中国物理B ›› 2021, Vol. 30 ›› Issue (6): 60302-060302.doi: 10.1088/1674-1056/abd747

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Lie transformation on shortcut to adiabaticity in parametric driving quantum systems

Jian-Jian Cheng(程剑剑), Yao Du(杜瑶), and Lin Zhang(张林)   

  1. School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710119, China
  • 收稿日期:2020-10-10 修回日期:2020-11-28 接受日期:2020-12-30 出版日期:2021-05-18 发布日期:2021-05-18
  • 通讯作者: Lin Zhang E-mail:zhanglincn@snnu.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11447025 and 11847308).

Lie transformation on shortcut to adiabaticity in parametric driving quantum systems

Jian-Jian Cheng(程剑剑), Yao Du(杜瑶), and Lin Zhang(张林)   

  1. School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710119, China
  • Received:2020-10-10 Revised:2020-11-28 Accepted:2020-12-30 Online:2021-05-18 Published:2021-05-18
  • Contact: Lin Zhang E-mail:zhanglincn@snnu.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11447025 and 11847308).

摘要: Shortcut to adiabaticity (STA) is a speedway to produce the same final state that would result in an adiabatic, infinitely slow process. Two typical techniques to engineer STA are developed by either introducing auxiliary counterdiabatic fields or finding new Hamiltonians that own dynamical invariants to constraint the system into the adiabatic paths. In this paper, an efficient method is introduced to naturally cover the above two techniques with a unified Lie algebraic framework and neatly remove the design difficulties and loose assumptions in the two techniques. A general STA scheme for different potential expansions concisely achieves with the aid of squeezing transformations.

关键词: shortcut to adiabaticity, parametric driving, Lewis-Riesenfeld invariants

Abstract: Shortcut to adiabaticity (STA) is a speedway to produce the same final state that would result in an adiabatic, infinitely slow process. Two typical techniques to engineer STA are developed by either introducing auxiliary counterdiabatic fields or finding new Hamiltonians that own dynamical invariants to constraint the system into the adiabatic paths. In this paper, an efficient method is introduced to naturally cover the above two techniques with a unified Lie algebraic framework and neatly remove the design difficulties and loose assumptions in the two techniques. A general STA scheme for different potential expansions concisely achieves with the aid of squeezing transformations.

Key words: shortcut to adiabaticity, parametric driving, Lewis-Riesenfeld invariants

中图分类号:  (Tunneling, traversal time, quantum Zeno dynamics)

  • 03.65.Xp
03.65.Fd (Algebraic methods) 42.50.Dv (Quantum state engineering and measurements)