Production of non-local 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 S_aN_aSN_bS_b set-up provide a source of non-local quartets spatially separated as two correlated pairs in S_a and S_b, if the distance between the interfaces N_aS and SN_b is comparable to the coherence length in S. Low-temperature dc-transport of non-local 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.