Beating ringdowns of near-degenerate mechanical resonances

Kavli Affiliate: Simon Groblacher

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| Summary:

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 coupled
high Q-factor ($>10^4$) modes 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 modes, and validate this with experimental results. The
frequency difference between the modes 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 resonator 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.

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