Biphoton phase-space correlations from Gouy-phase measurements using double slits

TL;DR

This paper demonstrates how Gouy phase measurements in a double-slit setup can reveal phase space entanglement variations of biphotons generated by SPDC, linking optical phase shifts to quantum correlations.

Contribution

It introduces an analytical method connecting Gouy phase differences to biphoton entanglement via the logarithmic negativity in an asymmetrical double slit experiment.

Findings

Gouy phase differences encode biphoton phase space entanglement.

Analytical relation between Gouy phase and logarithmic negativity.

Phase space entanglement varies with experimental parameters.

Abstract

Quantum correlations encoded in photonic Laguerre-Gaussian modes were shown to be related to the Gouy phase shifts (D. Kawase et al., Phys. Rev. Lett. 101, 050501 (2008)) allowing for a non-destructive manipulation of photonic quantum states. In this work we exploit the relation between phase space correlations of biphotons produced by spontaneously parametric down conversion (SPDC) as encoded in the logarithmic negativity (LN) and the Gouy phase as they are diffracted through an asymmetrical double slit setup. Using an analytical approach based on a double-gaussian approximation for type-I SPDC biphotons, we show that measurements of Gouy phase differences provide information on their phase space entanglement variation, governed by the physical parameters of the experiment and expressed by the LN via covariance matrix elements.