中国物理B ›› 2014, Vol. 23 ›› Issue (4): 40305-040305.doi: 10.1088/1674-1056/23/4/040305

• GENERAL • 上一篇    下一篇

Analysis of dynamical properties for the two-site Bose–Hubbard model with an algebraic method

孟祥佳a, 冯海冉b, 郑雨军a   

  1. a School of Physics, Shandong University, Jinan 250100, China;
    b Department of Physics and Information Engineering, Jining University, Qufu 273155, China
  • 收稿日期:2013-06-15 修回日期:2013-09-17 出版日期:2014-04-15 发布日期:2014-04-15
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 91021009 and 21073110).

Analysis of dynamical properties for the two-site Bose–Hubbard model with an algebraic method

Meng Xiang-Jia (孟祥佳)a, Feng Hai-Ran (冯海冉)b, Zheng Yu-Jun (郑雨军)a   

  1. a School of Physics, Shandong University, Jinan 250100, China;
    b Department of Physics and Information Engineering, Jining University, Qufu 273155, China
  • Received:2013-06-15 Revised:2013-09-17 Online:2014-04-15 Published:2014-04-15
  • Contact: Zheng Yu-Jun E-mail:yzheng@sdu.edu.cn
  • About author:03.75.Kk; 03.75.Lm; 32.80.Pj
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 91021009 and 21073110).

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摘要： In this work, we propose an algebraic recursion method to study the dynamical evolution of the two-site Bose-Hubbard model. We analyze its properties from the viewpoints of single partite purity, energy, and trace distance, in which the model is considered as a typical bipartite system. The analytical expressions for the quantities are derived. We show that the purity can well reflect the transition between different regimes for the system. In addition, we demonstrate that the transition from the delocalization regime to the self-trapping regime with the ratio η increasing not only happens for an initially local state but also for any initial states. Furthermore, we confirm that the dynamics of the system presents a periodicity for η=0 and the period is tc=π/2J when the initial state is symmetric.

关键词: two-site Bose-Hubbard system, dynamical evolution, purity, energy, trace distance

Abstract: In this work, we propose an algebraic recursion method to study the dynamical evolution of the two-site Bose-Hubbard model. We analyze its properties from the viewpoints of single partite purity, energy, and trace distance, in which the model is considered as a typical bipartite system. The analytical expressions for the quantities are derived. We show that the purity can well reflect the transition between different regimes for the system. In addition, we demonstrate that the transition from the delocalization regime to the self-trapping regime with the ratio η increasing not only happens for an initially local state but also for any initial states. Furthermore, we confirm that the dynamics of the system presents a periodicity for η=0 and the period is tc=π/2J when the initial state is symmetric.

Key words: two-site Bose-Hubbard system, dynamical evolution, purity, energy, trace distance

中图分类号:  (Dynamic properties of condensates; collective and hydrodynamic excitations, superfluid flow)

  • 03.75.Kk
03.75.Lm (Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations)