Statistical properties and decoherence of two-mode photon-subtracted squeezed vacuum

TL;DR

This paper analyzes the statistical properties and decoherence effects of two-mode photon-subtracted squeezed vacuum states, deriving analytical expressions for their Wigner functions and exploring conditions under which they exhibit nonclassicality.

Contribution

It introduces a new analytical framework for the Wigner function of photon-subtracted two-mode squeezed vacuum states and examines their decoherence behavior in thermal environments.

Findings

The state can be represented as a squeezed two-variable Hermite polynomial excitation vacuum.

The Wigner function is derived analytically and expressed via Jacobi polynomials.

Decoherence causes the Wigner function to become positive after a certain decay time.

Abstract

We investigate the statistical properties of the photon-subtractions from the two-mode squeezed vacuum state and its decoherence in a thermal environment. It is found that the state can be considered as a squeezed two-variable Hermite polynomial excitation vacuum and the normalization of this state is the Jacobi polynomial of the squeezing parameter. The compact expression for Wigner function (WF) is also derived analytically by using the Weyl ordered operators' invariance under similar transformations. Especially, the nonclassicality is discussed in terms of the negativity of WF. The effect of decoherence on this state is then discussed by deriving the analytical time evolution results of WF. It is shown that the WF is always positive for any squeezing parameter and photon-subtraction number if the decay time exceeds an upper bound (}$\kappa t>{1/2}\ln \frac{2\bar{n}+2}{2\bar{n}+1}).