Quantum Electromechanics on Silicon Nitride Nanomembranes

We present a platform based upon silicon nitride nanomembranes for integrating superconducting microwave circuits with planar acoustic and optical devices such as phononic and photonic crystals. Utilizing tensile stress and lithographic patterning of a silicon nitride nanomembrane we are able to reliably realize planar capacitors with vacuum gap sizes down to $s \approx 80$nm. In combination with spiral inductor coils of micron pitch, this yields microwave ($\approx 8$GHz) resonant circuits of high impedance ($Z_{0} \approx 3.4$k$\Omega$) suitable for efficient electromechanical coupling to nanoscale acoustic structures. We measure an electromechanical vacuum coupling rate of $g_0\mathrm{/}2\pi =41.5$~Hz to the low frequency ($4.48$MHz) global beam motion of a patterned phononic crystal nanobeam, and through parametric microwave driving reach a backaction cooled mechanical mode occupancy as low as $n_m=0.58$.