Josephson current through a Kondo molecule

We investigate transport of Cooper pairs through a double quantum dot (DQD) in the Kondo regime and coupled to superconducting leads. Within the non-perturbative slave boson mean-field theory we evaluate the Josephson current for two different configurations, the DQD coupled in parallel and in series to the leads. We find striking differences between these configurations in the supercurrent as a function of the ratio t/\Gamma, where t is the interdot coupling and \Gamma is the coupling to the leads: the critical current I_c decreases monotonously with t/\Gamma for the parallel configuration whereas I_c exhibits a maximum at t/\Gamma=1 in the serial case. These results demonstrate that a variation of the ratio t/\Gamma enables to control the flow of supercurrent through the Kondo resonance of the DQD.