Numerical and analytical studies of mutual locking of Josephson tunnel junctions

Mutual locking of Josephson tunnel junctions in a simple resistive circuit has been studied numerically. Locking is found to exist over voltage ranges of considerable size, on the order of 20%–30%. The voltage–locking range depends on random parameter variations; however, it increases as the number of junctions N increases, nearly becoming constant for large N. Available output power is expected to be proportional to frequency and to the number of junctions. New locking effects are described, the most unusual of which is a sequence of period-doubling bifurcations leading to a chaotic state in which the junctions’ phases vary aperiodically, while their time-averaged voltages remain equal. The effect of noise is considered, as well as operation at frequencies of the order of the gap frequency.