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

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 τ ≥ 0 apart. The generation of the Gaussian state by the parametric amplifier insures that the temporal second-order coherence functiondepends only on τ , via τ/t, for the givenGaussian state parameters, Gaussian state preparation time t, and average number n̄ of thermal photons. It is interesting that the time evolution for displaced thermal states shows a power decay in τ/t rather than an exponential one as is the case for general, displaced–squeezed thermal states. ARTICLE HISTORY Received 25 August 2015 Accepted 20 October 2015