Resonant steps in parallel Josephson junction arrays: parametric instabilities of whirling modes

Circular arrays of underdamped Josephson junctions exhibit a series of resonant steps in the return path of the subgap region in the current-voltage characteristics. We show that the voltage locations of the steps can be predicted by studying the parametric instabilities of whirling periodic solutions, and experimentally verify the prediction in a ring of 8 underdamped junctions. The whirling modes become unstable in certain voltage intervals, and a branch (a resonant step) of more complicated solutions emerges from the endpoint of each interval. We extend the analysis to open-ended arrays and find that for f=0, the onset of a zero-field step has the same underlying mechanism. For f>0, combinations of lattice eigen-frequencies are excited.<>