Situ Compensation of Triaxial Magnetic Field Gradient for Atomic Magnetometers

Ke Yang, Jixi Lu, Yanning Ma, Zixuan Wang, Bowen Sun, Yaoguo Wang, Bangcheng Han

Published Jan 1, 2022• 18 citations
Publisher

Abstract

Magnetic field gradients affect numerous modern sensitive measurements and physics studies using atomic ensemble, resulting in the loss of coherence. In some cases, the presence of small gradients can reduce the performance significantly. In this study, we propose an effectivein situmethod to compensate the triaxial magnetic field gradient for atomic magnetometers, based on multichannel atomic signals in one vapor cell. We design two novel gradient coils by solving closed-form equations to improve the accuracy and efficiency of compensation. We demonstrate the performance of the compensation method in a spin-exchange relaxation-free atomic magnetometer, which reduces the magnetic linewidth by 4.2%–7.6% under the same conditions at a compensation resolution of 50 pT/cm. The proposed coils generate gradients only along two axes and achieve triaxial decoupling, which compensates for the gradient completely without iteration. Our results may aid in suppressing atomic spin relaxations due to magnetic field gradients in several modern measurements and improve their performance, such as the detection of electric dipole moments, ultralow-field nuclear magnetic resonance, and biomagnetism.

DOI
10.1109/tim.2022.3162607

Related papers

A Non-Modulated Triaxial Magnetic Field Compensation Method for Spin-Exchange Relaxation-Free Magnetometer Based on Zero-Field Resonance

Junpeng Zhao, Gang Liu, Jixi Lu +5 more

In this study, we demonstrate a non-modulated triaxial magnetic field compensation method for spin-exchange relaxation-free (SERF) atomic magnetometers. We realize simultaneous compensation of the magnetic field along the pump and probe directions by maximizing the first order differential value of the zero-field resonance signal. The magnetic field perpendicular to the pump-probe plane is compensated by zeroing the DC response of the magnetometer. The zero-field resonance is obtained by applying a linearly changed magnetic field along the direction perpendicular to that of the pump-probe plane. The first order differential of the zero-field resonance is acquired using the second order central difference method in real time. Compared with the conventional compensation methods, this method does not involve modulation and demodulation. Therefore, it requires no lock-in amplifier, thus making it more applicable in miniature atomic devices. Moreover, this method compensates the magnetic field along the pump and probe directions using only one criterion. It avoids the cross-talk effect between the pump and probe directions in the presence of non-orthogonal coils. The experiment results show that the compensation resolution is 9 pT, 7 pT and 0.05 pT for the probe, pump, and direction perpendicular to the pump-probe plane, respectively.

IEEE Access•Jan 1, 2019•20 citations

Triaxial Coils In Situ Calibration Method Based on Measuring the Alternating Magnetic Field-Induced Dynamic Response of the SERF Magnetometer

Kun Wang, Danyue Ma, Siran Li +4 more

The calibration results of the triaxial coils affect the atomic magnetometer’s measurement sensitivity. For precise in situ calibration, we first studied the transient atomic dynamics of a dual-beam spin-exchange relaxation free (SERF) atomic magnetometer under alternating magnetic fields. We obtained the corresponding dynamic free-induction-decay (FID) curves by alternately applying square wave signals to the${x}$-,${y}$-, and${z}$-axis coil, and then extracted the precession frequencies by fast Fourier transform (FFT) to achieve a decoupled calibration of the triaxial coil constants. Our calibration results were in better agreement under different experimental conditions than traditional parameter fitting methods with a relative error of less than 1.5% compared to conventional fluxgate calibration methods. Furthermore, we simultaneously measured nonorthogonal angles between each pair of axes: x–y, y–z, and z–x, respectively, which are used to correct the magnetic fields error. This method is suitable for coil calibration and nonorthogonal correction of integrated and miniaturized dual beam magnetometers.

IEEE Sensors Journal•Jul 7, 2023•15 citations

Enhanced Gradient Field Compensation in Multi‐Channel Atomic Magnetometers with Adaptive Algorithms

Yaohua Zhang, Zhuo Wang, Cao Li +3 more

Abstract The utilization of spin‐exchange relaxation‐free (SERF) effects in atomic magnetometers is demonstrated significant potential for ultrasensitive biomagnetic field measurements. However, the presence of residual gradient fields could introduce additional spin‐exchange relaxation, which will attenuate the response of the magnetometer. Consequently, it is crucial to compensate these residual gradients for maintaining high sensitivity and accuracy in SERF magnetometers. This study developed an optimized technique that leveraged both gradient and homogeneous coils to rapidly mitigate position‐dependent gradients. By applying adaptive moment estimation (Adam) optimization, the quadratic loss function is efficiently solved and the optimal current is determined. This experiment demonstrated over 90% suppression of the residual fields and a significant reduction in the inter‐channel deviations by an order of magnitude. In a simulated large gradient field environment, the sensitivities of multi‐channel magnetometers improved from 100 to 15 after compensation. The proposed method showcased substantial enhancements in residual homogeneity and sensor sensitivity, underscoring its efficiency. Compared with nested coil approaches, the coordinated use of gradient and homogeneous coils, along with Adam optimization, offered a robust, efficient, and rapid solution for gradient compensation. The proposed method effectively mitigated the adverse effects of residual fields and enhanced the performance of multi‐channel SERF magnetometers. Importantly, this approach represents a more practical solution for gradient field compensation within a single cell, particularly for future commercial applications of array SERF magnetometers.

Advanced Quantum Technologies•Feb 17, 2025•2 citations

In situ triaxial magnetic field compensation for the spin-exchange-relaxation-free atomic magnetometer

Jiancheng Fang, Jie Qin

The spin-exchange-relaxation-free (SERF) atomic magnetometer is an ultra-high sensitivity magnetometer, but it must be operated in a magnetic field with strength less than about 10 nT. Magnetic field compensation is an effective way to shield the magnetic field, and this paper demonstrates an in situ triaxial magnetic field compensation system for operating the SERF atomic magnetometer. The proposed hardware is based on optical pumping, which uses some part of the SERF atomic magnetometer itself, and the compensation method is implemented by analyzing the dynamics of the atomic spin. The experimental setup for this compensation system is described, and with this configuration, a residual magnetic field of strength less than 2 nT (±0.38 nT in the x axis, ±0.43 nT in the y axis, and ±1.62 nT in the z axis) has been achieved after compensation. The SERF atomic magnetometer was then used to verify that the residual triaxial magnetic fields were coincident with what were achieved by the compensation system.

Review of Scientific Instruments•Oct 1, 2012•69 citations

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

Optical magnetic combination method for suppressing the Rb polarization-induced magnetic gradient in Rb-Xe NMR co-magnetometers

Tengyue Wang, Jinpeng Peng, Zhanchao Liu +2 more

The Rb polarization-induced magnetic field gradient affects the Xe nuclear spin relaxation properties and degrades the long-term stability of the NMR co-magnetometers. This paper proposes a combination suppressing scheme, which uses the second-order magnetic field gradient coils to compensate for the Rb polarization-induced magnetic gradient under counter-propagating pump beams. Based on the theoretical simulation, we find that the spatial distribution of the Rb polarization-induced magnetic gradient and the magnetic field distribution generated by gradient coils are complementary. The experimental results indicate that the compensation effect is 10% higher under the counter-propagating pump beams scheme compared with the compensation effect under the conventional single beam. Besides, due to a more uniform spatial distribution of electronic spin polarization, the Xe nuclear spin polarizability is improved and the signal-to-noise ratio (SNR) of NMR co-magnetometers could be further enhanced. The study provides an ingenious method for suppressing magnetic gradient in the optically polarized Rb-Xe ensemble, which is expected to improve the performance of the atomic spin co-magnetometers.

Optics Express•May 3, 2023•13 citations
Magnetic field gradients affect numerous modern sensitive measurements and physics studies using atomic ensemble, resulting in the loss of coherence. In some cases, the presence of small gradients can reduce the performance significantly. In this study, we propose an effectivein situmethod to compensate the triaxial magnetic field gradient for atomic magnetometers, based on multichannel atomic signals in one vapor cell. We design two novel gradient coils by solving closed-form equations to improve the accuracy and efficiency of compensation. We demonstrate the performance of the compensation method in a spin-exchange relaxation-free atomic magnetometer, which reduces the magnetic linewidth by 4.2%–7.6% under the same conditions at a compensation resolution of 50 pT/cm. The proposed coils generate gradients only along two axes and achieve triaxial decoupling, which compensates for the gradient completely without iteration. Our results may aid in suppressing atomic spin relaxations due to magnetic field gradients in several modern measurements and improve their performance, such as the detection of electric dipole moments, ultralow-field nuclear magnetic resonance, and biomagnetism.
In this study, we demonstrate a non-modulated triaxial magnetic field compensation method for spin-exchange relaxation-free (SERF) atomic magnetometers. We realize simultaneous compensation of the magnetic field along the pump and probe directions by maximizing the first order differential value of the zero-field resonance signal. The magnetic field perpendicular to the pump-probe plane is compensated by zeroing the DC response of the magnetometer. The zero-field resonance is obtained by applying a linearly changed magnetic field along the direction perpendicular to that of the pump-probe plane. The first order differential of the zero-field resonance is acquired using the second order central difference method in real time. Compared with the conventional compensation methods, this method does not involve modulation and demodulation. Therefore, it requires no lock-in amplifier, thus making it more applicable in miniature atomic devices. Moreover, this method compensates the magnetic field along the pump and probe directions using only one criterion. It avoids the cross-talk effect between the pump and probe directions in the presence of non-orthogonal coils. The experiment results show that the compensation resolution is 9 pT, 7 pT and 0.05 pT for the probe, pump, and direction perpendicular to the pump-probe plane, respectively.
The calibration results of the triaxial coils affect the atomic magnetometer’s measurement sensitivity. For precise in situ calibration, we first studied the transient atomic dynamics of a dual-beam spin-exchange relaxation free (SERF) atomic magnetometer under alternating magnetic fields. We obtained the corresponding dynamic free-induction-decay (FID) curves by alternately applying square wave signals to thex{x}x-,y{y}y-, andz{z}z-axis coil, and then extracted the precession frequencies by fast Fourier transform (FFT) to achieve a decoupled calibration of the triaxial coil constants. Our calibration results were in better agreement under different experimental conditions than traditional parameter fitting methods with a relative error of less than 1.5% compared to conventional fluxgate calibration methods. Furthermore, we simultaneously measured nonorthogonal angles between each pair of axes: x–y, y–z, and z–x, respectively, which are used to correct the magnetic fields error. This method is suitable for coil calibration and nonorthogonal correction of integrated and miniaturized dual beam magnetometers.
Abstract The utilization of spin‐exchange relaxation‐free (SERF) effects in atomic magnetometers is demonstrated significant potential for ultrasensitive biomagnetic field measurements. However, the presence of residual gradient fields could introduce additional spin‐exchange relaxation, which will attenuate the response of the magnetometer. Consequently, it is crucial to compensate these residual gradients for maintaining high sensitivity and accuracy in SERF magnetometers. This study developed an optimized technique that leveraged both gradient and homogeneous coils to rapidly mitigate position‐dependent gradients. By applying adaptive moment estimation (Adam) optimization, the quadratic loss function is efficiently solved and the optimal current is determined. This experiment demonstrated over 90% suppression of the residual fields and a significant reduction in the inter‐channel deviations by an order of magnitude. In a simulated large gradient field environment, the sensitivities of multi‐channel magnetometers improved from 100 to 15 after compensation. The proposed method showcased substantial enhancements in residual homogeneity and sensor sensitivity, underscoring its efficiency. Compared with nested coil approaches, the coordinated use of gradient and homogeneous coils, along with Adam optimization, offered a robust, efficient, and rapid solution for gradient compensation. The proposed method effectively mitigated the adverse effects of residual fields and enhanced the performance of multi‐channel SERF magnetometers. Importantly, this approach represents a more practical solution for gradient field compensation within a single cell, particularly for future commercial applications of array SERF magnetometers.
The spin-exchange-relaxation-free (SERF) atomic magnetometer is an ultra-high sensitivity magnetometer, but it must be operated in a magnetic field with strength less than about 10 nT. Magnetic field compensation is an effective way to shield the magnetic field, and this paper demonstrates an in situ triaxial magnetic field compensation system for operating the SERF atomic magnetometer. The proposed hardware is based on optical pumping, which uses some part of the SERF atomic magnetometer itself, and the compensation method is implemented by analyzing the dynamics of the atomic spin. The experimental setup for this compensation system is described, and with this configuration, a residual magnetic field of strength less than 2 nT (±0.38 nT in the x axis, ±0.43 nT in the y axis, and ±1.62 nT in the z axis) has been achieved after compensation. The SERF atomic magnetometer was then used to verify that the residual triaxial magnetic fields were coincident with what were achieved by the compensation system.
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.
The Rb polarization-induced magnetic field gradient affects the Xe nuclear spin relaxation properties and degrades the long-term stability of the NMR co-magnetometers. This paper proposes a combination suppressing scheme, which uses the second-order magnetic field gradient coils to compensate for the Rb polarization-induced magnetic gradient under counter-propagating pump beams. Based on the theoretical simulation, we find that the spatial distribution of the Rb polarization-induced magnetic gradient and the magnetic field distribution generated by gradient coils are complementary. The experimental results indicate that the compensation effect is 10% higher under the counter-propagating pump beams scheme compared with the compensation effect under the conventional single beam. Besides, due to a more uniform spatial distribution of electronic spin polarization, the Xe nuclear spin polarizability is improved and the signal-to-noise ratio (SNR) of NMR co-magnetometers could be further enhanced. The study provides an ingenious method for suppressing magnetic gradient in the optically polarized Rb-Xe ensemble, which is expected to improve the performance of the atomic spin co-magnetometers.