Piezoelectric resonators in the quantum regime

Acoustic modes—in the form of collective vibrations trapped between the parallel and polished surfaces of a crystalline cavity—provide an intriguing opportunity for probing the quantum-mechanical regime of macroscopical mechanical resonators. Moreover, the exceptional quality factors in a compact size from mm to μm motivate the integration of acoustic resonators into quantum circuits to explore the applications of a quantum hybrid system.While the acoustic modes of a crystal are commonly isolated from electrical dynamics, piezoelectricityis employed to transduce energy between the two domains. In the first part of this thesis, we investigate the means to improve the quality factor of a low frequency plano-convex monolithic quartz resonator. The resonator is 7mm indiameter and 250 μm in thickness, made only of only piezoelectric crystalline material. By the removal of clamping losses and incorporating a distant non-contact measurement setup, we demonstrate quality factors as high as 108 at cryogenic temperatures close to the quantum ground state. Additionally, we model the electromechanical clamping losses of a particular grounding setup using temperature-dependent data and the acoustic transmission line based Mason’s model. In the latter part of this thesis, we couple a bulk acoustic high-overtone resonator (HBAR) with a transmon qubit. The electrical actuation of GHz-frequency sound in a HBAR is based on a μm-thin piezo film grown on a low-loss crystalline non-piezo bulk substrate. With an analogy to an acoustic musical instrument, the driven oscillations are amplified at the resonant frequencies of the acoustic cavity, with the addition that a small subset of such modes are selectively listened by the qubit. By the introduction of the acoustic overtones, high quality factors are accessible at the high frequencies of a transmon qubit, while the coupling between the two systems is distributed over the multitude of modes. I model this coupling in detail with respect to the system parameters for guiding the design of related quantum acoustic devices. I cover several different parameter regimes and explore the rich physics taking place in the multimodal hybrid system: Landau-Zener Stuckelberg interference, photon assisted sideband transitions and parametrically modulated coupling that involve the resonant periodical exchange of energy quanta known as vacuum Rabi oscillations, and drive-dependent multiphonon transitions. Despite the otherwise common difficulty to observe quantum mechanics in a harmonic oscillator, we observe purely quantum mechanical effects in the macroscopic resonator, such as a specific square root dependence of the transition energies on the quantum number.