Ground state cooling of a quantum electromechanical system with a silicon nitride membrane in a 3D loop-gap cavity

Cavity electro-(opto-)mechanics gives us a quantum tool to access mechanical modes in a massive object. Here we develop a quantum electromechanical system in which a vibrational mode of a SiN _x membrane are coupled to a three-dimensional loop-gap superconducting microwave cavity. The tight confinement of the electric field across a mechanically compliant narrow-gap capacitor realizes the quantum strong coupling regime under a red-sideband pump field and the quantum ground state cooling of the mechanical mode. We also demonstrate strong coupling between two mechanical modes, which is induced by two-tone parametric drives and mediated by a virtual photon in the cavity.