Production Of Nonlocal Quartets And Phase-Sensitive Entanglement In A Superconducting Beam Splitter

Three BCS superconductors S-a, S-b, and S and two short normal regions N-a and N-b in a three-terminal SaNaSNbSb setup provide a source of nonlocal quartets spatially separated as two correlated pairs in S-a and S-b, 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 S-a and S-b can occur in equilibrium, and also if S-a and S-b are biased at opposite voltages. At higher temperatures, thermal excitations result in correlated current fluctuations which depend on the superconducting phases phi(a) and phi(b) in S-a and S-b. Phase-sensitive entanglement is obtained at zero temperature if N-a and N-b are replaced by discrete levels.