Circuit quantum acoustodynamics with a fluxonium qubit

Quantum information is fragile, and the physical systems we use to protect it are often complex. Even with rapid advances in superconducting circuits over the past two decades, this leading platform for quantum engineering utilizes substantial electronic and spatial resources per qubit. This inspires a search for hardware-efficient strategies to build on the success of superconducting circuits. One such strategy involves the integration of mechanical resonators, offering smaller spatial footprints, sensitive detection of mass or force, and prospects for long energy-relaxation lifetimes. Coupling rates between circuits and mechanics are enhanced by the use of strongly piezoelectric materials, extending the reach of circuit quantum electrodynamics into the domain of mechanical systems. In this thesis I describe efforts to achieve strong coupling between a superconducting qubit and a piezoelectric mechanical resonator with frequency below 1 GHz. The main result is a device achieving phonon-number-resolving readout of a 690 MHz mechanical resonator. Phonon-number resolution was first observed using few-GHz nanomechanical resonators coupled to a transmon qubit at a similar frequency, leveraging strong piezoelectricity in thin-film lithium niobate. I show that integrating a lithium niobate mechanical resonator with a fluxonium qubit can access lower mechanical frequencies while preserving strong coupling and control capabilities at the single-phonon level. I describe initial attempts to measure coherence times of a phonon at 690 MHz, argue that these attempts were limited by thermal effects, and suggest cooling protocols to control thermal effects in future work. I conclude by discussing future experiments in strongly-coupled quantum acoustics, some of which may be enabled with near-term improvements in the fluxonium-mechanical system