Optical complex integration-transform for deriving complex fractional squeezing operator**Project supported by the National Natural Science Foundation of China (Grant No. 11775208) and Key Projects of Huainan Normal University, China (Grant No. 2019XJZD04).

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.