Dynamical instabilities of a resonator driven by a superconducting single-electron transistor

摘要

We investigate the dynamical instabilities of a resonator coupled to asuperconducting single-electron transistor (SSET) tuned to the Josephsonquasiparticle (JQP) resonance. Starting from the quantum master equation of thesystem, we use a standard semiclassical approximation to derive a closed set ofmean field equations which describe the average dynamics of the resonator andSSET charge. Using amplitude and phase coordinates for the resonator andassuming that the amplitude changes much more slowly than the phase, we explorethe instabilities which arise in the resonator dynamics as a function ofcoupling to the SSET, detuning from the JQP resonance and the resonatorfrequency. We find that the locations (in parameter space) and sizes of thelimit cycle states predicted by the mean field equations agree well withnumerical solutions of the full master equation for sufficiently weakSSET-resonator coupling. The mean field equations also give a good qualitativedescription of the set of dynamical transitions in the resonator state thatoccur as the coupling is progressively increased.