Quality of Spatial Entanglement Propagation

TL;DR

This paper investigates how spatial entanglement of photon pairs propagates, develops theoretical models including phase and amplitude effects, and validates findings with experiments, advancing understanding of entanglement dynamics in realistic scenarios.

Contribution

It introduces a generalized analysis of spatial entanglement propagation incorporating phase curvature and non-Gaussian wave functions, extending the classical beam quality parameter to biphotons.

Findings

Agreement between theory and experimental measurements

Demonstration of entanglement migration between amplitude and phase

Extension of beam quality concepts to biphoton states

Abstract

We explore, both experimentally and theoretically, the propagation dynamics of spatially entangled photon pairs (biphotons). Characterization of entanglement is done via the Schmidt number, which is a universal measurement of the degree of entanglement directly related to the non-separability of the state into its subsystems. We develop expressions for the terms of the Schmidt number that depend on the amplitude and phase of the commonly used double-Gaussian approximation for the biphoton wave function, and demonstrate migration of entanglement between amplitude and phase upon propagation. We then extend this analysis to incorporate both phase curvature in the pump beam and higher spatial frequency content of more realistic non-Gaussian wave functions. Specifically, we generalize the classical beam quality parameter M2 to the biphotons, allowing the description of more information-rich beams and more complex dynamics. Agreement is found with experimental measurements using direct imaging and Fourier optics.