Non-Exponential Relaxation in the Rotating Frame of a Driven Nanomechanical Mode

TL;DR

This paper observes non-exponential decay in the rotating frame of a driven nanomechanical resonator, revealing complex dissipation-induced symmetry breaking effects in nonlinear oscillations.

Contribution

It provides the first direct measurement of non-exponential relaxation dynamics in the rotating frame of a nonlinear nanomechanical system.

Findings

Decay of in-phase component is non-exponential.

Vibration amplitude decays exponentially with force removal.

Model links dynamics to dissipation-induced symmetry breaking.

Abstract

We present direct observation of the ring-down dynamics in the rotating frame of a resonantly driven single-mode nonlinear nanomechanical resonator. An additional close to resonance harmonic force excites nonlinear oscillations about the fixed point in the rotating frame. When the secondary drive is removed, we measure decay of the in-phase and quadrature components toward this fixed point. We show that the decay of the in-phase signal is non-exponential, even though the vibration amplitude decays exponentially if both forces are switched off. A minimalistic model captures these dynamics as well as the spectrum of the vibrations excited by the additional force, relating them to the dissipation-induced symmetry breaking of the dynamics in the rotating frame.