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 3.6 GHz 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(T_f = 10 mK), the localized mechanical resonance is found to couple at a rate of γ_i/2π = 400 Hz (Q_m = 9 x 10^6) to a thermal bath of temperature T_b ≈ 270 mK. 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.