Ghosts in the nanomachine: dynamical slowing-down in the phase-space of nanomechanical strings

The linear behavior of micro- and nanomechanical devices has been the topic of intense study over the past years. Their nonlinear behavior, on the other hand, continues to provide new and interesting dynamics. This work leverages a cavity opto-mechanical system whose very high sensitivity and low dissipation rate allows to capture the dynamics of fast transients that occur when strongly-driven nonlinear resonators relax to their equilibrium state. We experimentally study the ringdown dynamics of a nanomechanical Duffing resonator in both the time domain and in phase space. The resonator exhibits very different ringdown dynamics depending on whether it is subject to one or two tone driving. In the former case the ringdown follows a regular exponential decay, whereas the latter case shows exotic dynamics such as libration, slowing-down while scattering in phase-space, and ghost slowing-down. We demonstrate that this distinct difference can be attributed to the structure of the phase space itself. Surprisingly, we find that the energy in the resonator changes non-monotonously and that long delay between turning off the drive and the decay of the motion amplitude results in dynamical meta-states.