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EPJ Quantum Technology

Dynamic suppression of phase errors in optically pumped atomic magnetometers for applications in geomagnetic environments

Huanyu Zhou, Jin Li, Yi Zhang, Shuo Sun, Rongtong Zhu, Yan Xuan, Pengcheng Du, Zhuangsheng Zhu

Published Mar 20, 2026• 1 citation
Publisher

Abstract

Phase error is one of the primary factors leading to deviations between the readings of alkali-metal optically pumped atomic magnetometers (OPAMs) operating in closed-loop mode and the true magnetic field values. Because the phase error varies significantly with both the magnitude of the measured magnetic field and the orientation of the probe relative to the field direction, it imposes a major limitation on the use of OPAMs in real geomagnetic environments. To address this issue, a rapid suppression method for phase error in closed-loop OPAM operation is proposed. Specifically, the azimuth, pitch, and rotation angles are employed to quantitatively characterize the spatial orientation of the measured magnetic field with respect to the probe, and the phase error is measured and calibrated under closed-loop conditions. Experimental results indicate that the phase error mainly arises from changes in the rotation angle and the magnitude of the magnetic field, and is essentially insensitive to variations in azimuth and pitch angles. Based on this calibration, the effectiveness of the proposed suppression method was verified. When the instantaneous fluctuation of the phase error is less than π /6, the method can suppress the phase error to within π /180 within one second, with negligible impact on the OPAM’s dynamic performance. This work provides a dynamic phase error suppression approach for OPAMs, refines the theoretical understanding of OPAM phase errors, and lays a solid foundation for their design and application in geomagnetic environments.

DOI
10.1140/epjqt/s40507-026-00499-7

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•Feb 5, 2021•0 citations
Phase error is one of the primary factors leading to deviations between the readings of alkali-metal optically pumped atomic magnetometers (OPAMs) operating in closed-loop mode and the true magnetic field values. Because the phase error varies significantly with both the magnitude of the measured magnetic field and the orientation of the probe relative to the field direction, it imposes a major limitation on the use of OPAMs in real geomagnetic environments. To address this issue, a rapid suppression method for phase error in closed-loop OPAM operation is proposed. Specifically, the azimuth, pitch, and rotation angles are employed to quantitatively characterize the spatial orientation of the measured magnetic field with respect to the probe, and the phase error is measured and calibrated under closed-loop conditions. Experimental results indicate that the phase error mainly arises from changes in the rotation angle and the magnitude of the magnetic field, and is essentially insensitive to variations in azimuth and pitch angles. Based on this calibration, the effectiveness of the proposed suppression method was verified. When the instantaneous fluctuation of the phase error is less than π /6, the method can suppress the phase error to within π /180 within one second, with negligible impact on the OPAM’s dynamic performance. This work provides a dynamic phase error suppression approach for OPAMs, refines the theoretical understanding of OPAM phase errors, and lays a solid foundation for their design and application in geomagnetic environments.
Single-beam optically pumped atomic magnetometers (OPAMs) represent promising candidates for applications in geomagnetic field monitoring, biomedicine, and various other precision sensing domains owing to their exceptional sensitivity, high measurement accuracy, and cost-effectiveness. However, in orientation-based OPAMs utilizing circularly polarized light (CPL) pumping, the off-resonant light introduces light shift. The light shift acts as an additional magnetic field, reducing the measurement accuracy of OPAMs. Moreover, the dependence of the light shift on light intensity and frequency facilitates the conversion of light noise into magnetic noise, thereby degrading the sensitivity of OPAMs. In this study, we propose an optical pumping scheme based on space division multiplexing light (SDML) to suppress the light shift in OPAM. The approach employs two orthogonally polarized linearly polarized beams with a controlled phase difference to generate a spatially periodic distribution of left- and right-handed CPL. Optical pumping with the SDML induces oppositely directed light shifts in distinct spatial regions that effectively cancel each other. Finally, it is verified by experiments that the light shift is greatly suppressed based on SDML. Under detuned SDML pumping, both the light shift and light intensity noise are suppressed by over 50%, while maintaining a sensitivity comparable to that achieved with conventional CPL pumping. The proposed method demonstrates significant potential for magnetometers in light-noise-prone environments, and it can be generalized to other orientation-based magnetometers that rely on CPL pumping.
The light shift represents a major source of measurement error and system noise in optically pumped atomic magnetometers (OPAMs). Tuning the laser frequency to a specific value is a common and effective approach to suppressing light shift in many optical-pumping systems. However, when this method is applied to OPAMs, a significant issue arises: at the zero-light-shift frequency, the magnetometer’s sensitivity decreases markedly. Consequently, it is not possible to optimize simultaneously both the measurement accuracy affected by the light shift and the overall sensitivity of the magnetometer. To address this contradiction, the underlying mechanism was analyzed using the theory of light absorption and the principles governing light–atom interactions, leading to the proposal of a dual-frequency optical-pumping scheme. Experimental results demonstrate that this approach can suppress the light shift by more than 95% while maintaining the optimal sensitivity of the OPAM. The proposed dual-frequency scheme can also be extended to other circularly polarized optical-pumping systems, thereby facilitating both the enhancement of OPAM performance and its practical deployment in real-world applications.
Heading errors of atomic magnetometers refer to the dependence of measurement results on the sensor orientation with respect to the external magnetic field. There are three main sources of such errors: the light shift effect, the linear nuclear-spin Zeeman effect, and the nonlinear Zeeman effect. In this work, we suppress the first two effects by using the Bell-Bloom optical pumping method and probe the atomic signals while the pumping beam is off, and focus on the heading error induced by nonlinear Zeeman effect while the sensor operates in the geomagnetic field range. We demonstrate several schemes to suppress this remaining heading error within 1 nT using a single magnetometer or a comagnetometer. In the magnetometer system, two schemes are developed to average out the horizontal atomic polarization in space or in time, respectively. In the comagnetometer system, we combine the simultaneously measured Larmor frequencies of two different alkali atoms to either suppress the heading error or extract the orientation of the pumping beam relative to the bias field.
The deterioration of spin coherence has been a significant challenge in the field of quantum magnetic measurements based on optically pumped atomic magnetometers (OPAMs). However, measurement and evaluation methods for specific relaxation components of OPAMs under working conditions remain lacking, which impedes further improvement in OPAM performance. To address this, we propose a methodology for quantifying the relaxation components of an OPAM under realistic operating conditions. Using this method, we confirm the existence of an anomalous relaxation mechanism induced by radio-frequency (RF) magnetic fields and develop an empirical expression to describe its behavior. The results experimentally demonstrate that, in addition to the well-known spin-exchange relaxation, the dominant contributions to spin relaxation arise from optical pumping and RF magnetic fields. This work paves the way for sensitivity enhancement in quantum magnetometry and refines the theoretical understanding of relaxation mechanisms in OPAMs.
The measurement of ultra-weak magnetic fields relies on the conversion of magnetic field information to atom spins using alkali metals. In this context, the detection of magnetic fields is accomplished through rotation angle measurement of linearly polarized light. This paper proposes a novel method to suppress mechanical errors between polarizers in the rotation angle measurement, taking advantage of the optical setup characteristics in atomic magnetometers. The method involves applying two separate frequency modulations to the pump beam and probe beam, effectively eliminating mechanical errors between the polarizers as a direct current component using a double-channel lock-in amplifier. Additionally, the double modulation method offers a solution to suppress shot noise caused by incident beam fluctuations or transverse spin relaxation, as well as mechanical errors among optical elements in the light path, enabling high-precision measurements.
Precession frequencies measured by optically pumped scalar magnetometers are dependent on the relative angle between the sensor and the external magnetic field. This dependence is known to be induced mainly by the nonlinear Zeeman effect and the orientation-dependent light shift, resulting in the so-called heading errors if the magnetic field orientation is not well known or is not stable. In this work, we find that the linear nuclear Zeeman effect has also a significant impact on the heading errors. It not only shifts the precession frequency but causes asymmetry: the heading error for sensors orienting in the upper-half plane with respect to the external field is different from the case when the sensors work in the lower-half plane. This heading error also depends on the relative direction of the probe laser to the driving magnetic field. With a left-handed circularly-polarized pump laser, when the probe laser is parallel to the driving field, the angular dependence of the precession frequency is smaller when the sensor is in the upper plane. Otherwise, when they are perpendicular to each other, the heading error is smaller when the sensor is in the lower plane. Furthermore, to suppress the heading error, we propose to utilize a small magnetic field along the propagation direction of the pump laser. By tuning the magnitude of this auxiliary field, the heading-error curve is flattened around different angles, which can increase the accuracy in practice when the magnetometer works around a certain orientation angle.