Quantum dynamics of superconducting point contacts: Chiral anomaly, Landau-Zener transitions, and all that

Quantum effects in the dynamics of the Josephson phase difference in Josephson junctions with large electron transparency D are studied in the adiabatic regime, when the characteristic charging energy E_C of the junction is much smaller than the superconducting energy gap Δ. In isolated junctions, quantum phase fluctuations are large and manifest themselves as Coulomb blockade of Cooper pair tunneling. The amplitude of the Coulomb blockade oscillations is calculated for single-mode junctions with arbitrary D. In particular, it is shown that the chiral anomaly completely suppresses Coulomb blockade in ballistic junctions with D = 1, and the suppression process at D → 1 can be described as the Landau-Zener transition in imaginary time. In the regime when quantum phase fluctuations are small, they lead to quantum decay of supercurrent states due to macroscopic quantum tunneling of phase through the Josephson potential barrier. The decay rate is found in the nearly-ballistic junctions.