Speckle statistics of entangled photons

TL;DR

This paper investigates the statistical properties of speckle patterns formed by entangled photons passing through scattering media, revealing how correlations and sensitivity depend on system parameters and photon number.

Contribution

It provides a comprehensive analysis of multiphoton speckle correlations and their dependence on propagation regimes and photon number, extending understanding of quantum light in complex media.

Findings

Long-range speckle correlations dominate for large detectors.

Speckle sensitivity increases with photon number, as √N in directed-wave regime.

Speckle correlations differ between directed-wave and diffusive regimes.

Abstract

We consider the propagation of several entangled photons through an elastically scattering medium and study statistical properties of their speckle patterns. We find the spatial correlations of multiphoton speckles and their sensitivity to changes of system parameters. Our analysis covers both the directed-wave regime, where rays propagate almost ballistically while experiencing small-angle diffusion, and the real-space diffusive regime. We demonstrate that long-range correlations of the speckle patterns dominate experimental signatures for large-aperture photon detectors. We also show that speckle sensitivity depends strongly on the number of photons $N$ in the incoming beam, increasing as $\sqrt{N}$ in the directed-wave regime and as $N$ in the diffusive regime.