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Volume 9 Issue 4
Apr.  2022

IEEE/CAA Journal of Automatica Sinica

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Z. Wang, S. X. Liu, R. G. Wang, L. L. Yuan, J. Huang, Y. Y. Zhai, and S. Zou, “Atomic spin polarization controllability analysis: A novel controllability determination method for spin-exchange relaxation-free co-magnetometers,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 4, pp. 699–708, Apr. 2022. doi: 10.1109/JAS.2021.1004383
Citation: Z. Wang, S. X. Liu, R. G. Wang, L. L. Yuan, J. Huang, Y. Y. Zhai, and S. Zou, “Atomic spin polarization controllability analysis: A novel controllability determination method for spin-exchange relaxation-free co-magnetometers,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 4, pp. 699–708, Apr. 2022. doi: 10.1109/JAS.2021.1004383

Atomic Spin Polarization Controllability Analysis: A Novel Controllability Determination Method for Spin-Exchange Relaxation-Free Co-Magnetometers

doi: 10.1109/JAS.2021.1004383
Funds:  This work was supported in part by the National Natural Science Foundation of China (61673041, 62003022), and the Beijing Academy of Quantum Information Science Research Program (Y18G34)
More Information
  • This paper investigates the atomic spin polarization controllability of spin-exchange relaxation-free co-magnetometers (SERFCMs). This is the first work in the field of controllability analysis for the atomic spin ensembles systems, whose dynamic behaviors of spin polarization are described by the Bloch equations. Based on the Bloch equations, a state-space model of the atomic spin polarization for SERFCM is first established, which belongs to a particular class of nonlinear systems. For this class of nonlinear systems, a novel determination method for the global state controllability is proposed and proved. Then, this method is implemented in the process of controllability analysis on the atomic spin polarization of an actual SERFCM. Moreover, a theoretically feasible and reasonable solution of the control input is proposed under some physical constraints, with whose limitation of realistic conditions, the controller design can be accomplished more practically and more exactly. Finally, the simulation results demonstrate the feasibility and validation of the proposed controllability determination method.

     

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    Highlights

    • This paper is the first article of controllability analysis for systems of atomic spin ensembles, whose dynamic behaviors of spin polarization can be described by Bloch equations. Meanwhile, our conclusions have the potential to be expanded to other systems of precision measuring instruments, which are based on effects of atomic spin and dynamical evolution description by Bloch equations. Therefore, our theoretical results in this paper are not only pioneering but also of certain universality.
    • In this paper, for SERFCM, a nonlinear atomic spin polarization model has been derived from the Bloch equations. In this model, we concern both the variation of transverse as well as longitudinal polarization, and the notion of PSS is introduced according to the real condition. In this case, the model we establish has higher nonlinearity and more difficulty in theoretical analysis, but it is closer to SERFCM in practical engineering with more application value.
    • For a specific class of nonlinear systems, we propose and prove a criterion condition of global state controllability, which is the first work to analyze the atomic spin polarization controllability of SERFCM in the related research field. Meanwhile, this criterion condition can also be applied to the controllability analysis for that particular class of nonlinear systems. In addition, we propose a theoretically feasible and reasonable solution of the control input under some physical constraints, which are helpful for the controller design.

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