From Wigner hyperbolic rotation to fractional squeezing transformation
Wei-Feng Wu,
Peng Fu,
Hua-Kui Hu
Affiliations
Wei-Feng Wu
School of Mechanical and Electrical Engineering, Chizhou University, Chizhou 247000, Anhui, China; Research Center about Capacitive Touch Screen and Optical Vacuum Coating Engineering Technology of Chizhou, Anhui, China; Anhui Research Center of Semiconductor Industry, Generic Technology, China; Corresponding author.
Peng Fu
School of Mechanical and Electrical Engineering, Chizhou University, Chizhou 247000, Anhui, China; Research Center about Capacitive Touch Screen and Optical Vacuum Coating Engineering Technology of Chizhou, Anhui, China
Hua-Kui Hu
School of Mechanical and Electrical Engineering, Chizhou University, Chizhou 247000, Anhui, China; Anhui Research Center of Semiconductor Industry, Generic Technology, China
Based on the usual Wigner-Weyl transformation theory we find that the Wigner hyperbolic rotation in phase space will map onto fractional squeezing operator in Hilbert space. The merit of Weyl ordering and the coherent state representation of Fresnel operator is used in our derivation.
