Quantum fluctuations and quantum dynamics of small Josephson junctions

Abstract

The quantum properties of small Josephson junctions with both linear Ohmic and quasiparticle (“cosine”) dissipation are investigated by means of a real-time path-integral technique. Quantum diffusion of the quasicharge and quantum corrections to the classical conductivity are analyzed. The current-voltage characteristics and the effect of voltage steps are studied. It is shown that coherent voltage oscillations may exist not only for small, but also for large values of the junction tunneling conductivity. For not very small values of the quasiparticle conductivity of the junction the frequency of these oscillations is twice the Bloch oscillation frequency. The quantum dynamics of the phase difference across the junction is studied for a wide region of parameters. It is shown that linear and “cosine” dissipation mechanisms cause the presence of two dissipative phase transitions, which are qualitatively different from each other in many aspects.