Wigner function evolution in self-Kerr Medium derived by Entangled state representation

TL;DR

This paper introduces a new method using thermo entangled state representation to analyze the Wigner function evolution in a self-Kerr medium, revealing that photon number distribution remains unaffected by Kerr nonlinearity.

Contribution

The paper develops a novel Wigner function evolution formula for self-Kerr media with photon loss, showing photon number distribution independence from Kerr coupling.

Findings

Photon number distribution is unaffected by Kerr nonlinearity.

Wigner function evolution can be expressed as an overlap of pure states in an enlarged Fock space.

Photon loss effects are incorporated into the evolution formula.

Abstract

By introducing the thermo entangled state representation, we convert the calculation of Wigner function (WF) of density operator to an overlap between "two pure" states in a two-mode enlarged Fock space. Furthermore, we derive a new WF evolution formula of any initial state in self-Kerr Medium with photon loss and find that the photon number distribution for any initial state is independent of the coupling factor with Kerr Medium, where the number state is not affected by the Kerr nonlinearity and evolves into a density operator of binomial distribution.