Production of nonlocal quartets and phase-sensitive entanglement in a superconducting beam splitter

Three BCS superconductors Sa, Sb, and S and two short normal regions Na and Nb in a three-terminal SaNaSNb Sb setup provide a source of nonlocal quartets spatially separated as two correlated pairs in Sa and Sb, if the distance between the interfaces Na S and SNb is comparable to the coherence length in S. Low-temperature dc transport of nonlocal quartets from S to Sa and Sb can occur in equilibrium, and also if Sa and Sb are biased at opposite voltages. At higher temperatures, thermal excitations result in correlated current fluctuations which depend on the superconducting phases Φa and Φb in Sa and Sb. Phase-sensitive entanglement is obtained at zero temperature if Na and Nb are replaced by discrete levels.