  We report on an experiment achieving the dynamical generation of non-Gaussian
states of motion of a levitated optomechanical system. We access intrinsic
Duffing-like non-linearities by squeezing an oscillator's state of motion
through rapidly switching the frequency of its trap. We characterize the
experimental non-Gaussian state against expectations from simulations and give
prospects for the emergence of genuine non-classical features.
