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Physical Review Research

Zero-field atomic magnetometer to extract longitudinal magnetic field

Shuying Wang, Jixi Lu, Kaixuan Zhang, Le Zhao, Yibo Qi, Jiancheng Fang

Published Jul 18, 2025• 5 citations
Publisher

Abstract

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.

DOI
10.1103/yjc6-b26g

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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.
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.
In the field of biomagnetic measurements, one of the most important recent challenges is to perform measurements in a magnetically unshielded environment. This first requires that atomic magnetometers can operate in a finite magnetic field, and have enough high sensitivity. To meet these requirements, we develop a light-narrowed parametric resonance (LPR) magnetometer. By adding a modulation magnetic field to the large longitudinal magnetic field, our LPR magnetometer can measure small transverse magnetic fields with an intrinsic sensitivity of 3.5 fT/Hz 1/2 in a longitudinal magnetic field of μ T range. Moreover, we have also demonstrated that in contrast to the previous light-narrowed scalar magnetometers, our LPR magnetometer has the potential to achieve higher sensitivity. Because in our case spin-exchange relaxation suppression by using light narrowing can lead to an improvement of fundamental sensitivity limit regardless of which quantum noise is dominant, and hence the fundamental sensitivity is no longer limited by spin-exchange, and approaches the fundamental limit set by the spin-exchange and spin-destruction cross sections.
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.
We propose and demonstrate a radio-frequency (rf) atomic magnetometer based on parametric resonances. Previously, most rf atomic magnetometers are based on magnetic resonances and their sensitivities are often limited by spin-exchange relaxation. Here, we introduce a novel scheme for an rf magnetometer where the rf magnetic field is measured by exciting the parametric resonances instead of magnetic resonances using parametric modulation fields. In this way, the spin-exchange relaxation is almost eliminated. Benefiting from the low spin relaxation rate, the parametric resonance scheme exhibits a narrower linewidth and stronger signal, which results in a higher sensitivity. With a 6×6×3 mm^{3} Rb atomic vapor cell, we developed an rf atomic magnetometer with a noise floor of 2 fT/Hz^{1/2}, which is about one order of magnitude higher than the sensitivity achieved in the magnetic-resonance-based scheme. The presented rf detection scheme holds promise in advancing rf atomic magnetometers and brings new insight into their various applications.
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.
Abstract High-sensitivity triaxial magnetic field measurements are crucial in various scientific and industrial applications, with spin-exchange relaxation-free (SERF) atomic magnetometers (AMs) standing out for their exceptional sensitivity. However, conventional methods for achieving triaxial measurements in SERF magnetometers typically involve multiple modulated magnetic fields, which introduce crosstalk challenges in array-based configurations. We propose a static bias magnetic field assisted optical modulation triaxial AM to address this limitation. In this configuration, the detuned circularly polarized light is utilized to achieve synchronous modulation of the fictitious magnetic field and pumping rate while incorporating a static bias magnetic field to generate a transverse projection component. We develop a comprehensive triaxial response model that fully considers the effects of the longitudinal spin polarization deflection. Building upon this model, we derive the relationship between the transverse spin component and the triaxial magnetic field and introduce parameter optimization methods to obtain optimal parameters, thus enabling triaxial measurements of 12 fT Hz −1/2 , 10 fT Hz −1/2 , and 15 fT Hz −1/2 along the x-, y -, and z -axes. Our approach offers significant advantages over existing methods, particularly in minimizing crosstalk and mitigating spin-exchange relaxation introduced by multiple modulated magnetic fields. Moreover, the effective detection of simulated magnetocardiography signals highlights the practical applicability and reliability of the proposed method in real-world scenarios.