Abstract
We consider a Josephson junction formed by a quantum dot connected to two bulk superconductors in presence of Coulomb interaction and coupling to both an electromagnetic environment and a finite density of electronic quasi-particles. In the limit of large superconducting gap we obtain a Born-Markov description of the system dynamics. We calculate the current-phase relation and we find that the experimentally unavoidable presence of quasi-particles can dramatically modify the 0-pi standard transition picture. We show that photon-assisted quasi-particles absorption allows the dynamic switching from the 0- to the pi-state and vice-versa, washing out the 0-pi transition predicted by purely thermodynamic arguments.
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