Research Projects

Nonlinear interactions are intrinsic to natural systems, introducing complexities that linear models cannot encompass. These interactions lead to phenomena like bifurcations, self-organization, and synchronization. For instance, synchronization is observed in various systems, i.e., synchronized fireflies and coordinated neuronal firing. Structures like the mammalian cochlea (hearing organ) and insect halteres (functioning similarly to a gyroscope) utilize nonlinearity to improve efficiency. Over the past two decades, we have seen remarkable advancements in micro/nano-electromechanical systems (MEMS/NEMS), leading to high-performance technologies across diverse applications such as sensing, imaging, timing, signal processing, and logic devices. These devices also present intriguing opportunities for exploring fundamental physics, such as quantum phenomena in macroscopic objects, nonlinear dynamics with single and multiple degrees of freedom, and the coupling of mechanical motion to photons, spins, and electrons. Exploring and engineering nonlinear dynamics in mechanical devices has been a long-time research topic over a broad spectrum of scientific and technological areas. While convenient for engineering applications, nonlinear effects become more significant in smaller resonators. Two-dimensional electromechanical systems (2D-NEMS), with their low mass and high-quality factor, serve as highly sensitive sensors and provide an excellent platform for exploring nonlinear dynamics compared to conventional NEMS. The linear and nonlinear spring constants in 2D-NEMS can be adjusted over a wide range by applying relatively small electrostatic forces. When frequencies of the interacting modes are commensurate or nearly commensurate (an integer frequency ratio between vibrational modes), the nonlinear coupling and associated nonlinear energy transfer become stronger, a phenomenon known as internal resonance. Due to the large number of resonance frequencies in 2D-NEMS, tuning these frequencies enables a vast array of commensurate frequency combinations. This tunability offers a unique platform for investigating complex physical phenomena, including intermodal coupling, internal resonances, saturation effects, and synchronization. Despite this potential, studies on nonlinear mode coupling in 2D-NEMS remain limited. This project involves experimental work on the complex behaviors of 2D-NEMS in nonlinear dynamical regimes. The study focuses on nonlinear couplings and energy transfer in 2D-NEMS, focusing on intermodal coupling, internal resonance, and synchronization. This research also aims to develop a comprehensive framework for predicting and controlling the response of 2D resonators by modeling and numerical simulation for practical applications. Our experiments could create opportunities to generate quantum effects in nonlinear mechanical resonators, such as two-mode squeezing, entanglement, and accurate quantum state control.