Synchronization of underdamped Josephson-junction arrays

Our recent experiments show that arrays of underdamped Josephson junctions radiate coherently only above a threshold number of junctions switched onto the radiating state. For each junction, the radiating state is a resonant step in the current-voltage characteristics due to the interaction between the junctions in the array and an electromagnetic cavity. Here we show that a model of a one-dimensional array of Josephson junctions coupled to a resonator can produce many features of the coherent be havior above threshold, including coherent radiation of power and the shape of the array current-voltage characteristic. The model also makes quantitative predictions about the degree of coherence of the junctions in the array. However, in this model there is no threshold; the experimental below-threshold region behavior could not be reproduced.Received: 11 April 2003, Published online: 23 July 2003PACS: 74.50.+r Tunneling phenomena; point contacts, weak links, Josephson effects - 85.25.-j Superconducting devices     

Discrete breathers in two-dimensional Josephson-junction arrays

We have proposed theoretically and studied numerically the existence of discrete breathers (intrinsic localized modes) in the dynamics of a two-dimensional Josephson-junction array biased by radio-frequency fields. The solutions are linearly stable in the framework of the Floquet theory and robust in the presence of thermal fluctuations. We have also discussed the conditions for realizing an experimental detection of these modes.     

Three-dimensional Josephson-junction arrays in the quantum regime

We study the quantum phase transition properties of a three-dimensional periodic array of Josephson junctions with charging energy that includes both the self and mutual junction capacitances. We use the phase fluctuation algebra between number and phase operators, given by the Euclidean group E2, and we effectively map the problem onto a solvable quantum generalization of the spherical model. We obtain a phase diagram as a function of temperature, Josephson coupling, and charging energy. We also analyze the corresponding fluctuation conductivity and its universal scaling form in the vicinity of the zero-temperature quantum critical point.