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

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.