Strong Dispersive Coupling Between a Mechanical Resonator and a Fluxonium Superconducting Qubit

We demonstrate strong dispersive coupling between a fluxonium superconducting qubit and a 690 megahertz mechanical oscillator, extending the reach of circuit quantum acousto-dynamics (cQAD) experiments into a new range of frequencies. We have engineered a qubit-phonon coupling rate of g 2r x 14 MHz, and achieved a dispersive interaction that exceeds the decoherence rates of both systems while the qubit and mechanics are highly nonresonant (A/g >= 10). Leveraging this strong cou-pling, we perform phonon-number-resolved measurements of the mechanical resonator and investigate its dissipation and dephasing properties. Our results demonstrate the potential for fluxonium-based hybrid quantum systems, and a path for developing new quantum sensing and information processing schemes with phonons at frequencies below 700 MHz to significantly expand the toolbox of cQAD.