Photon entanglement entropy as a probe of many-body correlations and fluctuations

TL;DR

This paper develops a theoretical framework to analyze how entangled photon scattering in an optical cavity reveals many-body correlations through entropy production, highlighting the role of fluctuations and interactions.

Contribution

It introduces a perturbative model for photon entanglement entropy in cavity scattering, linking entropy to photon-photon interactions and many-body fluctuations.

Findings

Entropy vanishes with fast fluctuations.

Maximum entropy occurs with homogeneous broadening.

Entropy measures photon-photon interaction strength.

Abstract

Recent theoretical and experiments have explored the use of entangled photons as a spectroscopic probe of material systems. We develop here a theoretical description for entropy production in the scattering of an entangled biphoton state within an optical cavity. We develop this using perturbation theory by expanding the biphoton scattering matrix in terms of single-photon terms in which we introduce the photon-photon interaction via a complex coupling constant, $\xi$. We show that the von Neumann entropy provides a succinct measure of this interaction. We then develop a microscopic model and show that in the limit of fast fluctuations, the entanglement entropy vanishes whereas in the limit the coupling is homogeneous broadened, the entanglement entropy depends upon the magnitude of the fluctuations and reaches a maximum.