中国物理B ›› 2013, Vol. 22 ›› Issue (8): 80301-080301.doi: 10.1088/1674-1056/22/8/080301

• GENERAL • 上一篇    下一篇

Optical field’s quadrature excitation studied by new Hermite-polynomial operator identity

范洪义a b, 何锐b, 笪诚b, 梁祖峰c   

  1. a Department of Physics, Ningbo University, Ningbo 315211, China;
    b Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China;
    c Department of Physics, Hangzhou Normal University, Hangzhou 310036, China
  • 收稿日期:2013-02-18 修回日期:2013-03-11 出版日期:2013-06-27 发布日期:2013-06-27
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11175113 and 11275123).

Optical field’s quadrature excitation studied by new Hermite-polynomial operator identity

Fan Hong-Yi (范洪义)a b, He Rui (何锐)b, Da Cheng (笪诚)b, Liang Zu-Feng (梁祖峰)c   

  1. a Department of Physics, Ningbo University, Ningbo 315211, China;
    b Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China;
    c Department of Physics, Hangzhou Normal University, Hangzhou 310036, China
  • Received:2013-02-18 Revised:2013-03-11 Online:2013-06-27 Published:2013-06-27
  • Contact: Fan Hong-Yi, He Rui E-mail:fanhongyi@nbu.edu.cn; heruim@mail.ustc.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11175113 and 11275123).

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摘要： We study the optical field's quadrature excitation state Xm|0>, where X=(a+a)√2 is the quadrature operator. We find it is ascribed to the Hermite-polynomial excitation state. For the first time, we determine this state's normalization constant which turns out to be a Laguerre polynomial. This is due to the integration method within the ordered product of operators (IWOP). The normalization for the two-mode quadrature excitation state is also completed by virtue of the entangled state representation.

关键词: quadrature excitation, Hermite-polynomial excitation state, operator identities about Laguerre polynomials, IWOP method, entangled state representation

Abstract: We study the optical field's quadrature excitation state Xm|0>, where X=(a+a)√2 is the quadrature operator. We find it is ascribed to the Hermite-polynomial excitation state. For the first time, we determine this state's normalization constant which turns out to be a Laguerre polynomial. This is due to the integration method within the ordered product of operators (IWOP). The normalization for the two-mode quadrature excitation state is also completed by virtue of the entangled state representation.

Key words: quadrature excitation, Hermite-polynomial excitation state, operator identities about Laguerre polynomials, IWOP method, entangled state representation

中图分类号: 

  • 03.65.-a
02.30.Gp (Special functions)