中国物理B ›› 2014, Vol. 23 ›› Issue (3): 30303-030303.doi: 10.1088/1674-1056/23/3/030303

• GENERAL • 上一篇    下一篇

Master equation describing the diffusion process for a coherent state

刘堂昆a, 单传家a, 刘继兵a, 范洪义b   

  1. a College of Physics and Electronic Science, Hubei Normal University, Huangshi 435002, China;
    b Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China
  • 收稿日期:2013-06-05 修回日期:2013-09-05 出版日期:2014-03-15 发布日期:2014-03-15
  • 基金资助:
    Project supported by the National Basic Research Program of China (Grant No. 2012CB922103), the National Natural Science Foundation of China (Grant Nos. 11175113 and 11274104), and the Natural Science Foundation of Hubei Province of China (Grant No. 2011CDA021).

Master equation describing the diffusion process for a coherent state

Liu Tang-Kun (刘堂昆)a, Shan Chuan-Jia (单传家)a, Liu Ji-Bing (刘继兵)a, Fan Hong-Yi (范洪义)b   

  1. a College of Physics and Electronic Science, Hubei Normal University, Huangshi 435002, China;
    b Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China
  • Received:2013-06-05 Revised:2013-09-05 Online:2014-03-15 Published:2014-03-15
  • Contact: Liu Tang-Kun E-mail:tkliuhs@163.com
  • Supported by:
    Project supported by the National Basic Research Program of China (Grant No. 2012CB922103), the National Natural Science Foundation of China (Grant Nos. 11175113 and 11274104), and the Natural Science Foundation of Hubei Province of China (Grant No. 2011CDA021).

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摘要： The evolution of a pure coherent state into a chaotic state is described very well by a master equation, as is validated via an examination of the coherent state’s evolution during the diffusion process, fully utilizing the technique of integration within an ordered product (IWOP) of operators. The same equation also describes a limitation that maintains the coherence in a weak diffusion process, i.e., when the dissipation is very weak and the initial average photon number is large. This equation is dρ/dt=-κ[a+aρ-a+ρa-aρa++ρaa+]. The physical difference between this diffusion equation and the better-known amplitude damping master equation is pointed out.

关键词: master equation describing diffusion, coherent state evolution, chaotic state, integration within an ordered product (IWOP) of operators

Abstract: The evolution of a pure coherent state into a chaotic state is described very well by a master equation, as is validated via an examination of the coherent state’s evolution during the diffusion process, fully utilizing the technique of integration within an ordered product (IWOP) of operators. The same equation also describes a limitation that maintains the coherence in a weak diffusion process, i.e., when the dissipation is very weak and the initial average photon number is large. This equation is dρ/dt=-κ[a+aρ-a+ρa-aρa++ρaa+]. The physical difference between this diffusion equation and the better-known amplitude damping master equation is pointed out.

Key words: master equation describing diffusion, coherent state evolution, chaotic state, integration within an ordered product (IWOP) of operators

中图分类号:  (Quantum mechanics)

  • 03.65.-w
42.50.-p (Quantum optics) 02.90.+p (Other topics in mathematical methods in physics)