Resonant-cavity-induced phase locking and voltage steps in a Josephson array

We describe a simple dynamical model for an underdamped Josephson junction array coupled to a resonant cavity. From numerical solutions of the model in one dimension, we find that (i) current-voltage characteristics of the array have self-induced resonant steps (SIRS), (ii) at fixed disorder and coupling strength, the array locks into a coherent, periodic state above a critical number of active Josephson junctions, and (iii) when Nₐ active junctions are synchronized on an SIRS, the energy emitted into the resonant cavity is quadratic with Nₐ. All three features are in agreement with a recent experiment [P. Barbara, A. B. Cawthorne, S. V. Shitov, and C. J. Lobb, Phys. Rev. Lett. 82, 1963 (1999)].