Fluctuation-enhanced frequency mixing in a nonlinear micromechanical oscillator

TL;DR

This paper investigates how noise can enhance frequency mixing in a nonlinear micromechanical oscillator, demonstrating noise-induced amplitude enhancement at specific frequencies due to state transitions.

Contribution

It introduces the experimental observation of noise-enhanced frequency mixing in a bistable micromechanical oscillator, confirming theoretical predictions.

Findings

Noise induces amplitude enhancement at mixing frequencies.

Transitions between states synchronize with driving frequencies.

Enhancement occurs near equal state occupation conditions.

Abstract

We study noise-enhanced frequency mixing in an underdamped micromechanical torsional oscillator. The oscillator is electrostatically driven into bistability by a strong, periodic voltage at frequency $\omega_d$. A second, weak ac voltage is applied at a frequency $\omega$ close to $\omega_d$. Due to nonlinearity in the system, vibrations occur at both $\omega$ and $2\omega_d-\omega$. White noise is injected into the excitation, allowing the system to occasionally overcome the activation barrier and switch between the two states. At the primary drive frequency where the occupations of the two states are approximately equal, we observe noise-induced enhancement of the oscillation amplitudes at both $\omega$ and the down-converted frequency $2\omega_d-\omega$, in agreement with theoretical predictions. Such enhancement occurs as a result of the noise-induced interstate transitions becoming synchronous with the beating between the two driving frequencies.