We consider a double Gaussian approximation to describe the wavefunction of twin photons (also called a biphoton) created in a nonlinear crystal via a type-I spontaneous parametric downconversion (SPDC) process. We find that the wavefunction develops a Gouy phase while it propagates, being dependent of the two-photon correlation through the Rayleigh length. We evaluate the covariance matrix and show that the logarithmic negativity, useful in quantifying entanglement in Gaussian states, although Rayleigh-dependent, does not depend on the propagation distance. In addition, we show that the two-photon entanglement can be connected to the biphoton Gouy phase as these quantities are Rayleigh-length-related. Then, we focus the double Gaussian biphoton wavefunction using a thin lens and calculate a Gouy phase that is in reasonable agreement with the experimental data of D. Kawase et al. published in Ref. [1].
@article{arxiv.2010.15615,
title = {Gouy phase of type-I SPDC-generated biphotons},
author = {F. C. V. de Brito and I. G. da Paz and Brigitte Hiller and Jonas B. Araujo and Marcos Sampaio},
journal= {arXiv preprint arXiv:2010.15615},
year = {2020}
}