Dynamical tunnelling of a Nano-mechanical Oscillator

The study of the quantum to classical transition is of fundamental as well as technological importance, and focusses on mesoscopic devices, with a size for which either classical physics or quantum physics can be brought to dominate. A particularly diverse selection of such devices is available in cavity quantum-optomechanics. We show that these can be leveraged for the study of dynamical-tunnelling in a quantum chaotic system. This effect probes the quantum to classical transition deeply, since tunnelling rates sensitively depend on the ability of the quantum system to resolve the underlying classical phase space. We show that the effective Planck's constant, which determines this phase space resolution, can be varied over orders of magnitude as a function of tunable parameters in an opto-mechanical experiment. Specifically, we consider a membrane-in-the-middle configuration of a mechanical oscillator within an optical cavity, where the intracavity field is modulated periodically by the external laser source. We demonstrate that a mixed regular and chaotic phase space can be engineered in one spatial dimension, through a significant quartic opto-mechanical interaction. For that case, we explore the expected dynamical tunnelling rates using Floquet theory and map out values of the effective Planck's constant that should be within practical reach.