Anisotropic Spatial Entanglement

TL;DR

This paper investigates how the spatial entanglement of photon pairs generated via SPDC can be engineered by controlling pump beam asymmetry, revealing anisotropic entanglement properties and directional dependence of entanglement strength.

Contribution

It introduces the concept of anisotropic entanglement using elliptical pump beams and demonstrates how beam asymmetry affects entanglement in different transverse directions.

Findings

Entanglement degree depends on pump beam asymmetry.

Highly asymmetric pump beams can eliminate entanglement in one transverse direction.

Entanglement in the other transverse direction remains unaffected.

Abstract

The photon-pairs generated through spontaneous parametric down-conversion (SPDC) possess strong correlations in their transverse position and momentum degrees of freedom. For such photon pairs, the transverse position correlation length depends on the crystal thickness and the pump wavelength, whereas the transverse momentum correlation length depends on the beam waist and spatial coherence length of the pump. By controlling these parameters, it is possible to engineer the spatial entanglement. Here, we utilize the circular asymmetry of the pump by using an elliptical-Gaussian beam to change the degree of entanglement in transverse directions, which we call anisotropic entanglement. We show the interrelation between the degree of anisotropic entanglement and the asymmetry in the beam width. In addition, we also show that for a highly asymmetric pump beam, the entanglement along the y-direction completely vanishes, whereas the entanglement in the x-direction remains intact.