Anisotropic Purity of Entangled Photons From Cooper Pairs in Heterostructures

It was theoretically proposed that a forward-biased p-n junction with a superconducting layer (P-N-S), would produce pure, polarization entangled photons due to inherent spin-singlet pairing of electrons. However, any heterostructure interface generically induces Rashba spin-orbit coupling, which in turn generates a mixed singlet-triplet superconducting order parameter. Here we study the effect of triplet pairing on the purity of photons produced through Cooper pair recombination. A unique directional dependence of the state purity is found for a triplet superconductor with fixed $\vec{d}$: pure, entangled photons are produced when the photon polarization axis is parallel to $\vec{d}$. Induced triplet pairing in a singlet superconductor is shown to degrade the state purity, while induced singlet pairing in a triplet superconductor is shown to enhance the production of entangled pairs. These considerations may aid the design of functional devices to produce entangled photons.