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

TL;DR

This paper provides an exact quantum mechanical calculation of the temporal second-order coherence function for displaced-squeezed thermal states generated by a degenerate parametric amplifier, relevant for understanding photon correlations over time.

Contribution

It introduces a precise method to compute the temporal second-order coherence function for Gaussian states produced by a parametric amplifier, advancing quantum optics analysis.

Findings

Exact expression for the temporal second-order coherence function.

Dependence of the coherence function solely on time delay τ.

Application to Gaussian states in quantum optics.

Abstract

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 $\tau$.