A Nanoscale Parametric Feedback Oscillator

Villanueva, Luis Guillermo; Karabalin, R. B.; Matheny, Matthew H.; Kenig, Eyal; Cross, M. C.; Roukes, M. L.

doi:10.1021/nl2031162

Cited by 146 publications

(106 citation statements)

References 29 publications

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“…Symmetry breaking also leads to mode mixing and to parametric resonance in response to additive driving. This holds promise for a number of applications, such as controlled mode mixing [35][36][37] and phase noise cancellation [38][39][40] .…”

Section: Discussionmentioning

confidence: 99%

Symmetry breaking in a mechanical resonator made from a carbon nanotube

et al. 2013

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Nanotubes behave as semi-flexible polymers in that they can bend by a sizeable amount. When integrating a nanotube in a mechanical resonator, the bending is expected to break the symmetry of the restoring potential. Here we report on a new detection method that allows us to demonstrate such symmetry breaking. The method probes the motion of the nanotube resonator at nearly zero-frequency; this motion is the low-frequency counterpart of the second overtone of resonantly excited vibrations. We find that symmetry breaking leads to the spectral broadening of mechanical resonances, and to an apparent quality factor that drops below 100 at room temperature. The low quality factor at room temperature is a striking feature of nanotube resonators whose origin has remained elusive for many years. Our results shed light on the role played by symmetry breaking in the mechanics of nanotube resonators.

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Section: Discussionmentioning

confidence: 99%

Symmetry breaking in a mechanical resonator made from a carbon nanotube

et al. 2013

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“…4 In addition, they can also be used as time reference devices 5 and as basic tools to explore fundamental physical processes 6 and dynamical effects. 7 At small vibrational amplitudes these systems behave as linear mechanical devices.…”

Section: Introductionmentioning

confidence: 99%

Nonlinearity in nanomechanical cantilevers

et al. 2013

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Euler-Bernoulli beam theory is widely used to successfully predict the linear dynamics of micro-and nanocantilever beams. However, its capacity to characterize the nonlinear dynamics of these devices has not yet been rigorously assessed, despite its use in nanoelectromechanical systems development. In this article, we report the first highly controlled measurements of the nonlinear response of nanomechanical cantilevers using an ultralinear detection system. This is performed for an extensive range of devices to probe the validity of Euler-Bernoulli theory in the nonlinear regime. We find that its predictions deviate strongly from our measurements for the nonlinearity of the fundamental flexural mode, which show a systematic dependence on aspect ratio (length/width) together with random scatter. This contrasts with the second mode, which is always found to be in good agreement with theory. These findings underscore the delicate balance between inertial and geometric nonlinear effects in the fundamental mode, and strongly motivate further work to develop theories beyond the Euler-Bernoulli approximation.

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“…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.…”

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confidence: 99%

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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A Nanoscale Parametric Feedback Oscillator

Cited by 146 publications

References 29 publications

Symmetry breaking in a mechanical resonator made from a carbon nanotube

Symmetry breaking in a mechanical resonator made from a carbon nanotube

Nonlinearity in nanomechanical cantilevers

Phase Synchronization of Two Anharmonic Nanomechanical Oscillators

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