中国物理B ›› 2004, Vol. 13 ›› Issue (8): 1269-1275.doi: 10.1088/1009-1963/13/8/015

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A new class of quantum states generated by m-fold application of Bogoliubov's transformation

辛宗政1, 吴炜2, 吴令安3   

  1. (1)Department of Physics, Laboratory of Atoms and Radiation, Liaoning University, Shenyang 110036, China; (2)Department of Physics, Laboratory of Atoms and Radiation, Liaoning University, Shenyang 110036, China; Laboratory of Optical Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100080, China; (3)Laboratory of Optical Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100080, China
  • 收稿日期:2003-12-16 修回日期:2004-05-09 出版日期:2004-06-21 发布日期:2005-06-22
  • 基金资助:
    Project supported by the National ‘973' Programme for Fundamental Research, the Chinese Academy of Sciences, the National Natural Science Foundation of China (Grant No 60178013), and the Science and Technology Council of Liaoning Province (Grant No 200110

A new class of quantum states generated by m-fold application of Bogoliubov's transformation

Wu Wei (吴炜)ab, Wu Ling-An (吴令安)b, Xin Zong-Zheng (辛宗政)a   

  1. a Department of Physics, Laboratory of Atoms and Radiation, Liaoning University, Shenyang 110036, China; b Laboratory of Optical Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100080, China
  • Received:2003-12-16 Revised:2004-05-09 Online:2004-06-21 Published:2005-06-22
  • Supported by:
    Project supported by the National ‘973' Programme for Fundamental Research, the Chinese Academy of Sciences, the National Natural Science Foundation of China (Grant No 60178013), and the Science and Technology Council of Liaoning Province (Grant No 200110

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摘要： By applying higher powers of the Bogoliubov transformation operator b^{\dagger }=ν^*a+μ^*a^{\dagger } to the two-photon coherent states (or minimum uncertainty squeezed states) we construct a new type of quantum state which we call the generalized excited two-photon coherent states. Analytic expressions for the quantum statistical properties are derived, and through numerical computation the phase space quasi-probability distributions are found. These states can exhibit highly nonclassical behaviour depending on the degree of excitation m and other parameters. For particular values of two parameters λ and ρ, these generalized states reduce to other classes of coherent states formerly reported. Our theory thus presents a much broader approach to these types of quantum states.

关键词: generalized excited two-photon coherent states, pseudo-creation operator, nonclassical statistical properties

Abstract: By applying higher powers of the Bogoliubov transformation operator $b^{\dagger }=\nu^*a+\mu^*a^{\dagger}$ to the two-photon coherent states (or minimum uncertainty squeezed states) we construct a new type of quantum state which we call the generalized excited two-photon coherent states. Analytic expressions for the quantum statistical properties are derived, and through numerical computation the phase space quasi-probability distributions are found. These states can exhibit highly nonclassical behaviour depending on the degree of excitation m and other parameters. For particular values of two parameters $\lambda$ and $\rho$, these generalized states reduce to other classes of coherent states formerly reported. Our theory thus presents a much broader approach to these types of quantum states.

Key words: generalized excited two-photon coherent states, pseudo-creation operator, nonclassical statistical properties

中图分类号: 

  • 42.50.Ar
42.50.Dv (Quantum state engineering and measurements)