Chaotic dynamics of periodically driven rf superconducting quantum interference devices

We present numerical investigations of the intrinsic noise in periodically driven, high-frequency, rf superconducting quantum interference devices (SQUID's) due to the chaotic time evolution of the flux trapped in the superconducting ring. The amplitude and the frequency of the external sinusoidal magnetic flux are the control parameters of the SQUID dynamics. The present work shows in detail how the well-known quasistationary behavior evolves into chaos at high frequencies. A rich structure of subharmonic and chaotic bands is observed in the parameter space. Both intermittent and period-doubling routes to chaos are found; the latter is always preceded by a broken symmetry, and thus the former is the governing one for small amplitudes. We also discuss the experimental observability and manifestations of multiply periodic and chaotic SQUID response. In particular, the usual staircase dependence of the absorbed hysteresis power on the amplitude of the external flux is shown to be broken in a characteristic way for each main subharmonic. Thus we propose that simple dc measurements can detect important properties of the nonlinear SQUID dynamics.