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

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.