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Advanced Quantum Technologies

Sensitivity‐Enhanced Dual‐Axis Zero‐Field Atomic Magnetometer Based on Pulsed Magnetic Field Modulation

Shushan Gao, Bangcheng Han, Xiaoyu Li, Ziao Liu, Zhongyu Wang, Jianwei Sheng, Jixi Lu

Published Sep 15, 2025• 5 citations
Publisher

Abstract

Abstract Atomic magnetometers serve as a type of quantum sensing instrument, offering extensive applications in the field of extremely weak magnetic field measurement. Miniaturized zero‐field atomic magnetometers typically use continuous high‐frequency magnetic fields to modulate atomic spin precession for multi‐axis measurements. However, this modulation induces additional spin‐exchange relaxation, which significantly broadens the resonance linewidth. In this study, the pulsed magnetic field modulation is introduced instead of continuous modulation to reduce the effective duration of the magnetic field. This operation significantly diminishes perturbations of steady‐state spin distribution in Zeeman sublevels caused by Larmor precession during each modulation cycle, thus effectively mitigating decoherence effects. The relationship between spin‐exchange relaxation rate and pulsed field parameters is studied based on the generalized hyperfine Bloch equation, and a spin dynamics model under the pulsed modulation is developed. Agreement between experimental and theoretical results validates the suppression effect of spin‐exchange relaxation and the accuracy of this model. Experimental results indicate that the pulsed modulation scheme results in a 30% reduction in the spin‐exchange relaxation rate and achieves dual‐axis sensitivities of 1.5 and 2.5 fT Hz −1/2 , respectively, representing improvements of 25% and 20% over conventional continuous modulation methods.

DOI
10.1002/qute.202500424

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Abstract Atomic magnetometers serve as a type of quantum sensing instrument, offering extensive applications in the field of extremely weak magnetic field measurement. Miniaturized zero‐field atomic magnetometers typically use continuous high‐frequency magnetic fields to modulate atomic spin precession for multi‐axis measurements. However, this modulation induces additional spin‐exchange relaxation, which significantly broadens the resonance linewidth. In this study, the pulsed magnetic field modulation is introduced instead of continuous modulation to reduce the effective duration of the magnetic field. This operation significantly diminishes perturbations of steady‐state spin distribution in Zeeman sublevels caused by Larmor precession during each modulation cycle, thus effectively mitigating decoherence effects. The relationship between spin‐exchange relaxation rate and pulsed field parameters is studied based on the generalized hyperfine Bloch equation, and a spin dynamics model under the pulsed modulation is developed. Agreement between experimental and theoretical results validates the suppression effect of spin‐exchange relaxation and the accuracy of this model. Experimental results indicate that the pulsed modulation scheme results in a 30% reduction in the spin‐exchange relaxation rate and achieves dual‐axis sensitivities of 1.5 and 2.5 fT Hz −1/2 , respectively, representing improvements of 25% and 20% over conventional continuous modulation methods.
The zero-field atomic magnetometer is a type of high-sensitivity and miniaturized quantum sensing instrument, typically using continuous radio-frequency fields for parametric modulation to extract weak magnetic signals. However, this modulation induces additional spin-exchange relaxation that degrades spin coherence. Here we report a weak bias magnetic field-assisted pulsed field modulation scheme that significantly suppresses spin-exchange decoherence. The pulsed magnetic field reduces asynchronous phase accumulation by shortening the interaction time between the modulation field and the atomic spin ensemble, while the perpendicular bias field induces spin Larmor precession to periodically average modulation-induced relaxation, thereby suppressing the spin-exchange relaxation rate by a factor approximately equal to the pulse duty cycle. We develop a perturbative spin dynamics model to analyze the spin polarization response under this modulation. The experimental results demonstrate that this scheme overcomes the limitation imposed by the duty cycle threshold, suppresses the spin-exchange relaxation rate by more than 50%, and significantly enhances the magnetic response and sensitivity compared to conventional continuous modulation. This method can be extended to various alkali-metal spin systems relying on radio-frequency field operation, providing a new scheme for reducing modulation-induced spin-exchange decoherence.
The spin-exchange relaxation-free (SERF) atomic magnetometers exhibit ultrahigh sensitivity for the magnetic field measurement, and their performance is further enhanced through zero-field parameter modulation. However, this modulation introduces additional parameter coupling that limits the performance of magnetometers in multi-axis measurement. In this paper, we develop a modified dual-axis output equation based on the nonlinear interaction between the optical pumping rate and modulation field amplitude, mediated by the spin-exchange relaxation and polarization. We employ a multi-objective optimization algorithm incorporating the implicit constraints among these parameters to enable efficient, simultaneous optimization of both the pump rate and modulation amplitude. Experimental results show that under optimal parameters obtained by the algorithm, the dual-axis signal responses improve by approximately 20% and 30% over conventional optimization methods, achieving 2.5 fT/Hz1/2magnetic measurement sensitivities for the y-axis and 4.0 fT/Hz1/2for the x-axis, respectively.
Zero-field atomic ensembles enable the development of ultrahigh-sensitivity magnetometry. However, their intrinsic insensitivity to longitudinal magnetic fields along the pumping direction poses a fundamental limitation, restricting precise weak-field quantification and complex system decoupling. Herein, we propose a novel zero-field weak parametric modulation scheme capable of ultrahigh-sensitivity extraction of longitudinal magnetic fields. Transverse modulation is employed to manifest the electron spin polarization projection induced by the longitudinal fields. Based on the perturbation model established, first-order parametric resonance associated with the longitudinal magnetic field yields significant signal enhancement under low-frequency and weak modulation conditions, while simultaneously suppressing spin-exchange relaxation caused by magnetic field modulation. We experimentally achieved a longitudinal measurement sensitivity of 16 fT / Hz 1 / 2 , more than an order of magnitude improved over traditional schemes, with a bandwidth of 70 Hz. Benefiting from low spin relaxation, the noise floor of the transverse magnetic field measurement is preserved at 4 fT / Hz 1 / 2 . The proposed scheme pushes the boundaries of existing weak magnetic field measurement, providing critical capabilities for state-of-the-art precision experiments including new physical quantity detection.
Atomic magnetometers operated in spin-exchange relaxation-free (SERF) have the potential to replace superconducting quantum interference devices (SQUIDs) in the field of biomagnetism. Here, we demonstrate the dual-axis closed-loop control of a single-beam SERF magnetometer that allows sensing of two orthogonal magnetic fields simultaneously and independently with suppressed cross-talk effect, achieved by applying a rotating modulation field and using of the negative feedback. Operating in the dual-axis closed-loop mode with a miniature 4 × 4 × 4 mm 87Rb cell, we achieve magnetic field sensitivity of 20 fT/Hz1/2 and a bandwidth of 1.8 kHz. In addition to the experimental study of the sensitivity and bandwidth, we perform a theoretical analysis to the dual-axis response and develop an effective decoupling method. The implementation of closed-loop control enables the magnetometer to be robust against the disturbance of the ambient field, which could enlarge the dynamic range, enhance the systematic stability, and suppress the cross-talk effect. Such a simple, yet high-performance SERF magnetometer could be suitable as a promising candidate in the field of biomagnetism, allowing for a denser sensor array and opening up new possibilities for the noninvasive biomagnetic imaging.
Atomic magnetometer (AM) operated in a spin-exchange relaxation-free (SERF) regime features superior sensitivity and non-cryogenic operation, and thus is competitive with the best superconducting quantum interference devices. Previously, SERF AM with fT/Hz 1/2 level sensitivity commonly acted as a single-axis sensor. Here we demonstrate a dual-axis SERF AM capable of simultaneously and independently detecting x - and y -field components with a sensitivity of 20 fT/Hz 1/2 . As there is no necessity to worry about the cross-talk effects arising from field modulations, the dual-axis scheme proposed here is of particular interest to AM array and hence the biomagnetic applications.
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.