Cavity cooling of an optically trapped nanoparticle

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 components of the center-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 ${e}^{\ensuremath{-}1}$ of its initial momentum over time scales of hundredths of milliseconds.