Nonlinear dynamics and millikelvin cavity-cooling of levitated nanoparticles

Optomechanical systems explore and exploit the coupling between light and the mechanical motion of matter. A nonlinear coupling offers access to rich new physics, in both the quantum and classical regimes. We investigate a dynamic, as opposed to the usually studied static, nonlinear optomechanical system, comprising of a nanosphere levitated and cooled in a hybrid electro-optical trap. An optical cavity offers readout of both linear-in-position and quadratic-in-position (nonlinear) light-matter coupling, whilst simultaneously cooling the nanosphere to millikelvin temperatures for indefinite periods of time in high vacuum. We observe cooling of the linear and non-linear motion, leading to a ${10}^5$ fold reduction in phonon number $n_p$, attaining final occupancies of $n_p=100-1000$. This work puts cavity cooling of a levitated object to the quantum ground-state firmly within reach.