中国物理B ›› 2007, Vol. 16 ›› Issue (6): 1554-1558.doi: 10.1088/1009-1963/16/6/010

• GENERAL • 上一篇    下一篇

Wigner function of coherent state of N components

叶永华1, 曾高坚2   

  1. (1)Department of Physics, Xiangnan University, Chenzhou 423000, China; (2)Department of Technology, Hunan Normal University, Changsha 410081, China
  • 收稿日期:2006-07-31 修回日期:2006-12-27 出版日期:2007-06-20 发布日期:2007-06-20
  • 基金资助:
    Project supported by the Science Research Fund of Hunan Provincial Education Department of China (Grant No~06C795).

Wigner function of coherent state of N components

Ye Yong-Hua(叶永华)a) and Zeng Gao-Jian(曾高坚)b)   

  1. a Department of Physics, Xiangnan University, Chenzhou 423000, China; b Department of Technology, Hunan Normal University, Changsha 410081, China
  • Received:2006-07-31 Revised:2006-12-27 Online:2007-06-20 Published:2007-06-20
  • Supported by:
    Project supported by the Science Research Fund of Hunan Provincial Education Department of China (Grant No~06C795).

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摘要： In this paper, we study the Wigner function of coherent state of $N$ components, especially two components and three components. This function consists of two terms: the Gaussian term and the interference term with the negativity. The first term comprises $N$ Gaussian surfaces evenly centred on a circle of radius $|\beta|=|\alpha|$ with a separate angle of ${2\pi}/{N}$, and the second term is composed of $\frac{1}{2}N(N-1)$ Gaussian-cosine surfaces evenly centred in a circular region of radius $|\beta|<|\alpha|$. Here, $\alpha$ is the eigenvalue of the annihilation operator $a$, and $\beta$ is a variable in some complex space in which the Wigner function is defined. We have proved that the essential condition to eliminate the negativity of the Wigner function is that the mean photon count of the coherent state is equal to that of the Glouber coherent state.

Abstract: In this paper, we study the Wigner function of coherent state of $N$ components, especially two components and three components. This function consists of two terms: the Gaussian term and the interference term with the negativity. The first term comprises $N$ Gaussian surfaces evenly centred on a circle of radius $|\beta|=|\alpha|$ with a separate angle of ${2\pi}/{N}$, and the second term is composed of $\frac{1}{2}N(N-1)$ Gaussian-cosine surfaces evenly centred in a circular region of radius $|\beta|<|\alpha|$. Here, $\alpha$ is the eigenvalue of the annihilation operator $a$, and $\beta$ is a variable in some complex space in which the Wigner function is defined. We have proved that the essential condition to eliminate the negativity of the Wigner function is that the mean photon count of the coherent state is equal to that of the Glouber coherent state.

Key words: multi-component coherent states, Wigner function, non-classicality

中图分类号:  (Functional analytical methods)

  • 03.65.Db
03.65.Fd (Algebraic methods)