Chaotic canard explosions in a slow-fast nonlinear optomechanical oscillator

In the last few years suspended-mirror resonators have become a research hot-topic, since they are ideal candidates for many quantum optics experiments. In particular, the radiation-pressure coupling between the intracavity field and the mirror motion could enable the generation of nonclassical states of light, quantum nondemolition measurements of the field quadratures and eventually the creation entangled states of light and mirrors. However, even for light powers lower than those required in these experiments, the action of radiation pressure and photothermal effect (i.e. thermal expansion of the mirrors due to the absorbed intracavity light) becomes highly nonlinear. Since such processes, as well as the intracavity field itself, are competing and are governed by very distinct time-scales, optomechanical resonators possess all the typical features of slow-fast dynamical systems. However, at difference with 2D systems, the transition from the quasi-harmonic to the relaxational regime occurs via a period doubling cascade and subsequent chaotic canard explosions, where large-amplitude relaxation spikes are separated by an irregular number of subthreshold oscillations. We also show that this regime coexists with other periodic attractors, which evolves on a substantially faster time-scale. The experimental results are reproduced and analyzed by means of a detailed physical model of our system.