  Phonons are envisioned as coherent intermediaries between different types of
quantum systems. Engineered nanoscale devices such as optomechanical crystals
(OMCs) provide a platform to utilize phonons as quantum information carriers.
Here we demonstrate OMCs in diamond designed for strong interactions between
phonons and a silicon vacancy (SiV) spin. Using optical measurements at
millikelvin temperatures, we measure a linewidth of 13 kHz (Q-factor of
~440,000) for 6 GHz acoustic modes, a record for diamond in the GHz frequency
range and within an order of magnitude of state-of-the-art linewidths for OMCs
in silicon. We investigate SiV optical and spin properties in these devices and
outline a path towards a coherent spin-phonon interface.
