Thermalization properties at mK temperatures of a nanoscale optomechanical resonator with acoustic-bandgap shield

Optical measurements of a nanoscale silicon optomechanical crystal cavity with a mechanical resonance frequency of 3.6GHz are performed at sub-kelvin temperatures. We infer optical-absorption-induced heating and damping of the mechanical resonator from measurements of phonon occupancy and motional sideband asymmetry. At the lowest probe power and lowest fridge temperature (10mK), the localized mechanical resonance is found to couple at a rate of 400Hz (Q=9x10^6) to a thermal bath of temperature 270mK. These measurements indicate that silicon optomechanical crystals cooled to millikelvin temperatures should be suitable for a variety of experiments involving coherent coupling between photons and phonons at the single quanta level.