Effect of mechanical resonance on Josephson dynamics

Abstract

We study theoretically dynamics in a Josephson junction coupled to a mechanical resonator looking at the signatures of the resonance in dc electrical response of the junction. Such a system can be realized experimentally as a suspended ultraclean carbon nanotube brought in contact with two superconducting leads. A nearby gate electrode can be used to tune the junction parameters and to excite mechanical motion. We augment theoretical estimations with the values of setup parameters measured in one of the samples fabricated. We show that charging effects in the junction give rise to a mechanical force that depends on the superconducting phase difference and can excite the resonant mode. We develop a model that encompasses the coupling of electrical and mechanical dynamics. We compute the mechanical response (the effect of mechanical motion) in the regime of phase and dc voltage bias. We thoroughly investigate the regime of combined ac and dc bias where Shapiro steps are developed and reveal several distinct regimes characteristic for this effect. Our results can be immediately applied in the context of experimental detection of the mechanical motion in realistic superconducting nanomechanical devices.

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