  Cavity-optomechanical systems realized in single-crystal diamond are poised
to benefit from its extraordinary material properties, including low mechanical
dissipation and a wide optical transparency window. Diamond is also rich in
optically active defects, such as the nitrogen-vacancy (NV) and silicon-vacancy
(SiV) centers, which behave as atom-like systems in the solid state.
Predictions and observations of coherent coupling of the NV electronic spin to
phonons via lattice strain has motivated the development of diamond
nanomechanical devices aimed at realization of hybrid quantum systems, in which
phonons provide an interface with diamond spins. In this work, we demonstrate
diamond optomechanical crystals (OMCs), a device platform to enable such
applications, wherein the co-localization of ~ 200 THz photons and few to 10
GHz phonons in a quasi-periodic diamond nanostructure leads to coupling of an
optical cavity field to a mechanical mode via radiation pressure. In contrast
to other material systems, diamond OMCs operating in the resolved-sideband
regime possess large intracavity photon capacity (> 10$^5$) and sufficient
optomechanical coupling rates to reach a cooperativity of ~ 20 at room
temperature, allowing for the observation of optomechanically induced
transparency and the realization of large amplitude optomechanical
self-oscillations.
