Noise activated switching in a driven, nonlinear micromechanical oscillator

Abstract

We study noise induced switching in systems far from equilibrium by using an underdamped micromechanical torsional oscillator driven into the nonlinear regime. Within a certain range of driving frequencies, the oscillator possesses two stable dynamical states with different oscillation amplitudes. We induce the oscillator to escape from one dynamical state into the other by introducing noise in the excitation. By measuring the rate of random transitions as a function of noise intensity, we deduce the activation energy as a function of frequency detuning. Close to the critical point, the activation energy is expected to display system-independent scaling. The measured critical exponent is in good agreement with variational calculations and asymptotic scaling theory.

4 pages, 4 figures Changes: In Figure 1b we have added an arrow to point out where the bifurcation frequency is located. We modified the 3rd last paragraph. We corrected the citation for J. S. Aldridge and A. N. Cleland. We added a citation for Badzey et. al. We have rewritten the first and last paragraphs. We have corrected two typos: the alpha term in Eq. (5) and the definition of kappa in paragraph 5

References in corpus (6)

• Nonlinear Micromechanical Casimir Oscillator
• An RF-Driven Josephson Bifurcation Amplifier for Quantum Measurements
• Noise-enabled precision measurements of a Duffing nanomechanical resonator
• Thermally-Activated Magnetic Reversal Induced by a Spin-Polarized Current
• Temperature dependence of a nanomechanical switch
• Stochastic current switching in bistable resonant tunneling systems

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