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Chin. Phys. B, 2020, Vol. 29(3): 030306    DOI: 10.1088/1674-1056/ab6dc9
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Optical complex integration-transform for deriving complex fractional squeezing operator

Ke Zhang(张科)1,2,3, Cheng-Yu Fan(范承玉)1, Hong-Yi Fan(范洪义)2
1 Key Laboratory of Atmospheric Optics, Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei 230031, China;
2 University of Science and Technology of China, Hefei 230031, China;
3 Huainan Normal University, Huainan 232038, China
Abstract  We find a new complex integration-transform which can establish a new relationship between a two-mode operator's matrix element in the entangled state representation and its Wigner function. This integration keeps modulus invariant and therefore invertible. Based on this and the Weyl-Wigner correspondence theory, we find a two-mode operator which is responsible for complex fractional squeezing transformation. The entangled state representation and the Weyl ordering form of the two-mode Wigner operator are fully used in our derivation which brings convenience.
Keywords:  integration-transform      two-mode      entangled state      Weyl-Wigner correspondence theory  
Received:  12 November 2019      Revised:  17 January 2020      Published:  05 March 2020
PACS:  03.65.-w (Quantum mechanics)  
  42.50.-p (Quantum optics)  
  63.20.-e (Phonons in crystal lattices)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11775208) and Key Projects of Huainan Normal University, China (Grant No. 2019XJZD04).
Corresponding Authors:  Cheng-Yu Fan     E-mail:  cyfan@aiofm.ac.cn

Cite this article: 

Ke Zhang(张科), Cheng-Yu Fan(范承玉), Hong-Yi Fan(范洪义) Optical complex integration-transform for deriving complex fractional squeezing operator 2020 Chin. Phys. B 29 030306

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