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Quantum control with Lyapunov function and bang-bang solution in the optomechanics system

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Abstract

We propose a quantum control scheme with the help of Lyapunov control function in the optomechanics system. The principle of the idea is to design suitable control fields to steer the Lyapunov control function to zero as t → ∞ while the quantum system is driven to the target state. Such an evolution makes no limit on the initial state and one needs not manipulate the laser pulses during the evolution. To prove the effectiveness of the scheme, we show two useful applications in the optomechanics system: one is the cooling of nanomechanical resonator and the other is the quantum fluctuation transfer between membranes. Numerical simulation demonstrates that the perfect and fast cooling of nanomechanical resonator and quantum fluctuation transfer between membranes can be rapidly achieved. Besides, some optimizations are made on the traditional Lyapunov control waveform and the optimized bang-bang control fields makes Lyapunov function V decrease faster. The optimized quantum control scheme can achieve the same goal with greater efficiency. Hence, we hope that this work may open a new avenue of the experimental realization of cooling mechanical oscillator, quantum fluctuations transfer between membranes and other quantum optomechanics tasks and become an alternative candidate for quantum manipulation of macroscopic mechanical devices in the near future.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant Nos. 11575045, 11874114, and 11674060, the Natural Science Funds for Distinguished Young Scholar of Fujian Province under Grant No. 2020J06011, Project from Fuzhou University under Grant JG2020012, the Natural Science Foundation of Fujian Province under Grant No. 2018J01414, and the China Postdoctoral Science Foundation under Grant No. 2021M691150.

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Authors and Affiliations

  1. Fujian Key Laboratory of Quantum Information and Quantum Optics, Fuzhou University, Fuzhou, 350108, China

    Yu Wang, Yi-Hao Kang, Chang-Sheng Hu, Bi-Hua Huang & Yan Xia

  2. Department of Physics, Fuzhou University, Fuzhou, 350108, China

    Yu Wang, Yi-Hao Kang, Chang-Sheng Hu, Bi-Hua Huang & Yan Xia

  3. Department of Physics, Harbin Institute of Technology, Harbin, 150001, China

    Jie Song

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  1. Yu Wang
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Correspondence to Yan Xia.

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Wang, Y., Kang, YH., Hu, CS. et al. Quantum control with Lyapunov function and bang-bang solution in the optomechanics system. Front. Phys. 17, 32501 (2022). https://doi.org/10.1007/s11467-021-1119-0

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