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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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  • [1]
    M. Stobińska, A. Buraczewski, M. Moore, W. R. Clements, J. J. Renema, S. W. Nam, T. Gerrits, A. Lita, W. S. Kolthammer, A. Eckstein, and I. A. Walmsley, “Quantum interference enables constant-time quantum information processing,” Sci. Adv., vol. 5, no. 7, Jul. 2019. doi: 10.1126/sciadv.aau9674
    [2]
    J. M. Arrazola, V. Bergholm, K. Brádler, et al., “Quantum circuits with many photons on a programmable nanophotonic chip,” Nature, vol. 591, no. 7848, pp. 54–60, Mar. 2021. doi: 10.1038/s41586-021-03202-1
    [3]
    N. Ghaeminezhad and S. Cong, “Preparation of hadamard gate for open quantum systems by the Lyapunov control method,” IEEE/CAA J. Autom. Sinica, vol. 5, no. 3, pp. 733–740, May 2018. doi: 10.1109/JAS.2018.7511084
    [4]
    C. D. Xiang, S. Ma, S. Kuang, and D. Y. Dong, “Coherent H control for linear quantum systems with uncertainties in the interaction Hamiltonian,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 2, pp. 432–440, Feb. 2021. doi: 10.1109/JAS.2020.1003429
    [5]
    A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Optical atomic clocks,” Phys. Rev. Lett., vol. 87, no. 2, pp. 637–701, Jun. 2015.
    [6]
    B. P. Abbott, R. Abbott, T. D. Abbott, et al., “Observation of gravitational waves from a binary black hole merger,” Phys. Rev. Lett., vol. 116, no. 6, Feb. 2016. doi: 10.1103/PhysRevLett.116.061102
    [7]
    W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Schaffer, K. Beloy, D. Nicolodi, R. C. Brown, N. Hinkley, G. Milani, M. Schioppo, T. H. Yoon, and A. D. Ludlow, “Atomic clock performance enabling geodesy below the centimetre level,” Nature, vol. 564, no. 7734, pp. 87–90, Dec. 2018. doi: 10.1038/s41586-018-0738-2
    [8]
    J. H. Storm, P. Hommen, D. Drung, and R. Körber, “An ultra-sensitive and wideband magnetometer based on a superconducting quantum interference device,” Appl. Phys. Lett., vol. 110, no. 7, p. 072603, Feb. 2017.
    [9]
    S. K. Lamoreaux, J. P. Jacobs, B. R. Heckel, F. J. Raab, and E. N. Fortson, “New limits on spatial anisotropy from optically pumped 201Hg and 199Hg,” Phys. Rev. Lett., vol. 58, no. 7, p. 746, Feb. 1987.
    [10]
    D. Meyer and M. Larsen, “Nuclear magnetic resonance gyro for inertial navigation,” Gyroscopy Navig., vol. 5, no. 2, pp. 75–82, Apr. 2014. doi: 10.1134/S2075108714020060
    [11]
    J. Qin, S. Wan, Y. Chen, et al., “New Developments in Science and Technology-60th Anniversary Special Issue, Beihang University (BUAA),” Science, vol. 338, no. 6104, p. 274, 2012.
    [12]
    Q. Z. Cai, G. L. Yang, W. Quan, N. F. Song, Y. Q. Tu, and Y. L. Liu, “Error analysis of the K-Rb-21Ne comagnetometer space-stable inertial navigation system,” Sensors, vol. 18, no. 2, p. 670, Feb. 2018.
    [13]
    J. C. Fang and J. Qin, “Advances in atomic gyroscopes: A view from inertial navigation applications,” Sensors, vol. 12, no. 5, pp. 6331–6346, May 2012. doi: 10.3390/s120506331
    [14]
    V. A. Kostelecký and N. Russell, “Data tables for Lorentz and CPT violation,” Rev. Mod. Phys., vol. 83, no. 1, pp. 11–32, Jan. 2011. doi: 10.1103/RevModPhys.83.11
    [15]
    V. V. Flambaum and M. V. Romalis, “Limits on Lorentz invariance violation from coulomb interactions in nuclei and atoms,” Phys. Rev. Lett., vol. 118, no. 14, p. 142501, Apr. 2017.
    [16]
    M. Smiciklas, J. M. Brown, L. W. Cheuk, S. J. Smullin, and M. V. Romalis, “New test of local Lorentz invariance using a 21Ne-Rb-K comagnetometer,” Phys. Rev. Lett., vol. 107, no. 17, p. 171604, Oct. 2011.
    [17]
    J. M. Brown, “A new limit on Lorentz- and CPT-violating neutron spin interactions using a potassium-helium comagnetometer,” Ph.D. dissertation, Princeton Univ., Princeton, USA, 2011.
    [18]
    G. Vasilakis, J. M. Brown, T. W. Kornack, and M. V. Romalis, “Limits on new long range nuclear spin-dependent forces set with a K-3He comagnetometer,” Phys. Rev. Lett., vol. 103, no. 26, p. 261801, Dec. 2009.
    [19]
    M. Bulatowicz, R. Griffith, M. Larsen, J. Mirijanian, C. B. Fu, E. Smith, W. M. Snow, H. Yan, and T. G. Walker, “Laboratory search for a long-range T-odd, P-odd interaction from axionlike particles using dual-species nuclear magnetic resonance with polarized 129Xe and 131Xe gas,” Phys. Rev. Lett., vol. 111, no. 10, p. 102001, Sept. 2013.
    [20]
    J. C. Fang, J. Qin, S. A. Wan, Y. Chen, and R. J. Li, “Atomic spin gyroscope based on 129Xe-Cs comagnetometer,” Chin. Sci. Bull., vol. 58, no. 13, pp. 1512–1515, May 2013. doi: 10.1007/s11434-013-5759-5
    [21]
    J. C. Fang, S. A. Wan, and H. Yuan, “Dynamics of an all-optical atomic spin gyroscope,” Appl. Opt., vol. 52, no. 30, pp. 7220–7227, Oct. 2013. doi: 10.1364/AO.52.007220
    [22]
    J. C. Fang, Y. Chen, Y. Lu, W. Quan, and S. Zou, “Dynamics of Rb and 21Ne spin ensembles interacting by spin exchange with a high Rb magnetic field,” J. Phys. B: At. Mol. Opt. Phys., vol. 49, no. 13, p. 135002, Jun. 2016.
    [23]
    W. F. Fan, W. Quan, W. J. Zhang, L. Xing, and G. Liu, “Analysis on the magnetic field response for nuclear spin co-magnetometer operated in spin-exchange relaxation-free regime,” IEEE Access, vol. 7, pp. 28574–28580, Feb. 2019. doi: 10.1109/ACCESS.2019.2902181
    [24]
    L. W. Jiang, W. Quan, R. J. Li, L. H. Duan, W. F. Fan, Z. Wang, F. Liu, L. Xing, and J. C. Fang, “Suppression of the cross-talk effect in a dual-axis K-Rb-21Ne comagnetometer,” Phys. Rev. A, vol. 95, no. 6, p. 062103, Jun. 2017.
    [25]
    L. Xing, Z. Wang, J. Huang, W. Quan, W. F. Fan, and L. W. Jiang, “Laser intensity stabilization control for an atomic spin gyroscope,” in Proc. 13th IEEE Conf. Industrial Electronics and Applications, Wuhan, China, 2018, pp. 735–738.
    [26]
    J. C. Fang, R. J. Li, L. H. Duan, Y. Chen, and W. Quan, “Study of the operation temperature in the spin-exchange relaxation free magnetometer,” Rev. Sci. Instrum., vol. 86, no. 7, p. 073116, Jul. 2015.
    [27]
    Z. Wang, J. Huang, W. Quan, L. H. Duan, W. J. Zhang, and Y. Fu, “A data-driven state observation method for atomic spin-exchange relaxation-free comagnetometer,” in Proc. IEEE 8th Data Driven Control and Learning Systems Conf., Dali, China, 2019, pp. 876–882.
    [28]
    L. W. Jiang, W. Quan, Y. X. Liang, J. L. Liu, L. H. Duan, and J. C. Fang, “Effects of pump laser power density on the hybrid optically pumped comagnetometer for rotation sensing,” Opt. Exp., vol. 27, no. 20, pp. 27420–27430, Sept. 2019. doi: 10.1364/OE.27.027420
    [29]
    L. W. Jiang, W. Quan, F. Liu, W. F. Fan, L. Xing, L. H. Duan, W. M. Liu, and J. C. Fang, “Closed-loop control of compensation point in the K-Rb-21Ne comagnetometer,” Phys. Rev. Appl., vol. 12, no. 2, p. 024017, Aug. 2019.
    [30]
    W. F. Fan, W. Quan, F. Liu, L. Xing, and G. Liu, “Suppression of the bias error induced by magnetic noise in a spin-exchange relaxation-free gyroscope,” IEEE Sens. J., vol. 19, no. 21, pp. 9712–9721, Nov. 2019. doi: 10.1109/JSEN.2019.2929505
    [31]
    R. J. Li, W. Quan, W. F. Fan, L. Xing, and J. C. Fang, “Influence of magnetic fields on the bias stability of atomic gyroscope operated in spin-exchange relaxation-free regime,” Sens. Actuators A Phys., vol. 266, pp. 130–134, Oct. 2017. doi: 10.1016/j.sna.2017.09.023
    [32]
    R. E. Kalman, “Mathematical description of linear dynamical systems,” J. Soc. Ind. Appl. Math. A Control, vol. 1, no. 2, pp. 152–192, Jan. 1963. doi: 10.1137/0301010
    [33]
    C. H. Wang, Y. F. Zhao, and Y. Q. Chen, “The controllability, observability, and stability analysis of a class of composite systems with fractional degree generalized frequency variables,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 3, pp. 859–864, May 2019. doi: 10.1109/JAS.2019.1911501
    [34]
    X. C. Wang, Y. G. Xi, W. Z. Huang, and S. Jia, “Deducing complete selection rule set for driver nodes to guarantee network’s structural controllability,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 5, pp. 1152–1165, Sept. 2019. doi: 10.1109/JAS.2017.7510724
    [35]
    Z. Wang, H. Yuan, W. Quan, Y. Y. Zhai, B. Q. Zhou, and S. X. Liu, “Controllability analysis of a class of affine nonlinear system,” in Proc. Chinese Automation Congr., Xi’an, China, 2018, pp. 188–191.
    [36]
    M. A. Müller, D. Liberzon, and F. Allgöwer, “Norm-controllability of nonlinear systems,” IEEE Trans. Autom. Control, vol. 60, no. 7, pp. 1825–1840, Jul. 2015. doi: 10.1109/TAC.2015.2394953
    [37]
    S. Appelt, A. B. A. Baranga, C. J. Erickson, M. V. Romalis, A. R. Young, and W. Happer, “Theory of spin-exchange optical pumping of 3He and 129Xe,” Phys. Rev. A, vol. 58, no. 2, pp. 1412–1439, Aug. 1998. doi: 10.1103/PhysRevA.58.1412
    [38]
    Y. Chen, W. Quan, L. H. Duan, Y. Lu, L. W. Jiang, and J. C. Fang, “Spin-exchange collision mixing of the K and Rb ac stark shifts,” Phys. Rev. A, vol. 94, no. 5, p. 052705, Nov. 2016.
    [39]
    L. Huang, Theoretical Basis of Stability and Robustness. Beijing, China: Science Press, 2003.
    [40]
    L. Xing, W. Quan, W. F. Fan, R. J. Li, L. W. Jiang, and J. C. Fang, “Field optimization method of a dual-axis atomic magnetometer based on frequency-response and dynamics,” Meas. Sci. Technol., vol. 29, no. 5, p. 055005, Mar. 2018.
    [41]
    T. W. Kornack, R. K. Ghosh, and M. V. Romalis, “Nuclear spin gyroscope based on an atomic comagnetometer,” Phys. Rev. Lett., vol. 95, no. 23, p. 230801, Nov. 2005.

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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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