Classical dynamics of a nano-mechanical resonator coupled to a single-electron transistor

TL;DR

This paper models the classical dynamics of a nano-mechanical resonator coupled to a single-electron transistor, revealing how the SET influences the resonator's steady-state and current, with implications for experimental regimes.

Contribution

It derives a master equation for the coupled system and characterizes the SET's effect as a thermal bath, including effects of damping and temperature.

Findings

SET acts like a thermal bath on the resonator

Steady-state distribution characterized by effective temperature and damping

Intrinsic damping can dominate in accessible regimes

Abstract

We analyze the dynamics of a nano-mechanical resonator coupled to a single-electron transistor (SET) in the regime where the resonator behaves classically. A master equation is derived describing the dynamics of the coupled system which is then used to obtain equations of motion for the average charge state of the SET and the average position of the resonator. We show that the action of the SET on the resonator is very similar to that of a thermal bath, as it leads to a steady-state probability-distribution for the resonator which can be described by mean values of the resonator position, a renormalized frequency, an effective temperature and an intrinsic damping constant. Including the effects of extrinsic damping and finite temperature, we find that there remain experimentally accessible regimes where the intrinsic damping of the resonator still dominates its behavior. We also obtain the average current through the SET as a function of the coupling to the resonator.