Bound-in-Continuum qubits with Quantum Acoustodynamics

Propagating surface acoustic waves (SAW) can be piezo-electrically coupled with superconducting qubits via inter-digital transducers. In the quantum regime, this has recently been used to realize a surface acoustic version of cavity quantum electrodynamics. As the speed of the mechanical waves is $10^5$ times slower than light, this quantum acoustodynamics (QAD) architecture provides new opportunities for exploring the effects of emitters that are much larger than their wavelength, as well as introducing the possible miniaturization of the transmon-like qubit design to sub-mm scales. In this work, we investigate if a circuit QAD transmon inherits the benefits of a circuit QED transmon. We calculate the effects of coupling SAWs to a transmon-like superconducting qubit. Working in the continuum limit, we find the emergence of a bound-in-continuum resonance of the SAW modes, which has favorable damping properties simultaneous with anomalously large vacuum Rabi coupling. This result indicates that acoustic cavities may not be necessary for circuit QAD transmons.