Intensity correlations in the Wigner representation

TL;DR

This paper establishes a direct link between the second-order correlation function and the Wigner function of a quantum state, supported by experimental measurements and phase space analysis.

Contribution

It derives a compact expression relating $g^{(2)} (0)$ to the Wigner function and experimentally verifies this relationship through simultaneous measurements.

Findings

Theoretical expression linking $g^{(2)} (0)$ to the Wigner function.

Experimental confirmation of the theoretical prediction.

Successful reconstruction of the Wigner function via homodyne tomography.

Abstract

We derive a compact expression for the second-order correlation function $g^{(2)} (0)$ of a quantum state in terms of its Wigner function, thereby establishing a direct link between $g^{(2)} (0)$ and the state's shape in phase space. We conduct an experiment that simultaneously measures $g^{(2)} (0)$ through direct photocounting and reconstructs the Wigner function via homodyne tomography. The results confirm our theoretical predictions.