Thesis title: Symmetry-Engineered Bandgaps in Quartz Phononic Crystal Resonators with Application as Acoustic Quantum Memory

Abstract: Circuit quantum acoustodynamics couples superconducting qubits to long-lived mechanical resonators, whose acoustic modes can serve as compact, on-chip quantum memories. This dissertation develops suspended single-crystal quartz phononic crystal (PnC) resonators operating near 100 MHz as candidate memory elements for such a hybrid architecture. Quartz is chosen for its low intrinsic acoustic and microwave losses and the simple form of its elastic and piezoelectric tensors, which make a pure fundamental length-extension eigenmode straightforward to design and drive.

Two design iterations are presented. The first utilizes a crenelated PnC and is fabricated from Z-cut quartz on silicon substrates. It adapts an established acoustic Bragg-mirror-like geometry to work with a contactless electrode scheme compatible with parametric coupling to a superconducting qubit through a Josephson-junction-based coupler (SNAIL). The second utilizes a novel sinuous PnC design and is fabricated from the X-cut quartz of true zero-order waveplates through a process that is developed here. This sinuous design exchanges one of the crenelated PnC's mirror planes for a glide plane, rendering the geometric symmetry non-symmorphic and hybridizing modes of the phononic wire that would otherwise remain independent. The result is a large complete acoustic bandgap that does not rely on the material's crystalline anisotropy, reaching 87% relative to the center frequency when optimized for gap width. For the parameters used in the fabricated devices, the gap is 69% in the sinuous design, versus 19% for the crenelated design.

The sinuous devices reach quality factors above one million, the best being 1.34×10⁶, with mechanical lifetimes exceeding 2 ms for modes near 100 MHz measured at ~8 K—nearly doubling the crenelated design's figures and confirming that the wide complete gap translates into strong acoustic confinement in a fabricated device. These measurements characterize the platform in the classical, high-occupancy regime. Alongside the results, the dissertation presents the finite-element design, symmetry analysis, and fabrication of both designs.