Synchronization by reactive coupling and nonlinear frequency pulling

Cross, M. C.; Rogers, Jeffrey L.; Lifshitz, Ron; Zumdieck, Alexander

doi:10.1103/physreve.73.036205

Cited by 54 publications

(60 citation statements)

References 14 publications

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“…Reactive coupling inevitably leads to the amplitudes playing a key role in the synchronization, as previously shown theoretically [31,32]. The parameters Δω, α, and β, which we call the synchronization parameters, set the dynamics of the system: the stable fixed points of Eqs.…”

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confidence: 79%

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Phase Synchronization of Two Anharmonic Nanomechanical Oscillators

et al. 2014

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We investigate the synchronization of oscillators based on anharmonic nanoelectromechanical resonators. Our experimental implementation allows unprecedented observation and control of parameters governing the dynamics of synchronization. We find close quantitative agreement between experimental data and theory describing reactively coupled Duffing resonators with fully saturated feedback gain. In the synchronized state we demonstrate a significant reduction in the phase noise of the oscillators, which is key for sensor and clock applications. Our work establishes that oscillator networks constructed from nanomechanical resonators form an ideal laboratory to study synchronization-given their high-quality factors, small footprint, and ease of cointegration with modern electronic signal processing technologies. Synchronization is a ubiquitous phenomenon both in the physical and biological sciences. It has been observed to occur over a wide range of scales-from the ecological [1], with oscillation periods of years, to the microscale [2], with oscillation periods of milliseconds. Although synchronization has been extensively studied theoretically [3][4][5], relatively few experimental systems have been realized that provide detailed insight into the underlying dynamics. Here we show that oscillators based on nanoelectromechanical systems (NEMS) can readily enable the resolution of such details, while providing many unique advantages for experimental studies of nonlinear dynamics [6][7][8]. In addition, nanomechanical systems might prove useful for exploring quantum synchronization [9,10].Nanomechanical oscillators also have been exploited for a variety of applications [11][12][13]. In particular, nanoscale mechanics exhibits enhanced nonlinearity [14,15] and tunability [16,17], which has been used to suppress feedback noise [18,19] and create new types of electromechanical oscillators [20][21][22]. These oscillators may find application as mass [23], gas [24,25], or force sensors [26], without the need of an external frequency source.Building frequency sources from arrays of NEMS may yield enhanced applicability, but is challenging. For example, statistical deviations in batch fabrication inevitably lead to undesirable array dispersion [24]. If an array has appreciable frequency dispersion, global sensor responsivity gets reduced. However, if the elements of the array are made into a self-sustained oscillators and synchronized with one another, then the array responsivity will recover due to a reduction in phase noise [3]. Since NEMS have numerous applications, and are useful in studying nonlinear dynamics, we set an important milestone by demonstrating synchronization in nanomechanical systems.There are previous reports of synchronization in microor nanomechanical systems. However, these do not, in fact, demonstrate the phenomenon as conventionally defined [3] -that is, the phase locking of weakly coupled selfsustained oscillators. Shim et al.[27] reported synchronization of the driven excitations in coupled resonat...

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confidence: 79%

“…Here Δω is the difference between the resonant frequencies of the devices, α is the measure of frequency pulling (which is the increase in frequency proportional to the square of the amplitude), and β is the coupling strength. Note that our coupling here is not dissipative, but reactive, in contrast to most studies of synchronization to date [31].…”

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confidence: 97%

Phase Synchronization of Two Anharmonic Nanomechanical Oscillators

et al. 2014

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“…In other words, the development of a feedback loop is essential for establishing a nanomechanical synchronization system (see the recent review of Rhoads et al [206]). For instance, Cross et al [207,208] suggested a feedback constructed from a reactive coupling due to elastic or electrostatic interactions between nanomechanical resonators, and nonlinear frequency pulling.…”

Section: Coupled Resonancementioning

confidence: 99%

Nanomechanical resonators and their applications in biological/chemical detection: Nanomechanics principles

et al. 2011

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Recent advances in nanotechnology have led to the development of nano-electro-mechanical systems (NEMS) such as nanomechanical resonators, which have recently received significant attention from the scientific community. This has not only been for their capability for the label-free detection of bio/chemical-molecules at single-molecule (or atomic) resolution for future applications such as the early diagnostics of diseases such as cancer, but also for their unprecedented ability to detect physical quantities such as molecular weight, elastic stiffness, surface stress, and surface elastic stiffness for adsorbed molecules on the surface. Most experimental works on resonator-based molecular detection have been based on the principle that molecular adsorption onto a resonator surface increases the effective mass, and consequently decreases the resonant frequencies of the nanomechanical resonator. However, this principle is insufficient to provide fundamental insights into resonator-based molecular detection at the nanoscale; this is due to recently proposed novel nanoscale detection principles including various effects such as surface effects, nonlinear oscillations, coupled resonance, and stiffness effects. Furthermore, these effects have only recently been incorporated into existing physical models for resonators, and therefore the universal physical principles governing nanoresonator-based detection have not been completely described. Therefore, our objective in this review is to overview the current attempts to understand the underlying mechanisms in nanoresonator-based detection using physical models coupled to computational simulations and/or experiments. Specifically, we will focus on issues of special relevance to the dynamic behavior of nanoresonators and their applications in biological/chemical detection: the resonance behavior of micro/nano-resonators; resonator-based chemical/biological detection; physical models of various nanoresonators such as nanowires, carbon nanotubes, and graphene. We pay particular attention to experimental and computational approaches that have been useful in elucidating the mechanisms underlying the dynamic behavior of resonators across multiple and disparate spatial/length scales, and the resulting insight into resonator-based detection that has been obtained. We additionally provide extensive discussion regarding potentially fruitful future research directions coupling experiments and simulations in order to develop a fundamental understanding of the basic physical principles that govern NEMS and NEMS-based sensing and detection applications.

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“…The collective response of coupled arrays might be useful for signal enhancement and noise reduction [21,22], as well as for sophisticated mechanical signal processing applications. Such arrays have already exhibited interesting nonlinear dynamics, ranging from the formation of extended patterns [8,38], as one commonly observes in analogous continuous systems such as Faraday waves, to that of intrinsically localized modes [39,[58][59][60].…”

Section: Why Study Nonlinear Nems and Mems?mentioning

confidence: 99%