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IEEE Transactions on Instrumentation and Measurement

Nonlinear Response Analysis in the Multipass Cavity SERF Comagnetometer

Jie Zheng, Xiaolin Gong, Jie Zhang, Xiaofei Huang, Saixin Zhou, Xing Heng, Kai Wei

Published Jan 1, 2026• 0 citations
Publisher

Abstract

Enhancing the light-atom interaction is a critical approach to improving the sensitivity of the spin-based quantum sensors. However, as the optical rotation increases, the output signal exhibits nonlinear characteristics that consequently impair the critical operation of the SERF comagnetometer, thereby negating the sensitivity gain. To address this issue, the nonlinear response model of the SERF comagnetometer is established, and the evolution of the coupled spin ensemble near the self-compensation state is analyzed based on this model. Based on the analysis of nonlinear responses under different nuclear spin self-compensation capabilities, a quasi-static parameter measurement method is proposed, which minimizes nonlinear response disturbance while decoupling probe light intensity noise, thereby enhancing measurement sensitivity. Experimental validation on a SERF comagnetometer with an integrated 14-pass cell confirms the accuracy of the nonlinear model. The self-compensation state was successfully determined under a 19.8-fold optical rotation amplification, and the suppression of probe laser intensity noise through frequency fitting achieving a 1.4-fold sensitivity improvement at 1 Hz. This study provides a significant advancement in light-atom interaction enhancement systems and enhances the sensitivity of SERF comagnetometers.

DOI
10.1109/tim.2026.3687295

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Enhancing the light-atom interaction is a critical approach to improving the sensitivity of the spin-based quantum sensors. However, as the optical rotation increases, the output signal exhibits nonlinear characteristics that consequently impair the critical operation of the SERF comagnetometer, thereby negating the sensitivity gain. To address this issue, the nonlinear response model of the SERF comagnetometer is established, and the evolution of the coupled spin ensemble near the self-compensation state is analyzed based on this model. Based on the analysis of nonlinear responses under different nuclear spin self-compensation capabilities, a quasi-static parameter measurement method is proposed, which minimizes nonlinear response disturbance while decoupling probe light intensity noise, thereby enhancing measurement sensitivity. Experimental validation on a SERF comagnetometer with an integrated 14-pass cell confirms the accuracy of the nonlinear model. The self-compensation state was successfully determined under a 19.8-fold optical rotation amplification, and the suppression of probe laser intensity noise through frequency fitting achieving a 1.4-fold sensitivity improvement at 1 Hz. This study provides a significant advancement in light-atom interaction enhancement systems and enhances the sensitivity of SERF comagnetometers.
As a novel quantum sensor utilizing atomic spin coupling mechanisms, spin-exchange relaxation-free (SERF) comagnetometers demonstrate promising applications in precision metrology such as magnetic field and rotation sensing. However, the ultra-high precision measurement capability exhibits vulnerability to multiple disturbance factors, with pump light intensity fluctuations emerging as a critical instability source that compromises operational reliability during prolonged measurements. In this paper, a model-driven paradigm for pump light intensity error suppression in SERF comagnetometers is proposed. The nonlinear dynamics are rigorously linearized via Taylor expansion within their valid range to construct a state-space model, ultimately deriving the pump light intensity frequency response model. The proposed methodology undergoes experimental validation on a K-Rb-21Ne comagnetometry platform, confirming the predictive capability for stability degradation mechanisms. Through theoretical analysis and experimental verification, this study reveals that magneto-optical non-orthogonality, which introduces a differential component in the light intensity transfer function, creates an approximate proportional relationship between the output signal and pump light intensity within the operating bandwidth. Light intensity noise is decomposed, and light intensity errors are quantitatively evaluated via the frequency response model. To address this critical issue affecting inertial measurement accuracy, a closed-loop control-based suppression method with optimized feedback gain is proposed. By dynamically adjusting the closed-loop feedback gain through real-time intensity monitoring, the intensity instability associated with optical pumping is suppressed from 0.56% to 0.14%, concomitant with a 2.8-fold improvement in the long-term stability of the SERF comagnetometer.
SERF atomic co-magnetometer offers high sensitivity and navigation-grade potential. However, the performance of traditional single-pass detection methods is limited due to insufficient Faraday rotation signals. To address this issue, this paper proposes a vertical-reflection multi-pass detection method. By introducing hollow roof mirrors and half-wave plates, the optical interaction path is significantly extended while ensuring strict orthogonality between the pump and probe beams. This compact square shaped optical path design effectively amplifies the Faraday rotation effect, suppresses cross-axis coupling, and significantly improves the signal-to-noise ratio and measurement sensitivity. Through theoretical modeling analysis, this approach enhances the rotation signal while extending the optical path, thereby improving the system response. Experimental results demonstrate that the multi-pass structure improves the signal-to-noise ratio by several times compared to single-pass detection, and the design offers excellent integration potential, providing a feasible technical path for high-performance SERF quantum sensors for navigation and high-precision physical research
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.
Atomic spin sensors are essential for beyond-the-standard-model exploration, biomagnetic measurement, and quantum navigation. While the traditional DC mode spin-exchange relaxation-free (SERF) comagnetometer achieves ultrahigh sensitivity, further improvements require suppressing technical noise and surpassing standard quantum limit. In this work, we develop a K-Rb-21^{21}21Ne SERF atomic comagnetometer that dynamically polarizes the electron and nuclear spins, shielding signals from direct interference by pump light. We establish a three-phase evolutionary model for hybrid spin ensemble dynamics, yielding a complete analytical solution, and analyze the responses to various spin perturbations. Additionally, we achieve an averaged 38.5 %\%% suppression of the polarization noise and identify the key factors that limit sensitivity improvements. The dynamically polarized comagnetometer exhibits effective suppression of technical noise and holds the potential to overcome quantum noise limit, while offering promising applications in exploring new physics and precise magnetic field measurements.
Multi-passed probe light can enhance the signal of atomic magnetometers by increasing the effective optical path length between the alkali metal atomic ensemble and the probe light, thereby strengthening the sensitivity. In recent years, multi-passed probe light has become an important method for improving the response signal and sensitivity of atomic magnetometers. To achieve biaxial magnetic field measurement while maintaining high sensitivity, a biaxial measurement spin-exchange relaxation-free (SERF) atomic magnetometer with a multi-passed probe light is proposed in this paper. The theoretical model and experimental advantages of using multi-passed probe light in longitudinal magnetic field modulation (Z-mode) SERF atomic magnetometers are analyzed. In this paper, a new model of output response of the Z-mode SERF atomic magnetometer based on multi-passed probe light is established, a compact reflective optical path is designed to increase the optical path between the probe light and the polarized alkali metal atomic ensemble, enhance the signal response, and achieve the suppression of low-frequency 1/f noise through longitudinal magnetic field modulation. Experimental results confirmed that the magnetic field sensitivity in the x- and y-axis of the multi-passed probe light configuration improved by 29% and 18%, respectively, compared to the single-pass configuration.
Quantum manipulation technology and photoelectric detection technology have jointly facilitated the rapid development of ultra-sensitive atomic spin magnetometers. To improve the output signal and sensitivity of the spin-exchange-relaxation-free (SERF) atomic spin magnetometer, the noises influencing on the output signal and the sensitivity were analyzed, and the corresponding noise suppression methods were presented. The magnetic field noises, including the residual magnetic field noise and the light shift noise, were reduced to approximately zero by employing the magnetic field compensation method and by adjusting the frequency of the pump beam, respectively. With respect to the operation temperature, the simulation results showed that the temperature of the potassium atomic spin magnetometer realizing the spin-exchange relaxation-free regime was 180 °C. Moreover, the fluctuation noises of the frequency and the power were suppressed by using the frequency and the power stable systems. The experimental power stability results showed that the light intensity stability was enhanced 10%. Contrast experiments on the sensitivity were carried out to demonstrate the validity of the suppression methods. Finally, a sensitivity of 13 fT/Hz(1/2) was successfully achieved by suppressing noises and optimizing parameters.