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Defence Technology

Atomic density disturbance rejection in atomic gyroscopes via faraday polarimetric decoupling

Zehua Liu, Yifan Yan, Haoying Pang, Xinhui Liu, Jixi Lu, Xusheng Lei, Zhuo Wang, Wei Quan

Published Jul 25, 2025• 2 citations
Publisher

Abstract

Atomic spin gyroscopes are promising candidates for next-generation inertial navigation due to extremely high theoretical precision, relatively small size among atomic gyroscopes, and promising potential for miniaturization. In particular, the spin-exchange relaxation-free (SERF) atomic gyroscope relies on optical pumping to polarize atoms, enabling rotation sensing through the Faraday optical rotation angle (FORA). However, fluctuations in atomic density introduce systematic errors in FORA measurements, limiting long-term stability. We present a data-driven decoupling method that isolates atomic density fluctuations from the FORA signal by modeling spatially resolved light absorption in the vapor cell. The model accounts for the spatial distribution of spin polarization in the pump-light interaction volume, density-dependent relaxation rates, wall-induced relaxation, and polarization diffusion, and is implemented within a finite-element framework. Compared to the conventional Lambert-Beer law, which assumes one-dimensional homogeneity, our approach captures the full three-dimensional density and polarization distribution, significantly improving the accuracy of light absorption modeling. The resulting absorption-density maps are used to train a feedforward neural network, yielding a high-precision estimator for atomic density fluctuations. This estimator enables the construction of a decoupling equation that separates the density contribution from the FORA signal. Experimental validation shows that this method improves the bias instability at σ (100 s) of the gyroscope was improved by 73.1% compared to traditional platinum-resistance-based stabilization. The proposed framework is general and can be extended to other optical pumping-based sensors, such as optically pumped magnetometers.

DOI
10.1016/j.dt.2025.07.022

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Atomic spin gyroscopes are promising candidates for next-generation inertial navigation due to extremely high theoretical precision, relatively small size among atomic gyroscopes, and promising potential for miniaturization. In particular, the spin-exchange relaxation-free (SERF) atomic gyroscope relies on optical pumping to polarize atoms, enabling rotation sensing through the Faraday optical rotation angle (FORA). However, fluctuations in atomic density introduce systematic errors in FORA measurements, limiting long-term stability. We present a data-driven decoupling method that isolates atomic density fluctuations from the FORA signal by modeling spatially resolved light absorption in the vapor cell. The model accounts for the spatial distribution of spin polarization in the pump-light interaction volume, density-dependent relaxation rates, wall-induced relaxation, and polarization diffusion, and is implemented within a finite-element framework. Compared to the conventional Lambert-Beer law, which assumes one-dimensional homogeneity, our approach captures the full three-dimensional density and polarization distribution, significantly improving the accuracy of light absorption modeling. The resulting absorption-density maps are used to train a feedforward neural network, yielding a high-precision estimator for atomic density fluctuations. This estimator enables the construction of a decoupling equation that separates the density contribution from the FORA signal. Experimental validation shows that this method improves the bias instability at σ (100 s) of the gyroscope was improved by 73.1% compared to traditional platinum-resistance-based stabilization. The proposed framework is general and can be extended to other optical pumping-based sensors, such as optically pumped magnetometers.
Abstract Atomic spin comagnetometers based on the spin-exchange relaxation-free (SERF) effect offer significant potential for inertial sensing and support the development of long-endurance, high-precision navigation technologies. However, limited nuclear spin polarization constrains the long-term stability of these systems. Here, a flat-top optical pumping configuration is introduced for SERF comagnetometers, expanding the uniform-intensity region of the beam to approximately 62 % , which enhances atomic polarization by around 19 % and improves magnetic noise suppression by 32 % . Experimental results demonstrate notable improvements in both sensitivity and long-term stability, highlighting the effectiveness of flat-top beams in overcoming atomic polarization uniformity limitations and advancing SERF co-magnetometer performance.
In atomic spin sensors based on optical pumping, pump beam instabilities can drive atomic spin polarization fluctuations, referred to here as pump-induced spin polarization noise, which may limit sensitivity and long-term stability. Because the local pump field inside the cell can differ from that inferred from external optical diagnostics, it remains difficult to directly quantify the actual in situ spin polarization noise and to evaluate and suppress its contribution to the sensor noise floor. Here, we propose an in situ decoupling method based on spin dynamics, in which a large longitudinal detuning field suppresses magnetic field and rotation responses, while a transverse projection field converts pump-induced fluctuations in longitudinal spin polarization into a measurable transverse spin signal. Demonstrated in a K-Rb-21Ne spin exchange relaxation free (SERF) comagnetometer, the proposed method suppresses the magnetic-field response by approximately 180-fold and enhances the pump-power-noise response by approximately 380-fold, thereby enabling effective separation and evaluation of pump-induced spin polarization noise. The method employs the atomic ensemble as an in situ probe of the spin dynamic response to the local pump optical field. It enables quantitative identification of pump fluctuation associated noise and direct evaluation of optical field stability under actual operating conditions, thereby providing an experimental basis for optical field stabilization and noise suppression assessment in SERF comagnetometers and related alkali atomic spin sensors.
Bias stability is one of the most important characteristics of a spin-exchange relaxation-free gyroscope (SERFG). The previous research on the SERFG has demonstrated that atomic density fluctuation induced by the vapor cell temperature fluctuations in a SERFG limits its bias stability. In this paper, a steady-state response model of a SERFG dependent on the vapor cell temperature is established, and a method to reduce the vapor cell temperature error of the SERFG is developed. By adjusting the vapor cell temperature, the SERFG can be tuned to a working point where the output signal is insensitive to the cell temperature fluctuation, i.e., the insensitive point, so that the bias error induced by cell temperature fluctuations can be effectively suppressed. The proposed method is verified by experiments, and experimental results are in good agreement with the model. By using the proposed method, SERFG drift was reduced from 0.051 deg/h to 0.028 deg/h without adjusting the wavelength of the probe laser. This study presents a way to improve the SERFG performance, which is of reference value for quantitative error analysis and miniaturization in atomic gyroscopes.
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.
The number density of alkali atoms in vaper cell is an important parameter for atomic magnetometer. The vapor cell is usually heated to a high temperature for the number density exceed to 1018m−3to achieve the spin-exchange-relaxation-free (SERF) process. The optical rotation of multichannel atomic magnetometers is affected by the number density distribution. We present an effective method for monitoring and analyzing the spatial distribution homogeneity of the atomic number density in the alkali metal cell within the SERF magnetometer. The numerical results from researching the model of electric heating films and ovens show that the temperature gradient increases with an increase in the cell temperature. This causes an nonuniform number density distribution based on the saturated vapor pressure curve. We present a laser absorption spectroscopy method by using the high-resolution beam profiling camera to record the power of the beam before and after the cell. An optimized optical system of the atomic magnetometer has been established by measuring the the number density variation in the spatial distribution in mm scale. The number density variation coefficient, which is introduced to evaluate the distribution homogeneity, increases from 0.0257 to 0.0333 when the temperature of the oven wall rises from 140°C to 190 °C, showing the same trend as the simulation results. The optical rotation distribution is calculated according to the magnetometer output signal formula. This study is of great interest for optimizing the oven structure and improving the stability of atomic spin polarization and sensitivity of the multichannel magnetometer.
A nuclear spin gyroscope based on an alkali-metal–noble-gas co-magnetometer operated in spin-exchange relaxation-free (SERF) regime is a promising atomic rotation sensor for its ultra-high fundamental sensitivity. However, the fluctuation of probe light intensity is one of the main technical error sources that limits the bias stability of the gyroscope. Here we propose a novel method to suppress the bias error induced by probe light intensity fluctuations. This method is based on the inherent magnetic field response characteristics of the gyroscope. By the application of a bias magnetic field, the gyroscope can be tuned to a working point where the output signal is insensitive to probe light intensity variation, referred to herein as ‘zero point’, thus the bias error induced by intensity fluctuations can be completely suppressed. The superiority of the method was verified on a K–Rb–21Ne co-magnetometer, and a bias stability of approximately 0.01 °/h was obtained. In addition, the method proposed here can remove the requirement of the closed-loop control of probe light intensity, thereby facilitating miniaturization of the gyroscope volume and improvement of reliability.