中国物理B ›› 2009, Vol. 18 ›› Issue (4): 1512-1516.doi: 10.1088/1674-1056/18/4/037

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Single-mode photon number measurement for the squeezed two-mode number state

朱士群1, 许雪芬2   

  1. (1)School of Physical Science and Technology, Suzhou University, Suzhou 215006, China; (2)School of Physical Science and Technology, Suzhou University, Suzhou 215006, China;School of Mathematics and Physics, Jiangsu Teachers University of Technology, Changzhou 213001, China
  • 收稿日期:2008-12-10 修回日期:2009-01-20 出版日期:2009-04-20 发布日期:2009-04-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10774108).

Single-mode photon number measurement for the squeezed two-mode number state

Xu Xue-Fen(许雪芬)a)b) and Zhu Shi-Qun(朱士群)a)†   

  1. a School of Physical Science and Technology, Suzhou University, Suzhou 215006, China; b School of Mathematics and Physics, Jiangsu Teachers University of Technology, Changzhou 213001, China
  • Received:2008-12-10 Revised:2009-01-20 Online:2009-04-20 Published:2009-04-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10774108).

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摘要： Based on the fact that a two-mode squeezed number state is a two-variable Hermite polynomial excitation of the two-mode squeezed vacuum state, the result of one-mode l-photon measurement for the two-mode squeezed number state $S_2|m,n\rangle$ is discussed. It is found that a remaining field-mode simultaneously collapses into a number state $|n-m+l\rangle$ with the coefficient being a Jacobi polynomial of n, m and l, which manifestly exhibits the entanglement between the two modes, i.e. it depends on the number-difference between the two modes. The second mode collapses into an excited coherent state when the first mode is measured as a coherent state.

关键词: photon number measurement, two-mode squeezed number state, quantum entanglement

Abstract: Based on the fact that a two-mode squeezed number state is a two-variable Hermite polynomial excitation of the two-mode squeezed vacuum state, the result of one-mode l-photon measurement for the two-mode squeezed number state $S_2|m,n\rangle$ is discussed. It is found that a remaining field-mode simultaneously collapses into a number state $|n-m+l\rangle$ with the coefficient being a Jacobi polynomial of n, m and l, which manifestly exhibits the entanglement between the two modes, i.e. it depends on the number-difference between the two modes. The second mode collapses into an excited coherent state when the first mode is measured as a coherent state.

Key words: photon number measurement, two-mode squeezed number state, quantum entanglement

中图分类号:  (Quantum state engineering and measurements)

  • 42.50.Dv
03.65.Ud (Entanglement and quantum nonlocality) 03.65.Fd (Algebraic methods)