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Synchronization in a mechanical resonator array coupled quadratically to a common electromagnetic field mode.

G León Aveleyra1, C A Holmes1, G J Milburn1

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Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 15, 2014
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Summary

Groups of near-identical mechanical resonators in optomechanical systems fail to synchronize unless their frequencies match. Identical frequencies can lead to multistability in these coupled systems.

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Area of Science:

  • Optomechanics
  • Nonlinear Dynamics
  • Coupled Oscillators

Background:

  • Optomechanical systems couple electromagnetic fields and mechanical resonators.
  • Resonator frequency depends on mechanical displacement.
  • Quadratic coupling is considered for multiple mechanical resonators.

Purpose of the Study:

  • Investigate synchronization in optomechanical systems with multiple near-identical mechanical resonators.
  • Analyze the conditions for synchronization and emergent phenomena like multistability.

Main Methods:

  • Utilized amplitude equations around a critical point.
  • Analyzed systems with quadratic dependence of EM resonance frequency on resonator displacement.

Main Results:

  • Groups of near-identical bulk mechanical resonators with low driving fail to synchronize.
  • Synchronization occurs only when natural frequencies are identical.
  • Identical natural frequencies can result in multistable system behavior.

Conclusions:

  • Synchronization in low-driven, near-identical optomechanical resonator groups is highly sensitive to frequency matching.
  • Multistability is a potential outcome in synchronized, identical frequency systems, highlighting complex dynamics.