Homodyning the $g^{(2)}(0)$ of Gaussian states

TL;DR

This paper introduces a method to determine the zero-delay second-order correlation function of Gaussian states using a single homodyne detector, providing a practical approach for analyzing quantum states.

Contribution

The authors derive an analytic expression for $g^{(2)}(0)$ of Gaussian states in terms of covariance matrix elements and demonstrate its experimental application.

Findings

Method successfully reconstructs $g^{(2)}(0)$ from homodyne data.

Thresholds identified for nonclassicality based on coherent amplitude and squeezing.

Applicable to both single- and two-mode Gaussian states.

Abstract

We suggest a method to reconstruct the zero-delay-time second-order correlation function $g^{(2)}(0)$ of Gaussian states using a single homodyne detector. To this purpose, we have found an analytic expression of $g^{(2)}(0)$ for single- and two-mode Gaussian states in terms of the elements of their covariance matrix and the displacement amplitude. In the single-mode case we demonstrate our scheme experimentally, and also show that when the input state is nonclassical, there exist a threshold value of the coherent amplitude, and a range of values of the complex squeezing parameter, above which $g^{(2)}(0) < 1$. For amplitude squeezing and real coherent amplitude, the threshold turns out to be a necessary and sufficient condition for the nonclassicality of the state. Analogous results hold also for two-mode squeezed thermal states.