# Tuning the nonlinear dispersive coupling of nanomechanical string resonators

## TL;DR

This paper explores nonlinear dispersive mode coupling in nanomechanical silicon nitride string resonators, demonstrating tunable multimode interactions and mode hybridization effects with a theoretical model.

## Contribution

It introduces a theoretical model describing how mode hybridization influences nonlinear dispersive coupling in coupled nanomechanical resonators.

## Key findings

- Frequency shifts occur when modes enter nonlinear regimes.
- Strong elastic coupling enables tunable multimode avoided crossings.
- Mode hybridization affects nonlinear dispersive interactions.

## Abstract

We investigate nonlinear dispersive mode coupling between the flexural in- and out-of-plane modes of two doubly clamped, nanomechanical silicon nitride string resonators. As the amplitude of one mode transitions from the linear response regime into the nonlinear regime, we find a frequency shift of two other modes. The resonators are strongly elastically coupled via a shared clamping point and can be tuned in and out of resonance dielectrically, giving rise to multimode avoided crossings. When the modes start hybridizing, their polarization changes. This affects the nonlinear dispersive coupling in a non-trivial way. We propose a theoretical model to describe the dependence of the dispersive coupling on the mode hybridization.