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Nonlinear micro-electro-mechanical systems (MEMS) resonators open new opportunities in sensing and signal manipulation compared to their linear counterparts by enabling frequency tuning and increased bandwidth. Here, we design, fabricate…
We theoretically study the frequency stability of an opto-mechanical radio frequency oscillator based on resonant interaction of two optical and one mechanical modes of the same optical microcavity. A generalized expression for the phase…
We have developed a new methodology and a time-domain software package for the estimation of the oscillation frequency and the phase noise spectrum of non-linear noisy microwave circuits based on the direct integration of the system of…
In contrast to the well-known phenomenon of frequency stabilization in a synchronized noisy nonlinear oscillator, little is known about its amplitude stability. In this paper, we investigate experimentally and theoretically the amplitude…
Motivated by recent "circuit QED" experiments we investigate the noise properties of coherently driven nonlinear resonators. By using Josephson junctions in superconducting circuits, strong nonlinearities can be engineered, which lead to…
For a class of coupled limit cycle oscillators, we give a condition on a linear coupling operator that is necessary and sufficient for exponential stability of the synchronous solution. We show that with certain modifications our method of…
This article presents a comprehensive study and design methodology of co-integrated oscillators for nano mass sensing application based on resonant Nano-Electro-Mechanical-System (NEMS). In particular, it reports the capacitive with the…
Systems of dynamical elements exhibiting spontaneous rhythms are found in various fields of science and engineering, including physics, chemistry, biology, physiology, and mechanical and electrical engineering. Such dynamical elements are…
We report the observation of self-oscillations in a bottom-up nanoelectromechanical system (NEMS) during field emission driven by a constant applied voltage. An electromechanical model is explored that explains the phenomenon and that can…
Stochastic resonance is a general phenomenon usually observed in one-dimensional, amplitude modulated, bistable systems.We show experimentally the emergence of phase stochastic resonance in the bidimensional response of a forced…
The problem of estimating an unknown force driving a linear oscillator is revisited. When using linear measurement, feedback is often cited as a mechanism to enhance bandwidth or sensitivity. We show that as long as the oscillator dynamics…
Nonlinear damping, the change in damping rate with the amplitude of oscillations plays an important role in many electrical, mechanical and even biological oscillators. In novel technologies such as carbon nanotubes, graphene membranes or…
Processing quantum information on continuous variables requires a highly nonlinear element in order to attain universality. Noise reduction in processing such quantum information involves the use of a nonlinear phase state as a non-Gaussian…
The mechanism at the base of phase noise generation in electrical oscillators is reexamined from first principles. The well known Lorentzian spectral power distribution is obtained, together with a clearcut expression for the line-width…
Oscillations in nonequilibrium noisy systems are important physical phenomena. These oscillations can happen in autonomous biochemical oscillators such as circadian clocks. They can also manifest as subharmonic oscillations in periodically…
Driven non-linear resonators can display sharp resonances or even multistable behaviours amenable to induce strong enhancements of weak signals. Such enhancements can make use of the phenomenon of vibrational resonance whereby a weak…
Stochastic oscillators based on emerging nanodevices are attractive because of their ultra-low power requirement and ability to exhibit stochastic resonance, a phenomenon where synchronization to weak input signals is enabled due to ambient…
Controlling nonlinear effects in micro- and nano-electro-mechanical systems is essential for unlocking their full potential in sensing, signal processing, and frequency control. In this study, we develop a voltage-dependent Hamiltonian…
The harmonic oscillator is one of the most widely used model systems in physics: an indispensable theoretical tool in a variety of fields. It is well known that otherwise linear oscillators can attain novel and nonlinear features through…
Nonlinear dynamical systems such as coupled oscillators are being actively investigated as Ising machines for solving computationally hard problems in combinatorial optimization. Prior works have established the equivalence between the…