中国物理B ›› 2010, Vol. 19 ›› Issue (11): 114206-114208.doi: 10.1088/1674-1056/19/11/114206

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Solving nonlinear master equation describing quantum damping by virtue of the entangled state representation

胡利云1, 姜年权2, 范洪义3, 任刚3   

  1. (1)College of Physics and Communication Electronics, Jiangxi Normal University, Nanchang 330022, China; (2)College of Physics and Electric Information, Wenzhou University, Wenzhou 325035, China; (3)Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China
  • 收稿日期:2010-02-21 修回日期:2010-03-29 出版日期:2010-11-15 发布日期:2010-11-15
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 10775097 and 10874174) and the Research Foundation of the Education Department of Jiangxi Province of China (Grant No. GJJ10097).

Solving nonlinear master equation describing quantum damping by virtue of the entangled state representation

Fan Hong-Yi(范洪义)a), Ren Gang(任刚)a), Hu Li-Yun(胡利云)b), and Jiang Nian-Quan(姜年权)c)†   

  1. a Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China; b College of Physics and Communication Electronics, Jiangxi Normal University, Nanchang 330022, China;  c College of Physics and Electric Information, Wenzhou University, Wenzhou 325035, China
  • Received:2010-02-21 Revised:2010-03-29 Online:2010-11-15 Published:2010-11-15
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 10775097 and 10874174) and the Research Foundation of the Education Department of Jiangxi Province of China (Grant No. GJJ10097).

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摘要： This paper solves the newly constructed nonlinear master equation dρ/dt=κ[ 2f(N)aρ(1/f(N-1) )a+-a+aρ -ρa+a] , where f(N) is an operator-valued function of N=a+a, for describing amplitude damping channel, and derives the infinite operator sum representation of quasi-Kraus operators for the density operator. It also shows that in this nonlinear process the initial pure number state density operator will evolve into the binomial field (a mixed state) when f(N)=1/(√(N+1)).

Abstract: This paper solves the newly constructed nonlinear master equation dρ/dt=κ[2f(N)aρ(1/f(N-1) )a$\dagger$-a$\dagger$aρ -ρa$\dagger$a] , where f(N) is an operator-valued function of N=a$\dagger$a, for describing amplitude damping channel, and derives the infinite operator sum representation of quasi-Kraus operators for the density operator. It also shows that in this nonlinear process the initial pure number state density operator will evolve into the binomial field (a mixed state) when f(N)=1/√(N+1).

Key words: nonlinear master equation, operator sum representation, Kraus operator, binomial state

中图分类号:  (Ordinary differential equations)

  • 02.30.Hq
02.30.Sa (Functional analysis) 02.30.Tb (Operator theory) 03.65.Ud (Entanglement and quantum nonlocality)