AC Josephson current through quantum dots

We consider a setup consisting of two superconductors linked by a single-level quantum dot with strong Coulomb repulsion. An AC Josephson current is generated by applying a bias voltage to the superconductors. Our formalism bases on a diagramatic perturbation expansion in tunnel coupling, where the quasiparticle states are traced out from the total density matrix and the quantum dot as well as the Cooper pair condensates are treated explicitly. The Coulomb repulsion is taken into account nonperturbatively. We find that the first harmonic dominates the higher ones. Furthermore, we discuss the differences between the AC and the DC Josephson effect.