中国物理B ›› 2008, Vol. 17 ›› Issue (1): 38-42.doi: 10.1088/1674-1056/17/1/007

• GENERAL • 上一篇    下一篇

Berry phase in a generalized nonlinear two-level system

刘继兵1, 李家华1, 宋佩君1, 李伟斌2   

  1. (1)Department of Physics, Huazhong University of Science and Technology, Wuhan 430074, China; (2)Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
  • 出版日期:2008-01-20 发布日期:2008-01-20
  • 基金资助:
    Project supported partially by the National Natural Science Foundation of China (Grant Nos 10575040 and 10634060).

Berry phase in a generalized nonlinear two-level system

Liu Ji-Bing(刘继兵)a)†, Li Jia-Hua(李家华)a), Song Pei-Jun(宋佩君)a), and Li Wei-Bin(李伟斌)b)   

  1. a Department of Physics, Huazhong University of Science and Technology, Wuhan 430074, China; b Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
  • Online:2008-01-20 Published:2008-01-20
  • Supported by:
    Project supported partially by the National Natural Science Foundation of China (Grant Nos 10575040 and 10634060).

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摘要： In this paper, we investigate the behaviour of the geometric phase of a more generalized nonlinear system composed of an effective two-level system interacting with a single-mode quantized cavity field. Both the field nonlinearity and the atom--field coupling nonlinearity are considered. We find that the geometric phase depends on whether the index $k$ is an odd number or an even number in the resonant case. In addition, we also find that the geometric phase may be easily observed when the field nonlinearity is not considered. The fractional statistical phenomenon appears in this system if the strong nonlinear atom--field coupling is considered. We have also investigated the geometric phase of an effective two-level system interacting with a two-mode quantized cavity field.

Abstract: In this paper, we investigate the behaviour of the geometric phase of a more generalized nonlinear system composed of an effective two-level system interacting with a single-mode quantized cavity field. Both the field nonlinearity and the atom--field coupling nonlinearity are considered. We find that the geometric phase depends on whether the index $k$ is an odd number or an even number in the resonant case. In addition, we also find that the geometric phase may be easily observed when the field nonlinearity is not considered. The fractional statistical phenomenon appears in this system if the strong nonlinear atom--field coupling is considered. We have also investigated the geometric phase of an effective two-level system interacting with a two-mode quantized cavity field.

Key words: geometric phase, nonlinear system, atom--field coupling

中图分类号:  (Phases: geometric; dynamic or topological)

  • 03.65.Vf
03.65.Ta (Foundations of quantum mechanics; measurement theory) 03.67.Lx (Quantum computation architectures and implementations) 05.45.-a (Nonlinear dynamics and chaos) 42.50.-p (Quantum optics)