Highly efficient multimode nonlinear coupling in square-membrane micromechanical resonator at room temperature

High-quality-factor micro/nano-mechanical resonators have attracted considerable interest as they provide a versatile platform for exploring fundamental nonlinear physics and implementing novel functional devices. While such applications usually require efficient coupling among different vibrational degrees of freedom through strong mechanical nonlinearities, it is still challenging to achieve a sufficiently wide dynamic range and realize a many-body system consisting of strongly interacting identical mechanical resonators due to insufficient mechanical nonlinearities and limitations in nanofabrication technologies. Here, we demonstrate efficient nonlinear interactions among multiple vibrational modes in a single multimode micromechanical resonator. We use a Si₃N₄ square-membrane resonator possessing multiple modes with mutually nearly commensurate natural frequencies. We piezoelectrically drive and optically characterize the profiles of amplitude and phase of up to 7 vibrational modes that exhibit mechanical quality factors over 7×10⁵ and hardening Duffing nonlinear oscillations. Furthermore, we demonstrate highly efficient intermodal coupling among multiple vibrational modes at room temperature and theoretically analyze the experimental observations.