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arXiv:1407.0144 · Physical Review A

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

Adam Vallés, Vincenzo D’Ambrosio, Martin Hendrych, Michal Mičuda, Lorenzo Marrucci, Fabio Sciarrino, Juan P. Torres

Published Nov 20, 2014• 32 citations
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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.

DOI
10.1103/physreva.90.052326

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Single photons emerging from Pancharatnam-Berry phase optical elements (q plates) exhibit entanglement in the degrees of freedom of spin and orbital angular momentum. We put forward an experimental scheme for probing the spin-orbit correlations of single photons. It is found that the Clauser-Horne-Shimony-Holt parameter S for the single-photon spin-orbit entangled state could be as high as 2√2, evidently violating the Bell-like inequality and thus invalidating the noncontextual hidden variable theories.
In single-particle or intraparticle entanglement, two degrees of freedom of a single particle, e.g., momentum and polarization of a single photon, are entangled. Single-particle entanglement is a resource that can be exploited both in quantum communication protocols and in experimental tests of noncontextuality based on the Kochen-Specker theorem. Here we show that single-particle entangled states of single photons can be produced from attenuated classical sources of light. To experimentally certify the single-particle entanglement, we perform a Bell test, observing a violation of the Clauser, Horne, Shimony, and Holt inequality. We show that single-particle entanglement can be achieved even in a classical light beam, provided that first-order coherence is maintained between the degrees of freedom involved in the entanglement. This demonstrates that cheap, compact, and low-power photon sources can be used to generate single-particle entangled photons which could be a resource for quantum technology applications.
We investigate quantum nonlocality of a single-photon entangled state under feasible measurement techniques consisting of on-off and homodyne detections along with unitary operations of displacement and squeezing. We test for a potential violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality, in which each of the bipartite party has a freedom to choose between two measurement settings, with each measurement yielding a binary outcome. We find that single-photon quantum nonlocality can be detected when two or less of the four total measurements are carried out by homodyne detection. The largest violation of the CHSH inequality is obtained when all four measurements are squeezed-and-displaced on-off detections. We test the robustness of violations against imperfections in on-off detectors and single-photon sources, finding that the squeezed-and-displaced measurement schemes perform better than the displacement-only measurement schemes.
Different degrees of freedom of single photons have been entangled and are used as a resource for various quantum technology applications. We present a simple scheme to perform Bell's test and show the violation of CHSH inequality in a path-entangled single photon state using interferometric and its equivalent non-interferometric approach in beam splitter setting. We demonstrate this experimentally by generating and controlling path-entangled state using both, heralded and un-heralded single photons from spontaneous parametric down-conversion. The experimental results we present show the transition to violation of CHSH inequality when the purity of single photons state visibility increase above 70\% , P>0.7\mathcal{P} > 0.7P>0.7. Our procedure using single beam splitter and two detector module for un-heralded single photon source allows a simple way to test for purity of any single photon source and to study quantum correlations on systems driven by dynamics where single particle entanglement with position space is prominent.