  We demonstrate a simple and robust geometry for optical trapping in vacuum of
a single nanoparticle based on a parabolic mirror and the optical gradient
force, and we demonstrate rapid parametric feedback cooling of all three
motional degrees of freedom from room temperature to a few mK. A single laser
at 1550nm, and a single photodiode, are used for trapping, position detection,
and cooling for all three dimensions. Particles with diameters from 26nm to
160nm are trapped without feedback to 10$^{-5}$mbar and with feedback engaged
the pressure is reduced to 10$^{-6}$mbar. Modifications to the harmonic motion
in the presence of noise and feedback are studied, and an experimental
mechanical quality factor $>4\times 10^7$ is estimated.
