Violation of Bell's inequality for Mathieu-Gauss vector modes
preprintposted on 2023-07-12, 16:00 authored by Edgar Medina-Segura, Francisco I. Mecillas-Hernandez, Thomas Konrad, Carmelo Rosales-Guzmán, Benjamin Perez-García
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.