Quantum nano-electromechanics with electrons, quasiparticles and Cooper pairs: effective bath descriptions and strong feedback effects

TL;DR

This paper investigates the interaction between mechanical resonators and superconducting single-electron transistors, revealing how Cooper-pair tunneling can cool the oscillator and induce strong feedback effects similar to optical cavity ponderomotive phenomena.

Contribution

It introduces an effective bath description for the coupled system and uncovers the role of Cooper-pair tunneling in controlling mechanical motion and feedback effects.

Findings

Cooper-pair tunneling can significantly cool the mechanical oscillator.

Negative damping effects lead to strong electro-mechanical feedback.

The system exhibits an energy-dependent effective temperature for the oscillator.

Abstract

Using a quantum noise approach, we discuss the physics of both normal metal and superconducting single electron transistors (SET) coupled to mechanical resonators. Particular attention is paid to the regime where transport occurs via incoherent Cooper-pair tunneling (either via the Josephson quasiparticle (JQP) or double Josephson quasiparticle (DJQP) process). We show that, surprisingly, the back-action of tunneling Cooper pairs (or superconducting quasiparticles) can be used to significantly cool the oscillator. We also discuss the physical origin of negative damping effects in this system, and how they can lead to a regime of strong electro-mechanical feedback, where despite a weak SET - oscillator coupling, the motion of the oscillator strongly effects the tunneling of the Cooper pairs. We show that in this regime, the oscillator is characterized by an energy-dependent effective temperature. Finally, we discuss the strong analogy between back-action effects of incoherent Cooper-pair tunneling and ponderomotive effects in an optical cavity with a moveable mirror; in our case, tunneling Cooper pairs play the role of the cavity photons.