Double quantum dot between two superconducting leads

A double quantum dot coupled to two superconducting leads is studied in the Coulomb blockade regime. The double dot mediates an effective Josephson coupling between the two superconducting leads, which in turn induce an exchange coupling between the spin states of the dots. The Josephson current depends on the spins on the dots, while the spin exchange coupling can be tuned by the superconducting phase difference. This spin-dependent Josephson current can be used to probe directly the correlated spin states (singlet or triplets).