Vibration Mode Induced Shapiro Steps and Backaction in Josephson Junctions

TL;DR

This paper models a superconducting tunnel junction coupled to a mechanical oscillator, revealing how oscillator motion modulates Josephson current, induces Shapiro steps, and introduces velocity-dependent backaction effects.

Contribution

It demonstrates the impact of mechanical vibrations on Josephson junctions, including the emergence of Shapiro steps and a novel backaction term, advancing understanding of electromechanical coupling in superconducting systems.

Findings

Josephson current is modulated by oscillator motion

Additional Shapiro steps appear in the I-V characteristic

A velocity-dependent backaction term is identified

Abstract

A model of a superconducting tunnel junction coupled to a mechanical oscillator is studied at zero temperature in the case of linear coupling between the oscillator and tunneling electrons. It is found that the Josephson current flowing between two superconductors is modulated by the motion of the oscillator. Coupling to harmonic oscillator produces additional Shapiro steps in $I-V$ characteristic of Josephson junction whose position is tuned by the frequency of the vibration mode. We also find a new velocity dependent term originating from the backaction of the ac Josephson current. This term is periodic in time and vanishes at zero bias voltage.