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IEEE Transactions on Instrumentation and Measurement

Real-Time In Situ Quantum Feedback Control of Electron Spin in Atomic Spin Gyroscopes

Hongyu Pei, Wei Quan, Linlin Yuan, Ze Cai, Zhihong Wu, Wenfeng Fan, Lihong Duan

Published Oct 18, 2023• 30 citations
Publisher

Abstract

The atomic spin gyroscope (ASG), based on spin-exchange relaxation-free (SERF) co-magnetometers, is poised to become the next generation of high-precision inertial sensors. However, the long-term stability of the gyro can be limited by electron spin polarization. In this study, we investigate a novel real-time, in situ quantum feedback control technique for electron spin polarization in ASGs. By varying the pumping rates, we analyze the gyroscope’s response to the modulation magnetic field, finding that electron polarization dramatically affects the magnetic field response properties of ASGs. It’s demonstrated that the amplitude or phase of the electron spin resonance can be locked for in situ control of electron spin polarization in real-time. A K-Rb-21Ne co-magnetometer is established to implement the proposed method, where a transverse modulating magnetic field is applied to resonate with the electron spin. The lock-in amplification (LIA) technique is used to obtain the amplitude or phase of the electron spin resonance, and the electron spin polarization is closed-loop controlled by locking the second harmonic resonance amplitude or phase. The gyro signal is extracted from the first harmonic of the electron spin resonance. Our experimental results show that real-time in situ feedback control of electron spin significantly improves ASG’s long-term stability and suppresses low-frequency noise. This proposed method has broad application prospects, including optically pumped magnetometers (OPMs), nuclear magnetic resonance gyroscopes (NMRGs), and co-magnetometers.

DOI
10.1109/tim.2023.3325515

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The atomic spin gyroscope (ASG), based on spin-exchange relaxation-free (SERF) co-magnetometers, is poised to become the next generation of high-precision inertial sensors. However, the long-term stability of the gyro can be limited by electron spin polarization. In this study, we investigate a novel real-time, in situ quantum feedback control technique for electron spin polarization in ASGs. By varying the pumping rates, we analyze the gyroscope’s response to the modulation magnetic field, finding that electron polarization dramatically affects the magnetic field response properties of ASGs. It’s demonstrated that the amplitude or phase of the electron spin resonance can be locked for in situ control of electron spin polarization in real-time. A K-Rb-21Ne co-magnetometer is established to implement the proposed method, where a transverse modulating magnetic field is applied to resonate with the electron spin. The lock-in amplification (LIA) technique is used to obtain the amplitude or phase of the electron spin resonance, and the electron spin polarization is closed-loop controlled by locking the second harmonic resonance amplitude or phase. The gyro signal is extracted from the first harmonic of the electron spin resonance. Our experimental results show that real-time in situ feedback control of electron spin significantly improves ASG’s long-term stability and suppresses low-frequency noise. This proposed method has broad application prospects, including optically pumped magnetometers (OPMs), nuclear magnetic resonance gyroscopes (NMRGs), and co-magnetometers.
Spin-exchange relaxation-free atomic spin gyroscope (SERF gyro) has ultrahigh theoretical sensitivity and is regarded as one of the most potential atomic gyroscopes. To investigate its rotation response, a high linear atomic spin precession detection module was developed firstly by modifying the fiber reflective Sagnac interferometer for atomic spin precession detection and operating it in closed-loop mode. The SERF gyro based on K-Rb-21Ne comagnetometer was built and tested and appeared obvious nonlinear response feature. The nonlinear rotation response model was deduced by assuming the rotation-induced nuclei spin procession detecting as an in-situ magnetometer inside the SERF gyro and the fitting curves are in good agreement with the experimental results. The optimized pump power for maximum sensitivity and measurable dynamic range were analyzed theoretically and demonstrated experimentally. The investigation results show that the nonlinear rotation response is an intrinsic property of SERF gyro and its measurable dynamic range is limited due to the saturation characteristic of the sum of pumping and relaxation rate. This indicates that SERF gyro is propitious to a position gyroscope with high sensitivity.
In traditional spin-exchange relaxation-free (SERF) gyroscopes, open-loop detection leaves the scale factor vulnerable to fluctuations in probe laser intensity and environmental temperature. To address this, an external-modulator-free closed-loop atomic spin gyroscope (ASG) is demonstrated using direct probe laser injection current modulation. A magnetic feedback loop maintains the total optical rotation at a zero point, decoupling the inertial signal from intensity and optical depth variations. Experimental results demonstrate a closed-loop rotation sensitivity of 2.8×10 −6 °/s/Hz 1/2 at 1 Hz. Compared to open-loop measurements under identical conditions (1×10 −5 ∘ /s/Hz 1/2 ), low-frequency noise is significantly suppressed. By eliminating bulky external modulators and effectively suppressing low-frequency noise, this design offers a highly competitive architecture for miniaturized atomic inertial sensors.
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.
• A dual-spectrum feedback architecture based on conventional closed-loop control is proposed, enabling real-time compensation for spin polarization error (SPE) in the K-Rb-21Ne atomic spin gyroscope, significantly enhancing long-term stability. • An adaptive dynamic control strategy based on a Lyapunov function is introduced to replace PID control, optimizing control parameters and improving system response speed and stability. • Experimental results show that the method improves SPE suppression by 54.4%, 74.5%, and 74.6% for clustering times of 100s, 500s, and 1000s, respectively. • Interference tests demonstrate that the method effectively eliminates steady-state offsets and enhances the system's adaptability to power density and polarization fluctuations, providing a long-term stability solution for optically pumped atomic devices. The long-term stability of atomic spin polarization plays a critical role in ensuring the sustained stability of atomic gyroscope outputs. However, drift in the laser pumping rate introduces the spin polarization error (SPE), necessitating high-precision closed-loop stabilization. Conventional single-beam-splitting closed-loop control methods overlook the time-varying characteristics of beam-splitting elements during prolonged operation, resulting in incomplete suppression of SPE in long-term measurements. To address this limitation, a dynamic light compensation framework is developed for the analysis and suppression of SPE in an atomic spin gyroscope. The proposed structure enables real-time monitoring of parameter variations in the beam-splitting elements and feeds this information back into the control loop to actively compensate for polarization errors induced by optical drift. Furthermore, an adaptive control method based on nonlinear inversion and disturbance observation is introduced, which estimates the internal state and compensates time-varying parameters in real time, thereby replacing conventional PID control and ensuring optimal closed-loop performance. Experimental results from a K-Rb- 21 Ne atomic gyroscope demonstrate real-time suppression of SPE, with improvements of 54.4%, 74.5%, and 74.6% for clustering times of 100, 500, and 1000 seconds, respectively. Interference tests show enhanced response speed and the elimination of steady-state offsets under power density and polarization disturbances. This method offers a novel solution for achieving long-term stability in optically pumped atomic devices, ensuring sustained measurement accuracy.
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.
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.