Dispersive coupling between light and a rare-earth ion doped mechanical resonator

By spectrally hole burning an inhomogeneously broadened ensemble of ions while applying a controlled perturbation, one can obtain spectral holes that are functionalized for maximum sensitivity to different perturbations. We propose to use such hole-burned structures for the dispersive optical interaction with rare-earth-ion dopants whose frequencies are sensitive to crystal strain due to the bending motion of a crystal cantilever. A quantitative analysis shows that good optical sensitivity to the bending motion is obtained if a magnetic-field gradient is applied across the crystal during hole burning and that the resulting optomechanical coupling strength is sufficient for observing quantum features such as zero-point vibrations.