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.
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