Spin-dependent Josephson current through double quantum dots and measurement of entangled electron states

We study a double quantum dot, each dot of which is tunnel coupled to superconducting leads. In the Coulomb blockade regime, a spin-dependent Josephson coupling between two superconductors is induced, as well as an antiferromagnetic Heisenberg exchange coupling between the spins on the double dot that can be tuned by the superconducting phase difference. We show that the correlated spin states---singlet or triplets---on the double dot can be probed via the Josephson current in a dc-superconducting quantum interference device setup.