  We report three-dimensional cooling of a levitated nanoparticle inside an
optical cavity. The cooling mechanism is provided by cavity-enhanced coherent
scattering off an optical tweezer. The observed 3D dynamics and cooling rates
are as theoretically expected from the presence of both linear and quadratic
terms in the interaction between the particle motion and the cavity field. By
achieving nanometer-level control over the particle location we optimize the
position-dependent coupling and demonstrate axial cooling by two orders of
magnitude at background pressures as high as $6\times10^{-2}$ mbar. We also
estimate a significant ($> 40$ dB) suppression of laser phase noise, and hence
of residual heating, which is a specific feature of the coherent scattering
scheme. The observed performance implies that quantum ground state cavity
cooling of levitated nanoparticles can be achieved for background pressures
below $10^{-7}$ mbar.
