Transport properties of a superconducting single-electron transistor coupled to a nanomechanical oscillator

TL;DR

This paper studies a superconducting single-electron transistor coupled to a nanomechanical oscillator, revealing backaction effects, noise characteristics, and the potential for cooling and bistability of the mechanical resonator.

Contribution

It provides a detailed analysis of the coupled system's transport properties, including analytical, higher-order, and numerical results, highlighting new phenomena like cooling and bistability.

Findings

Backaction effects influence the oscillator state.

Cooling of the mechanical resonator is achievable.

Bistable oscillator states occur at low couplings.

Abstract

We investigate a superconducting single-electron transistor capacitively coupled to a nanomechanical oscillator and focus on the double Josephson quasiparticle resonance. The existence of two coherent Cooper pair tunneling events is shown to lead to pronounced backaction effects. Measuring the current and the shot noise provides a direct way of gaining information on the state of the oscillator. In addition to an analytical discussion of the linear-response regime, we discuss and compare results of higher-order approximation schemes and a fully numerical solution. We find that cooling of the mechanical resonator is possible, and that there are driven and bistable oscillator states at low couplings. Finally, we also discuss the frequency dependence of the charge noise and the current noise of the superconducting single electron transistor.