Correlated anomalous phase diffusion of coupled phononic modes in a sideband-driven resonator

F. Sun, X. Dong, J. Zou, M. I. Dykman and H. B. Chan ()
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F. Sun: The Hong Kong University of Science and Technology
X. Dong: The Hong Kong University of Science and Technology
J. Zou: The Hong Kong University of Science and Technology
M. I. Dykman: Michigan State University
H. B. Chan: The Hong Kong University of Science and Technology

Nature Communications, 2016, vol. 7, issue 1, 1-8

Abstract: Abstract The dynamical backaction from a periodically driven optical cavity can reduce the damping of a mechanical resonator, leading to parametric instability accompanied by self-sustained oscillations. Here we study experimentally and theoretically new aspects of the backaction and the discrete time-translation symmetry of a driven system using a micromechanical resonator with two nonlinearly coupled vibrational modes with strongly differing frequencies and decay rates. We find self-sustained oscillations in both the low- and high-frequency modes. Their frequencies and amplitudes are determined by the nonlinearity, which also leads to bistability and hysteresis. The phase fluctuations of the two modes show near-perfect anti-correlation, a consequence of the discrete time-translation symmetry. Concurrently, the phase of each mode undergoes anomalous diffusion. The phase variance follows a power law time dependence, with an exponent determined by the 1/f-type resonator frequency noise. Our findings enable compensating for the fluctuations using a feedback scheme to achieve stable frequency downconversion.

Date: 2016
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DOI: 10.1038/ncomms12694

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