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Lewis-Riesenfeld Invariants in Two-level Quantum System Without the Rotating-Wave Approximation

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Abstract

Quantum adiabatic theorem is one of the most important conclusions in quantum mechanics, and is widely used in quantum theory and quantum information technology. However, since quantum adiabatic process is a very slow process, factors such as quantum environmental noise or decoherence will affect the results of quantum adiabatic calculation. Therefore, the shortcut to adiabaticity (STA) theory came into being. In this paper, we study the population inversion in a two-level quantum system within a given time, we propose a Lewis-Riesenfeld invariants technique to realize population transfer for the system without the rotating-wave approximation (RWA). According to the invariant condition, the system time-dependent invariant expression is obtained. The amplitudes of Rabi frequency and detuning in the system could be easily controlled by adjusting control parameters. For population inversion, we can get Rabi frequency and detuning by determining the parameters in the invariant. We analyze the dynamics of the system through invariant operators, therefore, no additional coupling is required. Thereby the high-fidelity population transfer can be implemented in two-level quantum system by our method, and it works even without RWA.

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Acknowledgments

This work is supported by the National Natural Science Foundation of China, Grant Numbers: 11947060, 11947085; Scientific Research Fundation of the Education Department of Jilin Province, Grants Number: JJKH20190764KJ; Specialized Fund for the Doctoral Research of Jilin Engineering Normal University, Grants Number: BSKJ201825, XYB201820.

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Authors and Affiliations

  1. Institute for Interdisciplinary Quantum Information Technology, Jilin Engineering Normal University, Changchun, 130052, China

    Hong Li, Si-Qi Zhang, Mei-Xuan Li & Xiao-Han Liu

  2. Jilin Engineering Laboratory for Quantum Information Technology, Changchun, 130052, China

    Hong Li, Si-Qi Zhang, Mei-Xuan Li & Xiao-Han Liu

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  1. Hong Li
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  2. Si-Qi Zhang
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  3. Mei-Xuan Li
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  4. Xiao-Han Liu
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Correspondence to Si-Qi Zhang.

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Li, H., Zhang, SQ., Li, MX. et al. Lewis-Riesenfeld Invariants in Two-level Quantum System Without the Rotating-Wave Approximation. Int J Theor Phys 59, 3613–3622 (2020). https://doi.org/10.1007/s10773-020-04621-y

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