Homodyning the [formula omitted] of 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.