Generation of tunable entanglement and violation of a Bell-like inequality between different degrees of freedom of a single photon

TL;DR

This paper presents a method to generate and tune entanglement between different degrees of freedom within a single photon, and demonstrates violation of a Bell-like inequality using polarization and spatial modes.

Contribution

It introduces a scheme for tunable entanglement between a photon's degrees of freedom and applies Bell inequality tests to characterize this entanglement.

Findings

Successfully generated tunable entanglement between polarization and spatial modes.

Demonstrated violation of a Bell-like inequality with a single photon.

Showed that tools like CHSH inequality can characterize intra-photon entanglement.

Abstract

We demonstrate a scheme to generate noncoherent and coherent correlations, i.e., a tunable degree of entanglement, between degrees of freedom of a single photon. Its nature is analogous to the tuning of the purity (first-order coherence) of a single photon forming part of a two-photon state by tailoring the correlations between the paired photons. Therefore, well-known tools such as the Clauser-Horne-Shimony-Holt (CHSH) Bell-like inequality can also be used to characterize entanglement between degrees of freedom. More specifically, CHSH inequality tests are performed, making use of the polarization and the spatial shape of a single photon. The four modes required are two polarization modes and two spatial modes with different orbital angular momentum.