Nonlinear effects in a strongly coupled Nanoelectromechanical System

TL;DR

This paper develops a voltage-controlled theoretical model for strongly coupled nanoelectromechanical resonators, demonstrating tunable nonlinear effects, frequency combs, and phase transitions relevant for advanced sensing and signal processing.

Contribution

It introduces a Hamiltonian framework that captures nonlinear coupling and bifurcations in nanoelectromechanical systems, linking theory with experimental tunability and dynamics.

Findings

Reproduces avoided crossing without AC drive

Generates tunable frequency comb spectra

Maps phase diagram of bifurcations and stability

Abstract

Controlling nonlinear effects in micro- and nano-electro-mechanical systems is essential for unlocking their full potential in sensing, signal processing, and frequency control. In this study, we develop a voltage-dependent Hamiltonian framework for a nanoelectromechanical resonator with two strongly coupled vibrational modes, representative of a nanostring platform. The mode frequencies and couplings of the system are tuned electrostatically using a DC voltage, which also controls the strength of the interactions. Our theoretical model reproduces the experimentally observed avoided crossing in the absence of an AC drive and generates tunable frequency-comb spectra when a parametric drive is applied. By scanning the DC voltage, we generate a phase diagram that links comb formation and sharp regime boundaries to underlying bifurcations, multi-stability, and attractor switching. Phase-resolved diagnostics based on a Kuramoto order parameter, together with autocorrelation and Poincar\'e analyses, quantify coherence and critical slowing down near these transitions. We further explore the relationship between nonlinear coupling, parametric excitation, and stability transitions within a single device of experimental relevance and establish a dynamical framework for engineering nanoelectromechanical resonators that offer enhanced tunability, functionality, and a predictive link to experimental outcomes.