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

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

2007-03-06

arxiv.org/abs/cond-mat/0703150v1

New J. Phys. 9 (2007) 84

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

23 pages, 6 Figures, Accepted for NJP

Scientific paper

10.1088/1367-2630/9/4/084

We investigate the dynamical instabilities of a resonator coupled to a superconducting single-electron transistor (SSET) tuned to the Josephson quasiparticle (JQP) resonance. Starting from the quantum master equation of the system, we use a standard semiclassical approximation to derive a closed set of mean field equations which describe the average dynamics of the resonator and SSET charge. Using amplitude and phase coordinates for the resonator and assuming that the amplitude changes much more slowly than the phase, we explore the instabilities which arise in the resonator dynamics as a function of coupling to the SSET, detuning from the JQP resonance and the resonator frequency. We find that the locations (in parameter space) and sizes of the limit cycle states predicted by the mean field equations agree well with numerical solutions of the full master equation for sufficiently weak SSET-resonator coupling. The mean field equations also give a good qualitative description of the set of dynamical transitions in the resonator state that occur as the coupling is progressively increased.

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