Direct measurement of the biphoton Wigner function through two-photon interference

TL;DR

This paper introduces a simple modification to the Hong-Ou-Mandel experiment that enables direct measurement of the biphoton Wigner function, providing comprehensive quantum state information and insights into entanglement and non-Gaussian states.

Contribution

It presents a novel method to directly measure the biphoton Wigner function using a modified HOM experiment, enhancing quantum state characterization capabilities.

Findings

Negative Wigner function indicates non-Gaussian entanglement.

The method applies to biphotons from parametric down conversion.

Experimental examples demonstrate the approach's effectiveness.

Abstract

The Hong-Ou-Mandel (HOM) experiment was a benchmark in quantum optics, evidencing the quantum nature of the photon. In order to go deeper, and obtain the complete information about the quantum state of a system, for instance, composed by photons, the direct measurement or reconstruction of the Wigner function or other quasi--probability distribution in phase space is necessary. In the present paper, we show that a simple modification in the well-known HOM experiment provides the direct measurement of the Wigner function. We apply our results to a widely used quantum optics system, consisting of the biphoton generated in the parametric down conversion process. In this approach, a negative value of the Wigner function is a sufficient condition for non-gaussian entanglement between two photons. In the general case, the Wigner function provides all the required information to infer entanglement using well known necessary and sufficient criteria. We analyze our results using two examples of parametric down conversion processes taken from recent experiments. The present work offers a new vision of the HOM experiment that further develops its possibilities to realize fundamental tests of quantum mechanics involving decoherence and entanglement using simple optical set-ups.