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The Effect of Mechanical Resonance on Josephson Dynamics

is a title of new arxiv submission made with Ciprian and Han Keijzers, PhD student from Quantum Transport group. This summarizes our long activity in course of which we strove to be close to experiment and the experiment strove for perfectness. This has not quite work yet, however the results are interesting and useful: certainly, they are for generations to come. Please read it here

The abstract: We study theoretically dynamics in a Josephson junction coupled to a mechanical resonator looking at the signatures of the resonance in d.c. electrical response of the junction. Such a system can be realized experimentally as a suspended ultra-clean 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 the samples fabricated.
We show that charging effects in the junction give rise to a mechanical force that depends on the superconducting phase difference. The force can excite the resonant mode provided the superconducting current in the junction has oscillating components with a frequency matching the resonant frequency of the mechanical resonator. 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 bias and d.c. voltage bias. We thoroughly investigate the regime of combined a.c. and d.c. 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 nano-mechanical devices.

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