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Advanced Quantum Technologies

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

Yaohua Zhang, Zhuo Wang, Cao Li, Junjian Tang, Yueyang Zhai, Yaxiang Wang

Published Feb 17, 2025• 2 citations
Publisher

Abstract

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.

DOI
10.1002/qute.202400346

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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.
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 spin-exchange-relaxation-free (SERF) atomic magnetometers (AMs), the attenuation of circularly polarized pump beam introduces spatial-dependent artificial magnetic fields in atomic spin polarization and light shift. In general, such a spatial-dependent effective magnetic field, especially prevalent in single-cell magnetometer arrays, cannot be uniformly compensated over the entire excitation region, resulting in a complex distributed compensation mask effect. In addition, any external effective-field-compensation methods inevitably complicate the final analysis of the unknown magnetic field measured. Here, we report a new excitation scheme that can substantially suppress spatial nonuniformity due to pump beam attenuation. Using counter-propagating pump beams with symmetrically red- and blue-detuning-paired frequencies, we demonstrate a significant reduction of spatial inhomogeneity in atomic spin polarization and light shift in comparison with the usual single-frequency unidirection and counter-propagating pump schemes. Employing this red-/blue-detuning-paired pump scheme, we construct a single-cell, four-channel SERF magnetometer array with high spatial homogeneity. We demonstrate ~10-fT/Hz1/2^{{1}/{2}}1/2sensitivity in the 5–45-Hz band for all four channels, with a gradient sensitivity of 2 fT/Hz1/21/2^{{1}/{2}}1/2/cm in the same band. This new scheme enables the development of single-vapor-cell, high-uniformity multichannel magnetic field mapping devices with potential applications in magnetoencephalography (MEG) and magnetocardiography (MCG), or in searching for exotic spin-dependent interactions.
Miniaturized high-sensitivity atomic magnetometers play a crucial role in biomagnetic measurements. The utilization of multipass cells enhances the sensitivity of atomic magnetometers. This study explores the benefits of employing a multipass cell in spin-exchange relaxation-free (SERF) atomic magnetometers through theoretical and experimental analysis. A signal-to-noise ratio (SNR) model was established by accounting for the optimal detuning frequency of the probe light and low-frequency 1/f noise. This enabled the optimal number of probe light passes through the vapor cell to be determined. Additionally, compact and symmetric reflective optical paths were designed to mitigate polarization gradients in atomic magnetometers with high atomic number density. Experimental results confirmed that the magnetic field sensitivity of the triple-pass configuration (1.8 fT/Hz1/2^{1/2}1/2) was 1.89 times that of the single-pass configuration (3.4 fT/Hz1/2^{1/2}1/2), consistent with the theoretical analysis. This study provides valuable theoretical guidance for analyzing the SNR performance of SERF atomic magnetometers and demonstrates the potential of multipass cells in enhancing their magnetic field sensitivity. The utilization of multipass cells presents a viable approach toward the realization of highly sensitive and portable miniaturized SERF atomic magnetometers.
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.
Abstract This study systematically investigates the spin relaxation characteristics of alkali‐metal atoms in spin‐exchange relaxation‐free (SERF) co‐magnetometers, focusing on mitigating the radiation trapping to reduce the alkali‐metal spin relaxation rate. Radiation trapping is one of the dominant mechanisms exacerbating spin relaxation in alkali‐metal atoms and is conventionally suppressed by introducing nitrogen () as a quenching agent. However, experiments reveal that the typical concentration in current SERF co‐magnetometers is insufficient to effectively suppress radiation trapping. By increasing the quenching gas concentration, additional attenuation of the radiation trapping effect is achieved. Meanwhile, to address the enhanced spin‐exchange collision relaxation arising from higher concentration, the operating temperature is adjusted to increase the alkali‐metal atom number density, thereby effectively curtailing this adverse effect. Experimental results demonstrate that the synergistic optimization of concentration and temperature reduces alkali‐metal spin relaxation by approximately 55% and decreases the noise power spectral density of the co‐magnetometer by 48.5% at 1 Hz. These findings confirm the effectiveness of this approach in improving the accuracy and sensitivity of SERF co‐magnetometers.
ABSTRACT Triaxial spin‐exchange relaxation‐free (SERF) atomic magnetometer has attracted widespread attention for its capability of measuring the total magnetic field vector information. In this paper, we propose a triaxial SERF atomic magnetometer through orthogonal non‐overlapping pumping beam with improved atom spin polarization spatial uniformity by using a uniformized pump beam and reflection compensation . The homogenized beams are adopted to achieve uniform transverse polarization, while double‐pass reflection compensation is integrated to realize uniform longitudinal polarization. The polarizability distribution based on an effective optical path‐length formalism was obtained via theoretical simulation. The bandwidth, dispersion curves, stability, and sensitivity were experimentally analyzed under three configurations: uniformized pump beam , gaussian pump beam‐reflection compensation , and uniformized pump beam‐reflection compensation . Results of experiments reveal that the proposed configuration enhances three‐axis bandwidth by roughly 10 and improves X, Y, and Z sensitivities by approximately 35, 60, and 30, respectively, achieving sensitivities of 20.56 fT/(X), 30.75 fT/(Y) and 20.54 fT/(Z) at 140 and 2 mW. These results demonstrate a structurally simple yet highly effective approach for achieving high uniformity and stability in three‐axis vector magnetic sensing, with strong potential for applications such as spatial magnetic‐field mapping and bio‐magnetic measurement research.