We have realized a nano-electromechanical hybrid system consisting of a silicon nitride beam dielectrically coupled to a superconducting microwave resonator. We characterize the sample by making use of the Duffing nonlinearity of the strongly driven beam. In particular, we calibrate the amplitude spectrum of the mechanical motion and determine the electromechanical vacuum coupling. A high quality factor of 480 000 at a resonance frequency of 14 MHz is achieved at 0.5 K. The experimentally determined electromechanical vacuum coupling of 11.5 mHz is quantitatively compared with finite element based model calculations.
The room temperature quality factor of the nanobeam has been determined by optical interferometry.