Quantum control of high overtone bulk acoustic phonons

Mechanical resonators are harmonic oscillators which means that their energy eigenstates are linearly spaced. The highly linear response makes observing and accessing quantum features in mechanical modes difficult. However, in quantum acoustic systems, the controllable quantum properties of a superconducting qubit can be extended to mechanical resonators. Accessing the individual energy levels of the harmonic oscillator is possible through the superconducting qubit since superconducting qubits have a non-uniform energy level separation through the inclusion of Josephson junctions. This allows to benefit from the complementary functionalities of the different systems in order to create, detect, and control quantum states of mechanical motion. The quantum acoustic devices that are studied in this thesis are created by coupling a superconducting qubit to a high overtone bulk acoustic resonator (HBAR). HBAR systems are promising with their qubit-compatible microwave frequencies and long decay times. Their high mode density allows accessing multiple acoustic modes in a small form factor on-chip. The resonator forms an acoustic cavity where the acoustic waves propagate inside a solid-state material forming a standing wave. The piezoelectric properties of the resonator materials allow for actuation and readout, as well as great enhancement of the coupling strength between the qubit and the resonator. In this thesis, quantum mechanical effects in a mechanical resonator are explored down to the level of a single quantum. A new quantum bulk acoustic device design is introduced that combines a strong coupling to the mechanical resonator with a high qubit coherence. This allows to observe vacuum Rabi swaps between the qubit and an acoustic mode in order to prepare a single mechanical excitation in the resonator. Another technique uses sideband transitions that are induced by parametric modulation of the qubit energy in order to generate selective coupling to different acoustic modes inside the HBAR. The coupling strength is determined by the amplitude of the parametric modulation. This method is used to drive photon-assisted Rabi oscillations between the qubit and the selected acoustic mode. These techniques are used to increase the control of the bulk acoustic phonons, which is necessary for new technological applications that use mechanical resonators as quantum resources.