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Applied Optics

Dynamics of an all-optical atomic spin gyroscope

Jiancheng Fang, Shuangai Wan, Heng Yuan

Published Oct 11, 2013• 33 citations
Publisher

Abstract

We present the transfer function of an all-optical atomic spin gyroscope through a series of differential equations and validate the transfer function by experimental test. A transfer function is the basis for further control system design. We build the differential equations based on a complete set of Bloch equations describing the all-optical atomic spin gyroscope, and obtain the transfer function through application of the Laplace transformation to these differential equations. Moreover, we experimentally validate the transfer function in an all-optical Cs-Xe129 atomic spin gyroscope through a series of step responses. This transfer function is convenient for analysis of the form of control system required. Furthermore, it is available for the design of the control system specifically to improve the performance of all-optical atomic spin gyroscopes.

DOI
10.1364/ao.52.007220

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We present the transfer function of an all-optical atomic spin gyroscope through a series of differential equations and validate the transfer function by experimental test. A transfer function is the basis for further control system design. We build the differential equations based on a complete set of Bloch equations describing the all-optical atomic spin gyroscope, and obtain the transfer function through application of the Laplace transformation to these differential equations. Moreover, we experimentally validate the transfer function in an all-optical Cs-Xe129 atomic spin gyroscope through a series of step responses. This transfer function is convenient for analysis of the form of control system required. Furthermore, it is available for the design of the control system specifically to improve the performance of all-optical atomic spin gyroscopes.
We present a method to determine and suppress the light shift in an atomic spin gyroscope. This method doesn't require additional drive source or frequency modulation, and it is based on the dynamics of an atomic spin gyroscope to determine a clean curve as a function of the frequency of the pump beam that predicts the zero light shift. We experimentally validate the method in a Cs-(129)Xe atomic spin gyroscope and verify the results through numerical simulations. This method can also be applied to an atomic spin magnetometer based on the spin-exchange relaxation-free exchange that experiences light shift. The method is useful for atomic spin devices because it can improve long-term performance and reduce the influence of the laser.
With the rapid development of quantum manipulation technique, atomic spin gyroscope has been demonstrated in recent years. Understanding the sources and the influence of error on the performance of atomic spin gyroscope is important during the design of such devices. The basic principle of atomic spin gyroscope was reviewed and the analysis of error sources presented began with the coupled Bloch equations describing the dynamics of atomic spin gyroscope including magnetic field, light shift and pump-probe non-orthogonality. It was shown analytically that the first order effects of the transverse magnetic fields and imperfections can be eliminated by turning the longitudinal magnetic field on the magnetic field compensation point. The effects of longitudinal magnetic field and light shift imperfections with other terms zeroed contributed only to scale factor of the atomic spin gyroscope. Furthermore, the effects magneto-optical crystal and magnetic shielding due to temperature drift were described and according approaches to suppress these errors were also proposed.
We report a novel Cs-(129)Xe atomic spin gyroscope (ASG) with closed-loop Faraday modulation method. This ASG requires approximately 30 min to start-up and 110 °C to operate. A closed-loop Faraday modulation method for measurement of the optical rotation was used in this ASG. This method uses an additional Faraday modulator to suppress the laser intensity fluctuation and Faraday modulator thermal induced fluctuation. We theoretically and experimentally validate this method in the Cs-(129)Xe ASG and achieved a bias stability of approximately 3.25 °∕h.
• 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.
We reported an efficient approach to analyze spin precessions of different hyperpolarized noble gases with atomic magnetometers based on system identification. Spin evolution of the magnetometer can be robustly approximated as the second order system by referring to the Bloch equation under the negligible self-interaction and its transfer function model can be deduced. We measured the dynamic responses of different atomic pairs, such as cesium magnetometer with a partner of xenon-129, potassium magnetometer with a partner of helium-3, and hybrid of cesium and rubidium magnetometer with a partner of neon-21. By referring to the experimental results, corresponding systematic parameters for the transfer function models have been identified based on least-square method, whose outputs were consistent with experimental results. Based on the models, the system stabilities and their variations with different gains have been analyzed with control theory, both of which are described here. Applying control theory to analyze dynamic responses of spin ensembles plays an important role for the future applications.
We describe a new nuclear spin gyroscope based on K-3He comagnetometer. In this type of Gyroscope, there is much space in improving the sensitivity of measurement, therefore, it's significant to study it. In the comagnetometer, the state equation of the system is very complicated, and we just give the relationship between comagnetometer signal and the rotation angle of gyroscpoe in Bloch picture. Finally, we extend the equation of system to quantum filtering equation, so that we could improve the stability of system and sensitivity of measurement by continuous measurement and quantum feedback control.