Temporal second-order coherence function for displaced-squeezed thermal states

Abstract

We calculate the quantum mechanical, temporal second-order coherence function for a single-mode, degenerate parametric amplifier for a system in the Gaussian state, viz. a displaced–squeezed thermal state. The calculation involves first dynamical generation at time t of the Gaussian state from an initial thermal state and subsequent measurements of two photons a time apart. The generation of the Gaussian state by the parametric amplifier insures that the temporal second-order coherence function depends only on , via , for the given Gaussian state parameters, Gaussian state preparation time t, and average number of thermal photons. It is interesting that the time evolution for displaced thermal states shows a power decay in rather than an exponential one as is the case for general, displaced–squeezed thermal states.