Gouy phase of type-I SPDC-generated biphotons

TL;DR

This paper models the Gouy phase evolution of biphotons generated via type-I SPDC using a double Gaussian approximation, linking entanglement measures to the Gouy phase and validating with experimental data.

Contribution

It introduces a Gaussian wavefunction model for biphotons that connects Gouy phase, entanglement, and propagation, with experimental validation.

Findings

Gouy phase depends on two-photon correlation and Rayleigh length.

Logarithmic negativity remains constant during propagation.

Biphoton Gouy phase aligns with experimental measurements.

Abstract

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].