中国物理B ›› 2015, Vol. 24 ›› Issue (2): 20301-020301.doi: 10.1088/1674-1056/24/2/020301

• GENERAL • 上一篇    下一篇

From fractional Fourier transformation to quantum mechanical fractional squeezing transformation

吕翠红a, 范洪义b, 李东韡a   

  1. a Faculty of Science, Jiangsu University, Zhenjiang 212013, China;
    b Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China
  • 收稿日期:2014-06-16 修回日期:2014-09-20 出版日期:2015-02-05 发布日期:2015-02-05
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 11304126), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20130532), the Natural Science Fund for Colleges and Universities in Jiangsu Province, China (Grant No. 13KJB140003), the Postdoctoral Science Foundation of China (Grant No. 2013M541608), and the Postdoctoral Science Foundation of Jiangsu Province, China (Grant No. 1202012B).

From fractional Fourier transformation to quantum mechanical fractional squeezing transformation

Lv Cui-Hong (吕翠红)a, Fan Hong-Yi (范洪义)b, Li Dong-Wei (李东韡)a   

  1. a Faculty of Science, Jiangsu University, Zhenjiang 212013, China;
    b Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China
  • Received:2014-06-16 Revised:2014-09-20 Online:2015-02-05 Published:2015-02-05
  • Contact: Lv Cui-Hong E-mail:lvch@mail.ujs.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 11304126), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20130532), the Natural Science Fund for Colleges and Universities in Jiangsu Province, China (Grant No. 13KJB140003), the Postdoctoral Science Foundation of China (Grant No. 2013M541608), and the Postdoctoral Science Foundation of Jiangsu Province, China (Grant No. 1202012B).

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摘要： By converting the triangular functions in the integration kernel of the fractional Fourier transformation to the hyperbolic function, i.e., tanα→tanhα,sinα→sinhα, we find the quantum mechanical fractional squeezing transformation (FrST) which satisfies additivity. By virtue of the integration technique within the ordered product of operators (IWOP) we derive the unitary operator responsible for the FrST, which is composite and is made of eiπa*a/2 and exp[ia/2(a2+a*2)]. The FrST may be implemented in combinations of quadratic nonlinear crystals with different phase mismatches.

关键词: fractional Fourier transformation, fractional squeezing transformation, unitary operator, the IWOP technique

Abstract: By converting the triangular functions in the integration kernel of the fractional Fourier transformation to the hyperbolic function, i.e., tanα→tanhα,sinα→sinhα, we find the quantum mechanical fractional squeezing transformation (FrST) which satisfies additivity. By virtue of the integration technique within the ordered product of operators (IWOP) we derive the unitary operator responsible for the FrST, which is composite and is made of eiπa*a/2 and exp[ia/2(a2+a*2)]. The FrST may be implemented in combinations of quadratic nonlinear crystals with different phase mismatches.

Key words: fractional Fourier transformation, fractional squeezing transformation, unitary operator, the IWOP technique

中图分类号:  (Quantum mechanics)

  • 03.65.-w
42.50.-p (Quantum optics) 02.90.+p (Other topics in mathematical methods in physics)