  Doppler cooling the center-of-mass motion of an optically levitated
microsphere via the velocity dependent scattering force from narrow whispering
gallery mode (WGM) resonances is described. Light that is red detuned from the
WGM resonance can be used to damp the center-of-mass motion in a process
analogous to the Doppler cooling of atoms. Leakage of photons out of the
microsphere when the incident field is near resonant with the narrow WGM
resonance acts to damp the motion of the sphere. The scattering force is not
limited by saturation, but can be controlled by the incident power. Cooling
times on the order of seconds are calculated for a 20 micron diameter silica
microsphere trapped within optical tweezers, with a Doppler temperature limit
in the microKelvin regime.
