Non-linear dynamics of a driven nanomechanical single electron transistor

TL;DR

This paper investigates the complex non-linear behavior of a nanomechanical resonator coupled with a single-electron transistor, revealing amplitude-dependent dynamics and noise-induced bistability.

Contribution

It introduces a simplified effective model capturing the non-linear response and bistability phenomena in the coupled system.

Findings

Resonator exhibits Duffing-like non-linear response.

Amplitude-dependent damping and frequency shifts are observed.

Charge noise induces slow switching between dynamical states.

Abstract

We analyze the response of a nanomechanical resonator to an external drive when it is also coupled to a single-electron transistor (SET). The interaction between the SET electrons and the mechanical resonator depends on the amplitude of the mechanical motion leading to a strongly non-linear response to the drive which is similar to that of a Duffing oscillator. We show that the average dynamics of the resonator is well-described by a simple effective model which incorporates damping and frequency renormalization terms which are amplitude dependent. We also find that for a certain range of parameters the system displays interesting bistable dynamics in which noise arising from charge fluctuations causes the resonator to switch slowly between different dynamical states.