Abstract
Quantum systems can display the quantum chaos characteristics under non-rotating wave approximation. Because of the complex multi-body effect, the inevitability of coupling with the environment and the existence of uncertainty relation, some parameters in quantum system are often uncertain. In order to determine the properties of quantum system, we need to accurately measure any parameters in the system. In this work, we first analyse the characteristics of quantum bits interacting with a single-mode radiation field. On this basis, we design a unique technique to accurately measure the uncertain parameter in the quantum bits. Finally, we complete the synchronization transmission of signal in quantum bits based on the sliding mode control technology.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Al-Mahbashi, G., Noorani, M.S.M., Bakar, S.A.: Projective lag synchronization in drive-response dynamical networks. Int. J. Mod. Phys. C 25, 771–776 (2014)
Arellano-Delgado, A., López-Gutiérrez, R.M., Martínez-Clark, R., Cruz-Hernández, C.: Small-world outer synchronization of small-world chaotic networks. J. Comput. Nonlinear Dyn. 13, 101008 (2018)
Belykh, V.N., Belykh, I.V., Hasler, M.: Connection graph stability method for synchronized coupled chaotic systems. Physica D 195, 159–187 (2004)
Dharani, S., Rakkiyappan, R., Park, J.H.: Pinning sampled-data synchronization of coupled inertial neural networks with reaction–diffusion terms and time-varying delays. Neurocomputing 227, 101–107 (2017)
Diver, M., Robb, G.R.M., Oppo, G.L.: Nonlinear and chaotic dynamics of a Bose–Einstein condensate in an optical cavity. Phys. Rev. A 89, 033602 (2014)
Dörfler, F., Bullo, F.: Synchronization in complex networks of phase oscillators: a survey. Automatica 50, 1539–1564 (2014)
Graß, T., Juliá-Díaz, B., Kuś, M., Lewenstein, M.: Quantum chaos in SU(3) models with trapped ions. Phys. Rev. Lett. 111, 090404 (2013)
Harrison, S.L., Sigurdsson, H., Lagoudakis, P.G.: Synchronization in optically trapped polariton Stuart–Landau networks. Phys. Rev. B 101, 155402 (2020)
Jalan, S., Singh, A., Acharyya, S., Kurths, J.: Impact of a leader on cluster synchronization. Phys. Rev. E 91, 022901 (2015)
Larson, J., Horsdal, M.: Photonic Josephson effect, phase transitions, and chaos in optomechanical systems. Phys. Rev. A 84, 021804 (2011)
Li, W.L., Li, C., Song, H.S.: Quantum synchronization in an optomechanical system based on Lyapunov control. Phys. Rev. E 93, 062221 (2016)
Li, W.L., Li, C., Song, H.S.: Theoretical realization and application of paritytime-symmetric oscillators in a quantum regime. Phys. Rev. A 95, 023827 (2017a)
Li, W.L., Li, C., Song, H.S.: Quantum synchronization and quantum state sharing in an irregular complex network. Phys. Rev. E 95, 022204 (2017b)
Li, W.L., Zhang, W.Z., Li, C., Song, H.S.: Properties and relative measure for quantifying quantum synchronization. Phys. Rev. E 96, 012211 (2017c)
Lü, L., Li, C.R., Li, G., Zhao, G.N.: Projective synchronization for uncertain network based on modified sliding mode control technique. Int. J. Adapt. Control Signal Process. 31, 429–440 (2017)
Mahdavi, N., Menhaj, M.B., Kurths, J., Lu, J.Q., Afshar, A.: Pinning impulsive synchronization of complex dynamical networks. Int. J. Bifurc. Chaos 22, 1250239 (2012)
Mari, A., Farace, A., Didier, N., Giovannetti, V., Fazio, R.: Measures of quantum synchronization in continuous variable systems. Phys. Rev. Lett. 111, 103605 (2013)
Pecora, L.M., Carroll, T.L.: Master stability functions for synchronized coupled systems. Phys. Rev. Lett. 80, 2109–2112 (1998)
Rakkiyappan, R., Sakthivel, N.: Pinning sampled-data control for synchronization of complex networks with probabilistic time-varying delays using quadratic convex approach. Neurocomputing 162, 26–40 (2015)
Selivanov, A., Fradkov, A., Fridman, E.: Passification-based decentralized adaptive synchronization of dynamical networks with time-varying delays. J. Frankl. Inst. 352, 52–72 (2015)
Siddique, A.B., Pecora, L., Hart, J.D., Sorrentino, F.: Symmetry-and input-cluster synchronization in networks. Phys. Rev. E 97, 042217 (2018)
Skardal, P.S., Taylor, D., Sun, J., Arenas, A.: Erosion of synchronization in networks of coupled oscillators. Phys. Rev. E 91, 010802 (2015)
Song, L.J., Yan, D., Ma, J., Wang, X.G.: Spin squeezing as an indicator of quantum chaos in the Dicke model. Phys. Rev. E 79, 046220 (2009)
Srinivasan, K., Chandrasekar, V.K., Gladwin Pradeep, R., Murali, K., Lakshmanan, M.: Different types of synchronization in coupled network based chaotic circuits. Commun. Nonlinear Sci. Numer. Simul. 39, 156–168 (2016)
Tumulty, J.S., Royster, M., Cruz, L.: Columnar grouping preserves synchronization in neuronal networks with distance-dependent time delays. Phys. Rev. E 101, 022408 (2020)
Zhang, K., Chen, W., Bhattacharya, M., Meystre, P.: Hamiltonian chaos in a coupled BEC-optomechanical-cavity system. Phys. Rev. A 81, 013802 (2010a)
Zhang, K., Chen, W., Bhattacharya, M., Meystre, P.: Hamiltonian chaos in a coupled BEC optomechanical cavity system. Phys. Rev. A 81, 013802 (2010b)
Zhou, S., Hong, Y.X., Yang, Y.M., Lü, L., Li, C.R.: Finite-time synchronization of uncertain delay spatiotemporal networks via unidirectional coupling technology. Pramana J. Phys. 94, 34 (2020)
Acknowledgements
This research was supported by the National Natural Science Foundation of China (Grant No. 11747318).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Lü, L., Zou, C., Li, C. et al. Signal transmission and parameter measurement in quantum bits interacting with a single-mode radiation field. Opt Quant Electron 52, 375 (2020). https://doi.org/10.1007/s11082-020-02495-2
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11082-020-02495-2