Coherent Control of Coupled Nonlinear Microelectromechanical Resonators Under Parametric Modulation

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. Utilising a weakly coupled double-ended tuning fork (DETF) resonator under strong parametric modulation, we demonstrate tunable energy transfer and mode interactions governed by classical analogs of well-established quantum phenomena. This approach is theoretically assessed thanks to a nonlinear reduced order model which 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 a significant increment in sensitivity exceeding two orders of magnitude. while simultaneously maintaining a broad measurement range. While our findings remain within the classical regime, the observed dynamics and the simulation extend to the advancements of other cognate fields such as in optomechanics and two-level systems.