Coupled electromechanical resonators that can be independently driven/detected and easily integrated with external circuits are essential for exploring mechanical modes based signal processing and multifunctional integration. One of the main challenges lies in controlling energy transfers between distinct resonators experiencing nanoscale displacements. Here, we present a room temperature electromechanical system that mimics a "phonon-cavity", in analogy with optomechanics. It consists in a silicon nitride membrane capacitively coupled to an aluminum drum-head resonator. We demonstrate electromechanically induced transparency and amplification through manipulating the mechanical displacements of this coupled system, creating interferences in the measured signal. The anti-damping effects, generated by phonon-cavity force, have been observed in both movable objects. We develop an analytical model that captures the analoguous optomechanical features in the classical limit and enables to fit quantitatively the measurements. Our results open up new possibilities for building compact and multifunctional mechanical systems, and exploring phonon-phonon coupling based optomechanics.
Keywords: coupled mechanical resonators; interference; membrane; phonon-cavity; transparency and amplification.