Interaction effects on quantum transport in superconducting nanoscale junctions

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We propose to theoretically study the equilibrium Josephson current-phase relation and the nonequilibrium current-voltage characteristics for various models of interacting quantum dots attached to a pair of superconducting electrodes (Josephson dot). The interplay between superconducting correlations (proximityinduced by the attached electrodes) and the interactions (either Coulomb or vibrational mode interactions) in such Josephson dots gives rise to rich and experimentally accessible physics. In particular, we plan to address: (i) effects due to the spin-orbit coupling, including the spontaneously broken time reversal symmetry; (ii) the nonequilibrium dynamics of a Josephson dot coupled to a two-level system, including the possibility of artificial Kondo screening by Cooper pairs and the backaction of the Cooper pair dynamics on the two-level system, and (iii) the effects of an enlarged SU(4) symmetry on the Josephson effect and the corresponding phase diagram realized in ultraclean carbon nanotubes. We will use both analytical methods (path-integral based field theory and diagrammatic perturbation theory) and quantum Monte Carlo simulations.