Diffusion-induced dephasing and bistability of nanoresonators

We study dephasing of an underdamped harmonic oscillator due to frequency fluctuations. The spectrum of the response to an external field is sensitive to the nature of the fluctuations. For nanomechanical resonators, if the dephasing is due to diffusion of adsorbed particles along the resonator, the spectrum varies from a single Lorentzian peak to two closely spaced peaks depending on the parameters. If the dephasing depends on the oscillator state, the oscillator can exhibit bistability of forced vibrations. We study this bistability for a nanomechanical resonator with diffusing adsorbed particles. The vibrations affect the particles by driving them toward the antinodes of the vibrational mode. Unexpectedly, even though diffusion is a random process, the bistability arises if it is sufficiently strong, i.e., fast compared to the vibrations decay time. For fast diffusion, we find the bistable response in the mean-field approximation. We also study, analytically and numerically, the rate of fluctuation-induced switching between the coexisting stable states.