中国物理B ›› 2018, Vol. 27 ›› Issue (9): 94206-094206.doi: 10.1088/1674-1056/27/9/094206

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇    下一篇

Fractional squeezing-Hankel transform based on the induced entangled state representations

Cui-Hong Lv(吕翠红), Su-Qing Zhang(张苏青), Wen Xu(许雯)   

  1. Faculty of Science, Jiangsu University, Zhenjiang 212013, China
  • 收稿日期:2018-03-10 修回日期:2018-05-11 发布日期:2018-09-25
  • 通讯作者: Cui-Hong Lv E-mail:lvch@mail.ujs.edu.cn
  • 基金资助:

    Project supported by the National Natural Science Foundation of China (Grant No. 11304126) and the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20130532).

Fractional squeezing-Hankel transform based on the induced entangled state representations

Cui-Hong Lv(吕翠红), Su-Qing Zhang(张苏青), Wen Xu(许雯)   

  1. Faculty of Science, Jiangsu University, Zhenjiang 212013, China
  • Received:2018-03-10 Revised:2018-05-11 Published:2018-09-25
  • Contact: Cui-Hong Lv E-mail:lvch@mail.ujs.edu.cn
  • Supported by:

    Project supported by the National Natural Science Foundation of China (Grant No. 11304126) and the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20130532).

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摘要：

Based on the fact that the quantum mechanical version of Hankel transform kernel (the Bessel function) is just the transform between |q,r> angle and (s,r'|, two induced entangled state representations are given, and working with them we derive fractional squeezing-Hankel transform (FrSHT) caused by the operator e-iα(a1†a2†+a1a2)e-iπa2†a2, which is an entangled fractional squeezing transform operator. The additive rule of the FrSHT can be explicitly proved.

关键词: induced entangled state representation, entangled fractional squeezing transform, fractional squeezing-Hankel transform

Abstract:

Based on the fact that the quantum mechanical version of Hankel transform kernel (the Bessel function) is just the transform between |q,r> angle and (s,r'|, two induced entangled state representations are given, and working with them we derive fractional squeezing-Hankel transform (FrSHT) caused by the operator e-iα(a1†a2†+a1a2)e-iπa2†a2, which is an entangled fractional squeezing transform operator. The additive rule of the FrSHT can be explicitly proved.

Key words: induced entangled state representation, entangled fractional squeezing transform, fractional squeezing-Hankel transform

中图分类号:  (Quantum optics)

  • 42.50.-p
03.65.-w (Quantum mechanics) 02.30.Gp (Special functions)