Stochastic switching of cantilever motion

Abstract

The cantilever is a prototype of a highly compliant mechanical system and has an instrumental role in nanotechnology, enabling surface microscopy, and ultrasensitive force and mass measurements. Here we report fluctuation-induced transitions between two stable states of a strongly driven microcantilever. Geometric nonlinearity gives rise to an amplitudedependent resonance frequency and bifurcation occurs beyond a critical point. The cantilever response to a weak parametric modulation is amplified by white noise, resulting in an optimum signal-to-noise ratio at finite noise intensity. This stochastic switching suggests new detection schemes for cantilever-based instrumentation, where the detection of weak signals is mediated by the fluctuating environment. For ultrafloppy, cantilevers with nanometer-scale dimensions operating at room temperature-a new transduction paradigm emerges that is based on probability distributions and mimics nature.

Negative nonlinear damping of a multilayer graphene mechanical resonator

“…We also note that resonators driven in the bifurcated regime can be very sensitive to environment noise that can induce premature switching from the high-to the low-amplitude branch [31], something not captured by our theoretical model. We note, however, that in our measurements, such switching would make the OMIA dips appear less shallow, and lead to an underestimation of the coefficient of the negative nonlinear damping rate, and therefore our measurements represent a lower bound on the magnitude of the negative nonlinear damping.…”

Nonlinear Mode Coupling and Synchronization of a Vacuum-Trapped Nanoparticle

“…We also expect interesting results from further investigating the nanoparticle's three-dimensional dynamics in response to multi-frequency driving fields [33], thermal excitation [24], and coupling to other levitated nanoparticles [34,35]. This includes pattern formation [36], chaos [3] and stochastic resonance [11,37,38]. Finally, in contrast to conventional nanomechanical oscillators, a levitated particle can rotate freely [39], thereby adding to the richness of the dynamics [40].…”

“…Nanomechanical oscillators naturally lend themselves to the experimental [1][2][3][4][5] and theoretical [6] study of nonlinear behavior and synchronization. The nonlinear regime can be exploited for applications including phonon-cavity cooling [7,8], precision frequency measurements [9], signal amplification via stochastic resonance [10,11], mass sensing [12] and quantum non-demolition measurements [13][14][15]. In addition, nonlinear mechanical oscillators have been proposed as memory elements [16,17] and to hallmark classical to quantum transitions [18].…”

Phase Stochastic Resonance in a Forced Nanoelectromechanical Membrane

“…These results may open interesting prospects for phase noise metrology or coherent signal transmission applications in nanomechanical oscillators. Moreover, our approach, due to its general character, may apply to various systems.Stochastic resonance whereby a small signal gets amplified resonantly by application of external noise has been introduced originally in paleoclimatology [1,19] to explain the recurrence of ice ages and has then been observed in many other areas including neurobiology [6,16] [3,33,34,42]. Implementation of stochastic resonances involves generally three ingredients : (i) the existence of metastable states separated by an activation energy, as in excitable or bistable nonlinear systems, (ii) a coherent excitation, whose amplitude is however too weak to induce deterministic hopping between the states, and (iii) stochastic processes inducing random jumps over the potential barrier.…”