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The phase description is a powerful tool for analyzing noisy limit cycle oscillators. The method, however, has found only limited applications so far, because the present theory is applicable only to the Gaussian noise while noise in the…
We report a study of a cavity optomechanical system driven by narrow-band electromagnetic fields, which are applied either in the form of uncorrelated noise, or as a more structured spectrum. The bandwidth of the driving spectra is smaller…
We present a detailed theoretical discussion of the effects of ubiquitous laser noise on cooling and the coherent dynamics in opto-mechanical systems. Phase fluctuations of the driving laser induce modulations of the linearized…
We experimentally study a fiber-based optical ring cavity integrated with a mechanical resonator mirror and an optical amplifier. The device exhibits a variety of intriguing nonlinear effects including synchronization and self-excited…
Optomechanical interactions between mechanical oscillators and an electromagnetic field induce controllable modifications in mechanical fluctuation. When multiple mechanical oscillators are coupled to a single electromagnetic mode, these…
Under general conditions imposed on an active stochastic oscillator, we study change in the size and shape of its average limit cycle as a function of temperature. Such dynamics occur in a multitude of nonequilibrium systems, including the…
We develop a systematic theory of quantum fluctuations in the driven parametric oscillator (OPO), including the region near threshold. This allows us to treat the limits imposed by nonlinearities to quantum squeezing and noise reduction, in…
We demonstrate optical squeezing below the shot-noise level generated through the interaction of an optical cavity field with two center-of-mass modes of a levitated nanoparticle, simultaneously cooled to occupation numbers well below…
We report theory, measurements and numerical simulations on nonlinear piezoelectric ultrasonic devices with stable limit cycles. The devices are shown to exhibit behavior familiar from the theory of coupled auto-oscillators. Frequency of…
We investigate theoretically the influence of laser phase noise on the cooling and heating of a generic cavity optomechanical system. We derive the back-action damping and heating rates and the mechanical frequency shift of the radiation…
We study the effect of additive Brownian noise on an ODE system that has a stable hyperbolic limit cycle, for initial data that are attracted to the limit cycle. The analysis is performed in the limit of small noise - that is, we modulate…
We report the confinement of an optomechanical micro-oscillator in a squeezed thermal state, obtained by parametric modulation of the optical spring. We propose and implement an experimental scheme based on parametric feedback control of…
The maximum amplitude of mechanical oscillators coupled to optical cavities are studied both analytically and numerically. The optical backaction on the resonator enables self-sustained oscillations whose limit cycle is set by the dynamic…
The investigation of the ultimate limits imposed by quantum mechanics on amplification represents an important topic both on a fundamental level and from the perspective of potential applications. We propose here a novel setup for an…
We analyze the quantum regime of the dynamical backaction cooling of a mechanical resonator assisted by a driven harmonic oscillator (cavity). Our treatment applies to both optomechanical and electromechanical realizations and includes the…
Coupled optical cavities, which support normal modes, play a critical role in optical filtering, sensing, slow-light generation, and quantum state manipulation. Recent theoretical work has proposed incorporating nonlinear materials into…
We investigate the creation of squeezed states of a vibrating membrane or a movable mirror in an opto-mechanical system. An optical cavity is driven by squeezed light and couples via radiation pressure to the membrane/mirror, effectively…
Reproducibility of a noisy limit-cycle oscillator driven by a random piecewise constant signal is analyzed. By reducing the model to random phase maps, it is shown that the reproducibility of the limit cycle generally improves when the…
We analyze the spectral properties of a resonator coupled to a superconducting single electron transistor (SSET) close to the Josephson quasiparticle resonance. Focussing on the regime where the resonator is driven into a limit-cycle state…
The noise from laser phase fluctuation sets a major technical obstacle to cool the nano-mechanical oscillators to the quantum region. We propose a cooling configuration based on the opto-mechanical coupling with two cavity modes to…