Beating Ringdowns of Near-Degenerate Mechanical Resonances
M.H.J. De Jong (Kavli institute of nanoscience Delft, TU Delft - QN/Groeblacher Lab, TU Delft - Dynamics of Micro and Nano Systems)
A. Cupertino (TU Delft - Tera-Hertz Sensing)
Dongil Shin (TU Delft - Team Georgy Filonenko)
Simon Gröeblacher (TU Delft - QN/Groeblacher Lab, Kavli institute of nanoscience Delft)
F. Alijani (TU Delft - Dynamics of Micro and Nano Systems)
PG Steeneken (TU Delft - QN/Steeneken Lab, TU Delft - Dynamics of Micro and Nano Systems, Kavli institute of nanoscience Delft)
Richard A. Norte (TU Delft - QN/Groeblacher Lab, Kavli institute of nanoscience Delft, TU Delft - Dynamics of Micro and Nano Systems)
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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-đť‘„-factor (greater than 104) 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 to both the externally driven regime 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 example, optomechanical energy transfer, synchronization, and gyroscopic sensors.