A spin-embedded diamond optomechanical resonator with mechanical quality factor exceeding one million

Diamond optomechanical crystal (OMC) devices with embedded color center spins are promising platforms for a broad range of applications in quantum sensing, networking, and computing applications, offering an interface between a GHz-frequency mechanical mode and both optical photons and coherent spins. A crucial but elusive step towards realizing this platform is to engineer a device with a high-quality factor mechanical mode while preserving the bulk-like coherence of embedded spins. Here we demonstrate sideband-resolved diamond OMCs with mechanical quality factors in excess of $10^6$ at cryogenic temperatures, and find coherence times up to $T_2$ = 270 $\mu$s for embedded nitrogen vacancy (NV) centers. Furthermore, we measure these devices across five orders of magnitude in intracavity optical power, demonstrating robust power handling and a high optomechanical cooperativity ($C\gg1$) at cryogenic temperatures that is essential for a broad range of quantum protocols requiring strong, coherent interactions between photons and phonons. These results are enabled by a robust, high-throughput method for forming single-crystal diamond membranes in combination with chemical vapor deposition (CVD) diamond overgrowth with nitrogen $\delta$-doping. We discuss the prospects of this platform for hybrid spin-mechanical devices in the quantum regime.