We study the dynamics of a laser-trapped nanoparticle in high vacuum. Using parametric coupling to an external excitation source, the linewidth of the nanoparticle's oscillation can be reduced by three orders of magnitude. We show that the oscillation of the nanoparticle and the excitation source are synchronized, exhibiting a well-defined phase relationship. Furthermore, the external source can be used to controllably drive the nanoparticle into the nonlinear regime, thereby generating strong coupling between the different translational modes of the nanoparticle. Our work contributes to the understanding of the nonlinear dynamics of levitated nanoparticles in high vacuum and paves the way for studies of pattern formation, chaos, and stochastic resonance.