Propagation of transverse intensity correlations of a two-photon state

TL;DR

This paper investigates how the transverse spatial correlations of entangled photon pairs evolve when passing through arbitrary linear optical systems, using fractional Fourier transforms to analyze and experimentally verify correlation behaviors.

Contribution

It introduces a comprehensive theoretical and experimental framework for analyzing the propagation of two-photon transverse correlations through fractional Fourier transform systems.

Findings

Joint detection probability can show correlation, anti-correlation, or no correlation depending on transform parameters.

Good agreement between theoretical predictions and experimental results.

Analytical results for ideal EPR states and numerical results for parametric down-conversion states.

Abstract

The propagation of transverse spatial correlations of photon pairs through arbitrary first-order linear optical systems is studied experimentally and theoretically using the fractional Fourier transform. Highly-correlated photon pairs in an EPR-like state are produced by spontaneous parametric down-conversion and subject to optical fractional Fourier transform systems. It is shown that the joint detection probability can display either correlation, anti-correlation, or no correlation, depending on the sum of the orders $\alpha$ and $\beta$ of the transforms of the down-converted photons. We present analytical results for the propagation of the perfectly correlated EPR state, and numerical results for the propagation of the two-photon state produced from parametric down-conversion. We find good agreement between theory and experiment.