Violation of Bell's inequality for Mathieu-Gauss vector modes

TL;DR

This paper demonstrates both theoretically and experimentally that Mathieu-Gauss vector modes, a class of light modes with elliptical symmetry, violate Bell-like inequalities, revealing non-classical correlations in their polarization and spatial degrees of freedom.

Contribution

It extends the understanding of Bell inequality violations to Mathieu-Gauss vector modes, a more general class of vector beams with elliptical symmetry.

Findings

Mathieu-Gauss vector modes violate CHSH-Bell inequality.

Experimental verification confirms theoretical predictions.

Reveals non-classical correlations in vector light modes.

Abstract

Vector beams display varying polarisation over planes transversal to their direction of propagation. The variation of polarisation implies that the electric field cannot be expressed as a product of a spatial mode and its polarisation. This non-separability has been analysed for particular vector beams in terms of non--quantum entanglement between the spatial and the polarisation-degrees of freedom, and equivalently, with respect to the degree of polarisation of light. Here we demonstrate theoretically and experimentally that Mathieu-Gauss vector modes violate a Bell-like inequality known as the Clauser-Horn-Shimony-Holt-Bell (CHSH-Bell) inequality. This demonstration provides new insights into that fact that a more general class of vector modes with elliptical symmetry also violate Bell inequalities.