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 de-superconducting quantum interference device setup.