Coupling a Superconducting Quantum Circuit to a Phononic Crystal Defect Cavity

Connecting nanoscale mechanical resonators to microwave quantum circuits opens new avenues for storing, processing, and transmitting quantum information. In this work, we couple a phononic crystal cavity to a tunable superconducting quantum circuit. By fabricating a one-dimensional periodic pattern in a thin film of lithium niobate and introducing a defect in this artificial lattice, we localize a 6-GHz acoustic resonance to a wavelength-scale volume of less than 1 cubic micron. The strong piezoelectricity of lithium niobate efficiently couples the localized vibrations to the electric field of a widely tunable high-impedance Josephson junction array resonator. We measure a direct phonon-photon coupling rate g/2 pi approximate to 1.6 MHz and a mechanical quality factor Q(m) approximate to 3 x 10(4), leading to a cooperativity C similar to 4 when the two modes are tuned into resonance. Our work has direct application to engineering hybrid quantum systems for microwave-to-optical conversion as well as emerging architectures for quantum information processing.