  We propose an experimental scheme to cool and measure the three-dimensional
(3D) motion of an optically trapped nanosphere in a cavity. Driven by three
lasers on TEM00, TEM01, and TEM10 modes, a single cavity can cool a trapped
nanosphere to the quantum ground states in all three dimensions under the
resolved-sideband condition. Our scheme can also detect an individual collision
between a single molecule and a cooled nanosphere efficiently. Such ability can
be used to measure the mass of molecules and the surface temperature of the
nanosphere. We also discuss the heating induced by the intensity fluctuation,
pointing instability, and the phase noise of lasers, and justify the
feasibility of our scheme under current experimental conditions.
