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 α and β 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.
@article{arxiv.0902.1660,
title = {Propagation of transverse intensity correlations of a two-photon state},
author = {D. S. Tasca and S. P. Walborn and F. Toscano and P. Pellat-Finet and P. H. Souto Ribeiro},
journal= {arXiv preprint arXiv:0902.1660},
year = {2009}
}