Cooling of the rotation of a nanodiamond via the interaction with the electron spin of the contained NV-center

We propose a way to cool the rotation of a nanodiamond, which contains a NV-center and is levitated by an optical tweezer. Following the rotation of the particle, the NV-center electron spin experiences varying external fields and so leads to spin-rotation coupling. By optically pumping the electrons from a higher energy level to a lower level, the rotation energy is dissipated. We give the analytical result for the damping torque exerted on the nanodiamond, and evaluate the final cooling temperature by the fluctuation-dissipation theorem. It's shown that the quantum regime of the rotation can be reached with our scheme.