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