  We experimentally squeeze the thermal motional state of an optically
levitated nanosphere, by fast switching between two trapping frequencies. The
measured phase space distribution of our particle shows the typical shape of a
squeezed thermal state, from which we infer up to 2.7dB of squeezing along one
motional direction. The experiment features a large number of thermal
excitations, therefore remaining in the classical regime. Nevertheless, we
argue that the manipulation scheme described here could be used to achieve
squeezing below the zero-point level, if preceded by ground state cooling of
the levitated mechanical oscillator. Additionally, a higher degree of squeezing
could in principle be achieved by repeating the frequency-switching protocol
multiple times.
