Infinitesimal propagation equation for atmospheric decoherence with multiphoton correlations

TL;DR

This paper extends the infinitesimal propagation equation to include multiphoton correlations for photons traveling along the same path through turbulence, enhancing understanding of atmospheric decoherence effects.

Contribution

It introduces a new differential equation accounting for multiphoton correlations in atmospheric turbulence, building on previous models for entangled photon pairs.

Findings

Equation includes additional terms for multiphoton correlations

Quantized field formulation from Lorentz invariance has minimal impact

Enhanced model for atmospheric decoherence with multiphoton effects

Abstract

Previously a set of coupled first order differential equations were derived for the decoherence of a pair of spatial mode entangled photons, propagating along different paths through turbulence. Here we extend this analysis to the situation where both photons travel along the same path, which introduces the effect of multiple photon correlations. The resulting equation now contains additional terms that take these multiphoton correlations into account. At the same time, we provide a more thorough formulation of the quantized field, starting from a Lorentz invariant formulation, which is then explicitly broken by the choice of a particular propagation direction. The effect of the latter improvement in the quantization on the form of the final equation is minimal.