Anti-phase locking in a two-dimensional Josephson junction array

Abstract

We consider theoretically phase locking in a simple two-dimensional Josephson junction array consisting of two loops coupled via a joint line transverse to the bias current. Ring inductances are supposed to be small, and special emphasis is taken on the influence of external flux. Is is shown, that in the stable oscillation regime both cells oscillate with a phase shift equal to $π$ (i.e. anti-phase). This result may explain the low radiation output obtained so far in two-dimensional Josephson junction arrays experimentally.