Thin-film quartz for high-coherence piezoelectric phononic crystal resonators

Piezoelectric phononic crystal resonators (PCRs) are a promising platform for acoustic quantum processing, yet their performance is currently limited by coupling to an ensemble of saturable two-level system (TLS) defects within the resonator material. Motivated by its excellent bulk mechanical properties and high crystallinity, we address this by fabricating PCRs using thin-film quartz as the substrate. At single-phonon powers and millikelvin temperatures---requisite conditions for quantum phononic processing---we demonstrate large internal mechanical quality factors, ${Q}_{i}>160\phantom{\rule{0.1em}{0ex}}000$. This represents an order-of-magnitude improvement in single-phonon lifetimes for piezoelectric PCR. We characterize the loss channels in these devices and find that, although improved, the low-power response is still limited by coupling to a TLS bath and that a significant portion of the TLSs are associated with the aluminum coupling electrodes. To explore the high-power response, we perform ring-down measurements and demonstrate high-power quality-factor--frequency products ${Q}_{i}\ensuremath{\cdot}f=1.4\ifmmode\times\else\texttimes\fi{}{10}^{16}$ Hz.