Coherent energy transfer in coupled nonlinear microelectromechanical resonators

Energy decay, describing the leakage of system energy to the environmental bath, is a universal behavior in oscillators. It has been utilized to elucidate energy transfer between vibrational modes of a resonator. In coupled resonators, achieving an ultra-low coupling rate is essential for observing energy interactions between resonators and environmental bath. Here, we observe periodic transient beating phenomenon by analyzing the transient responses of coupled nonlinear resonators with a coupling rate of 9.6 Hz. The energy transfer rate indicating the hybrid energy manipulation is impacted by asymmetry-induced energy localization and enhanced by nonlinearity. Time-resolved eigenstates, characterized by amplitude ratios, are employed as a quantitative tool to uncover the energy transfer and localization in coupled resonators under nonlinear operations. This work opens the possibilities to manipulate energy transfer, to probe energy localization, and to develop high-precision sensors utilizing the energy transfer between coupled nonlinear resonators.