Josephson effect in superconductor/normal-dot/superconductor junctions driven out of equilibrium by quasiparticle injection

We study theoretically the large variations of the supercurrent through a\nnormal dot that are induced by a small quasiparticle injection current from\nnormal leads connected to the dot. We find that the supercurrent decomposes\ninto a subgap contribution, which depends on the voltages applied to the normal\nleads, as well as a contribution with opposite sign from energies outside the\ngap, which is insensitive to the voltages. As the voltages gradually suppress\nthe subgap contribution, a critical voltage exists above which the contribution\nfrom energies outside the gap dominates, leading to a sign reversal of the\ncurrent-phase relation, namely a transition to a so-called $\\pi$-junction\nbehavior. We determine the critical voltage and analyze the robustness of the\neffect with respect to temperature and inelastic relaxation in the dot.\n