Abstract
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.