The dynamics of high-frequency DC RSQUID oscillators

Josephson circuit simulation software has been used to study the properties of a range of two-junction DC RSQUIDs configured as current-controlled heterodyne oscillators. We find that, if the loop inductance is small, their current-voltage curves are modified substantially due to self-induced Shapiro steps. When the heterodyne frequency is comparable with the Josephson frequency of the junctions the step amplitude becomes very large and additional features are seen, including sub-harmonic steps and step tails. We point out that conventional DC RSQUIDs generally have too large a loop inductance for some of these effects to be seen in the I-V curves, and we suggest that nanofabrication techniques could be used to make novel low-inductance RSQUIDs. We have also demonstrated that by applying a sinusoidally varying RF flux to a DC RSQUID it is possible to phase-modulate the heterodyne oscillation, which could have useful practical applications.