Toward resonant coupling between a nm-scale electromechanical membrane and a MHz qubit

We present experiments aimed at the creation and study of non-Gaussian states of a mesoscopic mechanical oscillator. On the mechanical front, we have developped, fabricated and operated phononic-crystal SiN membranes, with mechanical quality factors in the 10^8 to 10^9 range. To allow resonant coupling of the membrane (typically in the MHz band) to a two-level system, we have developped a heavy fluxonium superconducting qubit architecture, with a transition frequeny as low as 1.8 MHz.. Design, fabrication and operation of the qubit in a 10 mK environment are discussed, together with a charge sensing experiment The long-term goal of these experiments is to create and explore non-Gaussian states of an electromechanical membrane.