Metastability in Josephson transmission lines

Abstract

Thermal activation and macroscopic quantum tunneling in current-biased discrete Josephson transmission lines are studied theoretically. The degrees of freedom under consideration are the phases across the junctions which are coupled to each other via the inductances of the system. The resistively shunted junctions that we investigate constitute a system of N interacting degrees of freedom with an overdamped dynamics. We calculate the decay rate within exponential accuracy as a function of temperature and current. Slightly below the critical current, the decay from the metastable state occurs via a unique ("rigid") saddlepoint solution of the Euclidean action describing the simultaneous decay of the phases in all the junctions. When the current is reduced, a crossover to a regime takes place, where the decay occurs via an "elastic" saddlepoint solution and the phases across the junctions leave the metastable state one after another. This leads to an increased decay rate compared with the rigid case both in the thermal and the quantum regime. The rigid-to-elastic crossover can be sharp or smooth analogous to first- or second- order phase transitions, respectively. The various regimes are summarized in a current-temperature decay diagram.