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 SₐNₐSNbSb setup provide a source of nonlocal quartets spatially separated as two correlated pairs in Sₐ and Sb, if the distance between the interfaces NₐS 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.