Controlling the motion of levitated particles by coherent scattering

Levitated particles are a promising platform for cavity optomechanics owing to lack of clamping losses allowing, in principle, generation of nonclassical mechanical states and high-precision sensing of external forces. One important tool for controlling the particle motion, which has remained largely unexplored, is the trapping field itself. Recently, a crucial step in understanding its capabilities has been made by using coherent scattering of tweezer photons into a cavity mode to cool the motion of a levitated particle. Here, we build on these results and show that coherent scattering, accompanied by amplitude modulation of the trapping beam, can be used for more general control of particle motion. We show how this mechanism (leading to modulation of the mechanical potential, which is impossible with clamped mechanical resonators) can be used to generate strong mechanical one- and two-mode squeezing both in the transient and steady-state regimes. We also discuss how to use these techniques for efficient readout of the mechanical motion similar, in spirit, to two-tone, backaction-evading readout. With straightforward extensions of our ideas to all three motional modes of levitated particles, our results pave the way to full quantum control of particle motion.