Scaling laws for the bifurcation-escape rate in a nanomechanical resonator

TL;DR

This study combines experimental and theoretical approaches to analyze how escape rates from metastable states in a nanomechanical resonator scale near bifurcation points, confirming recent theoretical predictions.

Contribution

It provides the first experimental verification of power-law scaling laws for escape rates in a nanomechanical system near bifurcation points.

Findings

Escape times follow an exponential distribution.

Scaling laws accurately describe the escape rate dependence.

Power laws hold over a large parameter range.

Abstract

We report on experimental and theoretical studies of the fluctuation-induced escape time from a metastable state of a nanomechanical Duffing resonator in cryogenic environment. By tuning in situ the non-linear coefficient $\gamma$ we could explore a wide range of the parameter space around the bifurcation point, where the metastable state becomes unstable. We measured in a relaxation process the distribution of the escape times. We have been able to verify its exponential distribution and extract the escape rate $\Gamma$. We investigated the scaling of $\Gamma$ with respect to the distance to the bifurcation point and $\gamma$, finding an unprecedented quantitative agreement with the theoretical description of the stochastic problem. Simple power scaling laws turn out to hold in a large region of the parameter's space, as anticipated by recent theoretical predictions. These unique findings, implemented in a model dynamical system, are relevant to all systems experiencing under-damped saddle-node bifurcation.