Quantum control and characterization of phononic crystal cavities

The nonclassical behavior of mechanical objects is of both fundamental interest and potential technological utility. Mechanical resonators can be combined with superconducting microwave circuits to realize quantum technologies, acting as memories for computation and on-chip delay lines, with small footprints and large achievable coupling rates. The nonlinearity of the circuit enables quantum control of the mechanical mode, as well as nondemolition readout of the prepared mechanical states. This hybrid platform has seen great progress in recent years as both a flourishing technological avenue and as a platform to explore quantum behavior of mechanical motion. In this work, we describe a series of experiments which explore the versatile uses of a quantum acoustics platform built from piezoelectric nanomechanical resonators. First, we describe the design and experimental realization of a Purcell filter composed of lithium niobate Lamb-wave resonators. Next, we combine a superconducting transmon qubit with two phononic crystal resonators, also made of lithium niobate. We demonstrate full quantum control of the mechanical modes and perform quantum state tomography to extract the density matrices of the prepared states. In this effort, we also prepare and characterize a mechanical Bell-state between the two resonators, demonstrating a small-scale quantum acoustic processor. Last, using the same device, we use the qubit to perform phonon number-resolved detection of dissipation and dephasing of coherent states in the mechanical oscillator. We develop a model showing that the dissipation signatures are consistent with emission into a small ensemble of long-lived two-level system defects, thus elucidating the need for further refinement of fabrication techniques. Altogether, this dissertation represents an exploration of a wide range of different applications for a hybrid quantum acoustic platform