22 research outputs found
Fluctuation-enhanced frequency mixing in a nonlinear micromechanical oscillator
We study noise-enhanced frequency mixing in an underdamped micromechanical
torsional oscillator. The oscillator is electrostatically driven into
bistability by a strong, periodic voltage at frequency . A second,
weak ac voltage is applied at a frequency close to . Due to
nonlinearity in the system, vibrations occur at both and
. White noise is injected into the excitation, allowing the
system to occasionally overcome the activation barrier and switch between the
two states. At the primary drive frequency where the occupations of the two
states are approximately equal, we observe noise-induced enhancement of the
oscillation amplitudes at both and the down-converted frequency
, in agreement with theoretical predictions. Such enhancement
occurs as a result of the noise-induced interstate transitions becoming
synchronous with the beating between the two driving frequencies.Comment: 4 pages 5 figure
Coherent Signal Amplification in Bistable Nanomechanical Oscillators by Stochastic Resonance
Stochastic resonance is a counter-intuitive concept[1,2], ; the addition of
noise to a noisy system induces coherent amplification of its response. First
suggested as a mechanism for the cyclic recurrence of ice ages, stochastic
resonance has been seen in a wide variety of macroscopic physical systems:
bistable ring lasers[3], SQUIDs[4,5], magnetoelastic ribbons[6], and
neurophysiological systems such as the receptors in crickets[7] and
crayfish[8]. Although it is fundamentally important as a mechanism of coherent
signal amplification, stochastic resonance is yet to be observed in nanoscale
systems. Here we report the observation of stochastic resonance in bistable
nanomechanical silicon oscillators, which can play an important role in the
realization of controllable high-speed nanomechanical memory cells. Our
nanomechanical systems were excited into a dynamic bistable state and modulated
in order to induce controllable switching; the addition of white noise showed a
marked amplification of the signal strength. Stochastic resonance in
nanomechanical systems paves the way for exploring macroscopic quantum
coherence and tunneling, and controlling nanoscale quantum systems for their
eventual use as robust quantum logic devices.Comment: 18 pages, 4 figure
Nonlinear response of a driven vibrating nanobeam in the quantum regime
We analytically investigate the nonlinear response of a damped doubly clamped
nanomechanical beam under static longitudinal compression which is excited to
transverse vibrations. Starting from a continuous elasticity model for the
beam, we consider the dynamics of the beam close to the Euler buckling
instability. There, the fundamental transverse mode dominates and a quantum
mechanical time-dependent effective single particle Hamiltonian for its
amplitude can be derived. In addition, we include the influence of a
dissipative Ohmic or super-Ohmic environment. In the rotating frame, a
Markovian master equation is derived which includes also the effect of the
time-dependent driving in a non-trivial way. The quasienergies of the pure
system show multiple avoided level crossings corresponding to multiphonon
transitions in the resonator. Around the resonances, the master equation is
solved analytically using Van Vleck perturbation theory. Their lineshapes are
calculated resulting in simple expressions. We find the general solution for
the multiple multiphonon resonances and, most interestingly, a bath-induced
transition from a resonant to an antiresonant behavior of the nonlinear
response.Comment: 25 pages, 5 figures, submitted to NJ
Discovery of microscopic electronic inhomogeneity in the high-Tc superconductor Bi2Sr2CaCu2O8+x
The parent compounds of the copper oxide high-Tc superconductors are unusual
insulators. Superconductivity arises when they are properly doped away from
stoichiometry1. In Bi2Sr2CaCu2O8+x, superconductivity results from doping with
excess oxygen atoms, which introduce positive charge carriers (holes) into the
CuO2 planes, where superconductivity is believed to originate. The role of
these oxygen dopants is not well understood, other than the fact that they
provide charge carriers. However, it is not even clear how these charges
distribute in the CuO2 planes. Accordingly, many models of high-Tc
superconductors simply assume that the charge carriers introduced by doping
distribute uniformly, leading to an electronically homogeneous system, as in
ordinary metals. Here we report the observation of an electronic inhomogeneity
in the high-Tc superconductor Bi2Sr2CaCu2O8+x using scanning tunnelling
microscopy/spectroscopy. This inhomogeneity is manifested as spatial variations
in both the local density of states spectrum and the superconducting energy
gap. These variations are correlated spatially and vary on a surprisingly short
length scale of ~ 14 Angs. Analysis suggests that the inhomogeneity observed is
a consequence of proximity to a Mott insulator resulting in poor screening of
the charge potentials associated with the oxygen ions left behind in the BiO
plane after doping. Hence this experiment is a direct probe of the local nature
of the superconducting state, which is not easily accessible by macroscopic
measurements.Comment: 6 pages, 4 figure
Optically levitated nanoparticle as a model system for stochastic bistable dynamics
Nano-mechanical resonators have gained an increasing importance in nanotechnology owing to their contributions to both fundamental and applied science. Yet, their small dimensions and mass raises some challenges as their dynamics gets dominated by nonlinearities that degrade their performance, for instance in sensing applications. Here, we report on the precise control of the nonlinear and stochastic bistable dynamics of a levitated nanoparticle in high vacuum. We demonstrate how it can lead to efficient signal amplification schemes, including stochastic resonance. This work contributes to showing the use of levitated nanoparticles as a model system for stochastic bistable dynamics, with applications to a wide variety of fields.inancial support from the ERC- QnanoMECA (Grant No. 64790), the Spanish Ministry of Economy and Competitiveness, under grant FIS2016-80293-R and through the ‘Severo Ochoa’ Programme for Centres of Excellence in R&D (SEV-2015-0522), Fundació Privada CELLEX and from the CERCA Programme/Generalitat de Catalunya. J.G. has been supported by H2020-MSCA-IF-2014 under REA grant Agreement No. 655369. L.R. acknowledges support from an ETH Marie Curie Cofund Fellowship
Inhibition of rhythmic neural spiking by noise: the occurrence of a minimum in activity with increasing noise
The effects of noise on neuronal dynamical systems are of much current interest. Here, we investigate noise-induced changes in the rhythmic firing activity of single Hodgkin–Huxley neurons. With additive input current, there is, in the absence of noise, a critical mean value µ = µc above which sustained periodic firing occurs. With initial conditions as resting values, for a range of values of the mean µ near the critical value, we have found that the firing rate is greatly reduced by noise, even of quite small amplitudes. Furthermore, the firing rate may undergo a pronounced minimum as the noise increases. This behavior has the opposite character to stochastic resonance and coherence resonance. We found that these phenomena occurred even when the initial conditions were chosen randomly or when the noise was switched on at a random time, indicating the robustness of the results. We also examined the effects of conductance-based noise on Hodgkin–Huxley neurons and obtained similar results, leading to the conclusion that the phenomena occur across a wide range of neuronal dynamical systems. Further, these phenomena will occur in diverse applications where a stable limit cycle coexists with a stable focus
What Is Stochastic Resonance? Definitions, Misconceptions, Debates, and Its Relevance to Biology
Stochastic resonance is said to be observed when increases in levels of unpredictable fluctuations—e.g., random noise—cause an increase in a metric of the quality of signal transmission or detection performance, rather than a decrease. This counterintuitive effect relies on system nonlinearities and on some parameter ranges being “suboptimal”. Stochastic resonance has been observed, quantified, and described in a plethora of physical and biological systems, including neurons. Being a topic of widespread multidisciplinary interest, the definition of stochastic resonance has evolved significantly over the last decade or so, leading to a number of debates, misunderstandings, and controversies. Perhaps the most important debate is whether the brain has evolved to utilize random noise in vivo, as part of the “neural code”. Surprisingly, this debate has been for the most part ignored by neuroscientists, despite much indirect evidence of a positive role for noise in the brain. We explore some of the reasons for this and argue why it would be more surprising if the brain did not exploit randomness provided by noise—via stochastic resonance or otherwise—than if it did. We also challenge neuroscientists and biologists, both computational and experimental, to embrace a very broad definition of stochastic resonance in terms of signal-processing “noise benefits”, and to devise experiments aimed at verifying that random variability can play a functional role in the brain, nervous system, or other areas of biology