Exact temporal second-order coherence function for displaced-squeezed thermal states

We calculate exactly 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 the generation of the Gaussian state and subsequent measurements of two photons a time $\tau \geq 0$ apart. The generation of the Gaussian state by the parametric amplifier insures that the temporal second-order coherence function depends only on $\tau$.