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 from a new substrate: thin-film quartz. At single-phonon powers and millikelvin temperatures -- requisite conditions for quantum phononic processing -- we demonstrate large internal mechanical quality factors, $Q_i > 160,000$. 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 ringdown measurements and demonstrate high-power quality factor-frequency products $Q_i \cdot f = 1.4 \times 10^{16}$ Hz.