  We study the cooling of a dielectric nanoscale particle trapped in an optical
cavity. We derive the frictional force for motion in the cavity field, and show
that the cooling rate is proportional to the square of oscillation amplitude
and frequency. Both the radial and axial centre-of-mass motion of the trapped
particle, which are coupled by the cavity field, are cooled. This motion is
analogous to two coupled but damped pendulums. Our simulations show that the
nanosphere can be cooled to 1/e of its initial momentum over time scales of
hundredths of milliseconds.
