中国物理B ›› 2011, Vol. 20 ›› Issue (6): 60303-060303.doi: 10.1088/1674-1056/20/6/060303

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A new theorem relating quantum tomogram to the Fresnel operator

谢传梅1, 范洪义2   

  1. (1)College of Physics & Material Science, Anhui University, Hefei 230039, China;Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China; (2)Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China
  • 收稿日期:2010-06-29 修回日期:2011-03-07 出版日期:2011-06-15 发布日期:2011-06-15
  • 基金资助:
    Project supported by the Doctoral Scientiˉc Research Startup Fund of Anhui University, China (Grant No. 33190059) and the National Natural Science Foundation of China (Grant No. 10874174).

A new theorem relating quantum tomogram to the Fresnel operator

Xie Chuan-Mei (谢传梅)ab, Fan Hong-Yi (范洪义)b   

  1. a College of Physics & Material Science, Anhui University, Hefei 230039, China; b Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China
  • Received:2010-06-29 Revised:2011-03-07 Online:2011-06-15 Published:2011-06-15
  • Supported by:
    Project supported by the Doctoral Scientiˉc Research Startup Fund of Anhui University, China (Grant No. 33190059) and the National Natural Science Foundation of China (Grant No. 10874174).

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摘要： According to Fan-Hu's formalism (Fan Hong-Yi and Hu Li-Yun 2009 Opt. Commun. bf282 3734) that the tomogram of quantum states can be considered as the module-square of the state wave function in the intermediate coordinate-momentum representation which is just the eigenvector of the Fresnel quadrature phase, we derive a new theorem for calculating quantum tomogram of density operator, i.e., the tomogram of a density operator ρ is equal to the marginal integration of the classical Weyl correspondence function of F+ρF, where F is the Fresnel operator. Applications of this theorem to evaluating the tomogram of optical chaotic field and squeezed chaotic optical field are presented.

关键词: quantum tomogram, Fresnel operator, Weyl correspondence

Abstract: According to Fan-Hu's formalism (Fan Hong-Yi and Hu Li-Yun 2009 Opt. Commun.  282 3734) that the tomogram of quantum states can be considered as the module-square of the state wave function in the intermediate coordinate-momentum representation which is just the eigenvector of the Fresnel quadrature phase, we derive a new theorem for calculating quantum tomogram of density operator, i.e., the tomogram of a density operator ρ is equal to the marginal integration of the classical Weyl correspondence function of F+ρF, where F is the Fresnel operator. Applications of this theorem to evaluating the tomogram of optical chaotic field and squeezed chaotic optical field are presented.

Key words: quantum tomogram, Fresnel operator, Weyl correspondence

中图分类号:  (State reconstruction, quantum tomography)

  • 03.65.Wj
42.50.-p (Quantum optics) 03.65.-w (Quantum mechanics)