Tunable energy transfer in coupled nonlinear MEMS resonators under parametric modulation for enhanced sensor performance

Coherent control of coupled microelectromechanical resonators within the framework of classical nonlinear dynamics is of relevance in fundamental studies and the development of high-performance sensors. Coherent control can be achieved through the parametric modulation of one of the two coupled resonators. However, microelectromechanical resonators are commonly operated in the nonlinear regime, and a thorough description of key phenomena involving parametric modulation of coupled resonators, such as sideband generation and mode splitting, remains limited in this regime. We use a weakly coupled double-ended tuning fork (DETF) resonator under strong parametric modulation to demonstrate tunable energy transfer and mode interactions governed by classical analogs of well-established quantum phenomena. The method uses a red-sideband parametric signal to manipulate the coupling between two adjacent modes dynamically. This approach is theoretically assessed thanks to a nonlinear reduced-order model that takes into account the modal interactions and virtual coupling induced by the parametric modulation. Furthermore, the proof of concept of the proposed tuning mechanism is validated on a DC electric field sensor with enhanced sensitivity. The nonlinear parametrically driven sensor exhibits two orders of magnitude sensitivity boost while maintaining a broad measurement range. While our investigation focuses on coupled microresonator systems modeled within a classical framework, the observed dynamics and the simulation extend to the advancements of other cognate fields, such as optomechanics and two-level systems.