Strongly coupled modes in a weakly driven micromechanical resonator

TL;DR

This paper demonstrates strong coupling between vibration modes in a micromechanical resonator, enabling direct measurement of frequency response and providing insights into mode interactions and Q-factor limits.

Contribution

It introduces a method to observe strong mode coupling in micromechanical resonators and models the response using Euler-Bernoulli beam theory, predicting high Q-factors at room temperature.

Findings

Strong mode coupling observed at low amplitudes.

Frequency shift of 0.8 Hz measured in vacuum.

Predicted Q-factor upper limit of 4.5×10^5 at room temperature.

Abstract

We demonstrate strong coupling between the flexural vibration modes of a clamped-clamped micromechanical resonator vibrating at low amplitudes. This coupling enables the direct measurement of the frequency response via amplitude- and phase modulation schemes using the fundamental mode as a mechanical detector. In the linear regime, a frequency shift of $\mathrm{0.8\,Hz}$ is observed for a mode with a line width of $\mathrm{5.8\,Hz}$ in vacuum. The measured response is well-described by the analytical model based on the Euler-Bernoulli beam including tension. Calculations predict an upper limit for the room-temperature Q-factor of $\mathrm{4.5\times10^5}$ for our top-down fabricated micromechanical beam resonators.