We investigate the idea for probing spin states of two coupled quantum dots (CQDs) by the dc Josephson current flowing through them. This theory requires weak coupling between CQDs and electrodes, but allows arbitrary interdot tunnel coupling, intradot and interdot Coulomb interactions. We find that the Coulomb blockade peaks exhibit a nonmonotonous dependence on the Zeeman splitting of CQDs, which can be understood in terms of Andreev bound states. More importantly, the supercurrent in the Coulomb blockade valleys may provide information on the spin states of CQDs: for CQDs with total electron number $N=1,3\mathrm{}$ (odd), the supercurrent will reverse its sign if the CQD becomes a magnetic molecule; for a CQD with $N=2\mathrm{}$ (even), the supercurrent will decrease sharply around the transition between the spin singlet and triplet ground states of the CQD.

• Received 24 May 2002

DOI:https://doi.org/10.1103/PhysRevB.66.085306