Entanglement beating in free space through spin-orbit coupling.

It is well known that the entanglement of a quantum state is invariant under local unitary transformations. This rule dictates, for example, that the entanglement of internal degrees of freedom of a photon remains invariant during free-space propagation. Here, we outline a scenario in which this paradigm does not hold. Using local Bell states engineered from classical vector vortex beams with non-separable degrees of freedom, the so-called classically entangled states, we demonstrate that the entanglement evolves during propagation, oscillating between maximally entangled (purely vector) and product states (purely scalar). We outline the spin-orbit interaction behind these novel propagation dynamics and confirm the results experimentally, demonstrating spin-orbit coupling in paraxial beams. This demonstration highlights a hitherto unnoticed property of classical entanglement and simultaneously offers a device for the on-demand delivery of vector states to targets, for example, for dynamic laser materials processing, switchable resolution within stimulated emission depletion (STED) systems, and a tractor beam for entanglement.