The Effect of Mechanical Resonance on Josephson Dynamics

TL;DR

This paper theoretically investigates how mechanical resonance influences Josephson junction dynamics, highlighting signatures in electrical response and proposing experimental detection methods in nano-mechanical superconducting devices.

Contribution

It introduces a coupled electrical-mechanical model for Josephson junctions with mechanical resonators, including phase-dependent forces and resonance excitation mechanisms.

Findings

Charging effects induce phase-dependent mechanical forces.

Resonance can be excited when superconducting current oscillates at resonant frequency.

Distinct regimes in Shapiro steps reveal mechanical resonance signatures.

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.