Beating ringdowns of near-degenerate mechanical resonances

TL;DR

This paper introduces a novel method for analyzing near-degenerate mechanical resonances with high Q-factors, enabling detailed characterization of their coupled dynamics and beat patterns in both driven and thermal regimes.

Contribution

The authors develop a resonant detection technique for near-degenerate modes in microresonators, validated experimentally, applicable to various readout methods and systems.

Findings

Demonstrated beat patterns in ringdown signals due to near-degenerate coupling

Validated method with experimental results on high Q-factor microresonators

Applicable to optical, electrical, and different mechanical systems

Abstract

Mechanical resonators that possess coupled modes with harmonic frequency relations have recently sparked interest due to their suitability for controllable energy transfer and non-Hermitian dynamics. Here, we show coupling between high Q-factor ($>\!\!10^4$) resonances with a nearly 1:1 frequency relation in spatially-symmetric microresonators. We develop and demonstrate a method to analyze their dynamical behavior based on the simultaneous and resonant detection of both spectral peaks, and validate this with experimental results. The frequency difference between the peaks modulates their ringdown, and creates a beat pattern in the linear decay. This method applies both to the externally driven and the Brownian motion (thermal) regime, and allows characterization of both linear and nonlinear parameters. The mechanism behind this method renders it broadly applicable to both optical and electrical readout, as well as to different mechanical systems. This will aid studies using near-degenerate mechanical modes, for e.g., optomechanical energy transfer, synchronization and gyroscopic sensors.