The accuracy of quantum state estimation and dynamic signal tracking is crucial for the reliability and performance of quantum sensing instruments such as spin-exchange relaxation-free (SERF) co-magnetometers and gyroscopes. To improve the performance of the SERF gyroscope for future quantum navigation applications, an adaptive quantum estimation and closed-loop optimal control method based on fault detection and isolation (FDI) and an adaptive Kalman filter is proposed. Firstly, the system model of the SERF gyroscope is established, and a real-time angular velocity measurement method is provided. Then, the stochastic model of the SERF gyroscope is analyzed based on an adaptive quantum Kalman observer to track and compensate for real-time angular velocity error with the assistance of FDI. Finally, the real-time LQI (Linear-Quadratic-Integral) control method is adopted to improve the dynamic response and accuracy of the overall system. Simulations and experiments are conducted based on the SERF gyroscope platform. The results show that the system can achieve optimal tracking accuracy for polarization estimation and effectively isolate fault information. The dynamic response time has been improved by 58.2% under environmental disturbance, which provides a foundation for subsequent navigation applications.
The accuracy of quantum state estimation and dynamic signal tracking is crucial for the reliability and performance of quantum sensing instruments such as spin-exchange relaxation-free (SERF) co-magnetometers and gyroscopes. To improve the performance of the SERF gyroscope for future quantum navigation applications, an adaptive quantum estimation and closed-loop optimal control method based on fault detection and isolation (FDI) and an adaptive Kalman filter is proposed. Firstly, the system model of the SERF gyroscope is established, and a real-time angular velocity measurement method is provided. Then, the stochastic model of the SERF gyroscope is analyzed based on an adaptive quantum Kalman observer to track and compensate for real-time angular velocity error with the assistance of FDI. Finally, the real-time LQI (Linear-Quadratic-Integral) control method is adopted to improve the dynamic response and accuracy of the overall system. Simulations and experiments are conducted based on the SERF gyroscope platform. The results show that the system can achieve optimal tracking accuracy for polarization estimation and effectively isolate fault information. The dynamic response time has been improved by 58.2% under environmental disturbance, which provides a foundation for subsequent navigation applications.
The accuracy of quantum state estimation and dynamic signal tracking is crucial for the reliability and performance of quantum sensing instruments such as spin-exchange re-laxation-free (SERF) co-magnetometers and gyroscopes. To improve the performance of the SERF gyroscope for future quantum navigation application, an adaptive quantum estimation and closed-loop optimal control method based on fault detection and isolation (FDI) and adaptive Kalman filter is proposed. Firstly, the system model of the SERF gyroscope is established, and a real-time angular velocity measurement method is provided. Then, the stochastic model of the SERF gyroscope is analyzed based on an adaptive quantum Kalman observer to track and compensate for real-time angular velocity error with the assistance of FDI. Finally, the real-time LQI (Linear-Quadratic-Integral) control method is adopted to improve the dynamic response and accuracy of the overall system. Simulations and experiments are conducted based on the SERF gyroscope platform. The results show that the system can achieve optimal tracking accuracy for polarization estimation and effectively isolate fault information. The dynamic response time has been improved by 58.2% under environmental disturbance, which provide a foundation for subsequent navigation applications.
Integrating classical estimation and control theory with quantum systems holds potential for quantum measurement improvement. Here, we report a real-time linear quadratic regulator (LQR) optimal control for spin damping in electron-nuclear spin-coupling regime. The aim is a quicker response and enhanced noise suppression for precision quantum measurements. Using a Kalman quantum observer with electron spin data, we estimate the quantum state of nondirectly observable nuclear spin. LQR full-state feedback optimal control is applied to achieve faster spin-coupling damping. Demonstrated in an atomic spin gyroscope, our method significantly enhances dynamic response with a 4.3-fold improvement in rotational bandwidth. It also boosts long-term stability and measurement sensitivity by 62.9%, presenting a promising avenue to elevate spin-coupling ensemble performance in quantum measurements.
The extraction of weak signals plays a crucial role in quantum precision measurement, where the estimation results are often limited by low signal-to-noise ratios. Here, we demonstrate a parameter-estimation framework based on the adaptive extended Kalman filter for dynamic magnetic-field estimation in quantum systems using spin-noise measurements -- a challenging regime characterized by weak signals. By modeling the magnetic field as an unknown parameter, the proposed approach alleviates model dependence in state estimation. Furthermore, by introducing an adaptive algorithm with real-time noise estimation, our method overcomes the measurement noise intensity constraints of conventional extended Kalman filtering and enhances its practical applicability. Numerical simulations covering three representative magnetic-field dynamics validate the capability of the proposed framework, while experimental results demonstrate successful tracking of a seismo-magnetic-like signal beyond the intrinsic sensitivity of conventional spin-noise spectroscopy.
• 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.
Quantum entanglement, in the form of spin squeezing, is known to improve the sensitivity of atomic sensors to static or slowly varying fields. Sensing transient events presents a distinct challenge, requires different analysis tools, and has not been shown to benefit from entanglement in practically important scenarios such as spin-precession magnetometry. To address this, we apply concepts from continuous quantum measurements and estimation theory to optical atomic magnetometers, aiming to accurately model these devices, interpret their measurement data, control their dynamics, and achieve optimal sensitivity. Quantifying this optimal performance requires determining a fundamental quantum limit on sensitivity. We derive this limit, imposed by noise, and show that it scales at best linearly with sensing time and atom number N, ruling out any super-classical scaling. This limit is independent of the initial state, measurement, estimator, and measurement-based feedback, and depends only on the decoherence model and the strength of field fluctuations. Thus, finding an estimator that attains this bound proves the sensing strategy optimal. To approach this limit, we develop a quantum dynamical model scalable with N, based on a co-moving Gaussian approximation of the stochastic master equation, which includes measurement backaction and decoherence. This enables a real-time estimation and control architecture integrating an extended Kalman filter with a linear quadratic regulator. Simulating the magnetometer with our model and EKF+LQR strategy shows that quantum-limited tracking of constant and fluctuating fields is within reach of current atomic magnetometers. Our sensing strategy can also track biologically relevant signals, such as heartbeat-like waveforms, and drive the atomic ensemble into an entangled state, even when the measurement record is used for feedback but later discarded.
In recent years, developments in quantum sensing, laser, and atomic sensor technologies have also enabled advancement in the field of quantum navigation. Atomic-based gyroscopes have emerged as one of the most critical atomic sensors in this respect. In this review, a brief technology statement of spin exchange relaxation free (SERF) and nuclear magnetic resonance (NMR) type atomic comagnetometer gyroscope (CG) is presented. Related studies in the literature have been gathered, and the fundamental compositions of CGs with technical basics are presented. A comparison of SERF and NMR CGs is provided. A basic simulation of SERF CG was carried out because of its high theoretic bias stability limit. Besides, some highly critical challenges for CGs were examined and reported with compensation methods. The objective of this review is to offer a guide for researchers to develop high-precision atomic gyroscopes and to encourage further research.