Levitated optomechanics experiments are steadily approaching the quan tum regime. In this thesis, we explore the extrinsic coupling of levitated nanoparticles in optical tweezers in vacuum, with nonlinearities induced by optical and electrical control. Furthermore, we present a technique for the preparation of non-Gaussian states of the center-of-mass motion of these par ticles, leveraging both parametric modulation and the intrinsic nonlinearity of the optical potential. Additionally, a quantum model for optical detection with structured light fields is developed, enabling the analysis of a proposed experiment designed to minimize and control perturbations due to position measurement. These advances pave the way for refined control and manipula tion of quantum states in levitated systems in the near future.