Experimental violation of a Bell-like inequality with optical vortex beams

Abstract

Optical beams with topological singularities have a Schmidt decomposition. Hence, they display features typically associated with bipartite quantum systems; in particular, these classical beams can exhibit entanglement. This classical entanglement can be quantified by a Bell inequality formulated in terms of Wigner functions. We experimentally demonstrate the violation of this inequality for Laguerre–Gauss (LG) beams and confirm that the violation increases with increasing orbital angular momentum. Our experimental scheme, which is designed to give directly the parity of the Wigner function, yields negativity at the origin for ${\mathrm{LG}}_{10}$ beams, whereas for ${\mathrm{LG}}_{20}$ we always get a positive value.

Keywords

• classical entanglement
• optical beams
• Bell tests
• non-separability
• 03.65.Ud
• 42.50.Tx