Transverse distinguishability of entangled photons with arbitrarily shaped spatial near- and far-field distributions

TL;DR

This paper presents a theoretical and numerical model for describing the complex spatial distribution of entangled photons generated in nonlinear crystals, validated by experiments measuring visibility and distinguishability.

Contribution

The authors developed a comprehensive model that incorporates phase matching and crystal properties to predict spatial effects in entangled photon experiments.

Findings

Numerical predictions match experimental measurements of visibility and distinguishability.

The model accurately describes the spatial photon count distribution.

Experimental results show a distinguishability and visibility relation of D^2 + V^2 = 1.43.

Abstract

Entangled photons generated by spontaneous parametric down conversion inside a nonlinear crystal exhibit a complex spatial photon count distribution. A quantitative description of this distribution helps with the interpretation of experiments that depend on this structure. We developed a theoretical model and an accompanying numerical calculation that includes the effects of phase matching and the crystal properties to describe a wide range of spatial effects in two-photon experiments. The numerical calculation was tested against selected analytical approximations. We furthermore performed a double-slit experiment where we measured the visibility V and the distinguishability D and obtained $D^2 + V^2 = 1.43$. The numerical model accurately predicts these experimental results.