Noise-enabled precision measurements of a Duffing nanomechanical resonator

TL;DR

This paper experimentally investigates a high-Q nanomechanical resonator's nonlinear response, analyzing noise-induced transitions to improve parameter estimation for sensitive sensing applications.

Contribution

It provides the first detailed experimental measurement of noise-driven transition dynamics in a Duffing nanomechanical resonator, validating theoretical models and enabling precise parameter extraction.

Findings

Measured transition rates under controlled noise levels.

Extracted activation energies for basin transitions.

Determined critical and resonance frequencies with high accuracy.

Abstract

We report quantitative experimental measurements of the nonlinear response of a radiofrequency mechanical resonator, with very high quality factor, driven by a large swept-frequency force. We directly measure the noise-free transition dynamics between the two basins of attraction that appear in the nonlinear regime, and find good agreement with those predicted by the one-dimensional Duffing equation of motion. We then measure the response of the transition rates to controlled levels of white noise, and extract the activation energy from each basin. The measurements of the noise-induced transitions allow us to obtain precise values for the critical frequencies, the natural resonance frequency, and the cubic nonlinear parameter in the Duffing oscillator, with direct applications to high sensitivity parametric sensors based on these resonators.