Imaging Walk-Off Driven Distortions in EPR Photon Pair Correlations

TL;DR

This paper reveals how birefringence-induced walk-off affects the spatial correlations of EPR photon pairs, showing that it couples sum and difference coordinates and impacts quantum imaging and information processing.

Contribution

It demonstrates that walk-off effects persist beyond the thin-crystal approximation, coupling sum and difference coordinates in photon pair correlations.

Findings

Coupling of sum and difference coordinates due to walk-off.

Tapering of transverse correlations near the crystal image plane.

Experimental confirmation of the coupled correlation behavior.

Abstract

Spontaneous parametric down-conversion is the primary source of position-correlated and momentum-anticorrelated photon pairs that form the canonical Einstein-Podolsky-Rosen (EPR) state. Their transverse spatial correlations are usually analyzed within the thin-crystal approximation, where the two-photon wavefunction is assumed to factorize into independent functions of the sum and difference coordinates. In practice, however, birefringence-induced transverse walk-off breaks this factorization and couples these degrees of freedom. Here, we show that this coupling persists even for nominally thin crystals once the free-space propagation of the joint spatial intensity is taken into account. This sum-difference coordinate coupling leads to a distinctive tapering of the transverse correlations near the crystal image plane-an effect that standard factorized models cannot capture. Numerical simulations and experimental data clearly confirm this novel behavior. Our findings provide a more complete description of photon-pair generation in birefringent nonlinear media and clarify fundamental limits on spatially resolved quantum imaging and spatial-mode quantum information processing with EPR states.