From Wigner hyperbolic rotation to fractional squeezing transformation

Wei-Feng Wu; Peng Fu; Hua-Kui Hu

doi:10.1016/j.heliyon.2024.e27590

From Wigner hyperbolic rotation to fractional squeezing transformation

Heliyon. 2024 Mar 6;10(6):e27590. doi: 10.1016/j.heliyon.2024.e27590. eCollection 2024 Mar 30.

Authors

Wei-Feng Wu^{1

2

3}, Peng Fu^{1

2}, Hua-Kui Hu^{1

3}

Affiliations

¹ School of Mechanical and Electrical Engineering, Chizhou University, Chizhou 247000, Anhui, China.
² Research Center about Capacitive Touch Screen and Optical Vacuum Coating Engineering Technology of Chizhou, Anhui, China.
³ Anhui Research Center of Semiconductor Industry, Generic Technology, China.

Abstract

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.

Keywords: Coherent state representation; IWOP method; Weyl ordering; Wigner hyperbolic rotation; Wigner-Weyl transformation theory.