Librational feedback cooling with spinning silica microspheres*

An optically-levitated, 4.7 μm diameter silica microsphere can be driven into rotation by coupling a rotating electric field of constant magnitude to the permanent electric dipole moment found in microspheres grown via the Stöber process. In the frame co-rotating with the electric field, the microsphere's dipole moment undergoes libration about the instantaneous direction of the electric field. The librational degree of freedom can be cooled by applying a phase modulation to the rotation of the electric field that is proportional to the librational velocity, effectively damping the motion. The degree of cooling is quantified by applying a π/2 shift to the phase of the electric field and observing the resulting exponential decay of the librational motion to infer a damping time. The thermally driven spectrum of librational motion can also be examined to determine an effective temperature. In this prototype demonstration, we tune the damping time over four orders of magnitude, and the effective temperature over two orders of magnitude. Anomalous dissipation observed may shed light on charge multipole moments within the microspheres.