Radiation pressure has recently been used to effectively couple the quantum motion of\nmechanical elements to the fields of optical or microwave light. Integration of all three\ndegrees of freedomââ?¬â?mechanical, optical and microwaveââ?¬â?would enable a quantum\ninterconnect between microwave and optical quantum systems.We present a platform based\non silicon nitride nanomembranes for integrating superconducting microwave circuits with\nplanar acoustic and optical devices such as phononic and photonic crystals. Using planar\ncapacitors with vacuum gaps of 60nm and spiral inductor coils of micron pitch we realize\nmicrowave resonant circuits with large electromechanical coupling to planar acoustic\nstructures of nanoscale dimensions and femtoFarad motional capacitance. Using this\nenhanced coupling, we demonstrate microwave backaction cooling of the 4.48MHz\nmechanical resonance of a nanobeam to an occupancy as low as 0.32. These results indicate\nthe viability of silicon nitride nanomembranes as an all-in-one substrate for quantum\nelectro-opto-mechanical experiments.
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