Influence of noise intensity on the spectrum of an oscillator

This paper investigates the influence of high-intensity noise on the correlation spectrum of a two-dimensional (2-D) nonlinear oscillator. An exact analytical solution for the correlation spectrum of this 2-D oscillator is provided. The analytical derivations are well suited for oscillators with white noise of any intensity, but computational constraints on the solution of the partial differential equation may make it impractical for cases where the number of state variables exceeds three. The spectral results predicted by our analytical method are verified by numerical simulations of the noisy oscillator in the time domain. We find that the peak of the oscillator spectrum shifts toward higher frequencies as the noise intensity is increased, as opposed to the fixed oscillation frequency predicted in the existing literature. This phenomenon does not appear to have been reported previously in the context of phase noise in oscillators

Generation of microwave fields in cavities with laser-excited nonlinear media: competition between the second- and third-order optical nonlinearities

We discuss a scheme for the parametric amplification of the quantum fluctuations of the electromagnetic vacuum in a three-dimensional microwave resonator, and report the preliminary measurements to test its feasibility. In the present experimental scheme, the fundamental mode of a microwave cavity is nonadiabatically perturbed by modulating the index of refraction of the nonlinear optical crystal enclosed therein. Intense, multi-GHz laser pulses, such as those delivered by a mode-locked laser source, impinge on the crystal to accomplish the n-index modulation. We theoretically analyze the process of parametric generation, which is related to the third-order nonlinear coefficient \u3c7(3) of the nonlinear crystal, and assess the suitable experimental conditions for generating real photons from the vacuum. Second-order nonlinear processes are first analyzed as a possible source of spurious photons in quantum vacuum experiments when an ideal, mode-locked laser source is considered. The combination of a crystal non-null \u3c7(2) coefficient and a real mode-locked laser system\u2014i.e. one featuring offset-fromcarrier noise and unwanted secondary oscillations\u2014is also experimentally investigated, paving the way for future experiments in three-dimensional cavities

Detection of weak stochastic force in a parametrically stabilized micro opto-mechanical system

Measuring a weak force is an important task for micro-mechanical systems, both when using devices as sensitive detectors and, particularly, in experiments of quantum mechanics. The optimal strategy for resolving a weak stochastic signal force on a huge background (typically given by thermal noise) is a crucial and debated topic, and the stability of the mechanical resonance is a further, related critical issue. We introduce and analyze the parametric control of the optical spring, that allows to stabilize the resonance and provides a phase reference for the oscillator motion, yet conserving a free evolution in one quadrature of the phase space. We also study quantitatively the characteristics of our micro opto-mechanical system as detector of stochastic force for short measurement times (for quick, high resolution monitoring) as well as for the longer term observations that optimize the sensitivity. We compare a simple, naive strategy based on the evaluation of the variance of the displacement (that is a widely used technique) with an optimal Wiener-Kolmogorov data analysis. We show that, thanks to the parametric stabilization of the effective susceptibility, we can more efficiently implement Wiener filtering, and we investigate how this strategy improves the performance of our system. We finally demonstrate the possibility to resolve stochastic force variations well below 1% of the thermal noise

Evanescent single-molecule biosensing with quantum limited precision

Sensors that are able to detect and track single unlabelled biomolecules are an important tool both to understand biomolecular dynamics and interactions at nanoscale, and for medical diagnostics operating at their ultimate detection limits. Recently, exceptional sensitivity has been achieved using the strongly enhanced evanescent fields provided by optical microcavities and nano-sized plasmonic resonators. However, at high field intensities photodamage to the biological specimen becomes increasingly problematic. Here, we introduce an optical nanofibre based evanescent biosensor that operates at the fundamental precision limit introduced by quantisation of light. This allows a four order-of-magnitude reduction in optical intensity whilst maintaining state-of-the-art sensitivity. It enable quantum noise limited tracking of single biomolecules as small as 3.5 nm, and surface-molecule interactions to be monitored over extended periods. By achieving quantum noise limited precision, our approach provides a pathway towards quantum-enhanced single-molecule biosensors.Comment: 17 pages, 4 figures, supplementary informatio

Delayed-feedback chimera states: Forced multiclusters and stochastic resonance

A nonlinear oscillator model with negative time-delayed feedback is studied numeri- cally under external deterministic and stochastic forcing. It is found that in the unforced system complex partial synchronization patterns like chimera states as well as salt-and-pepper like soli- tary states arise on the route from regular dynamics to spatio-temporal chaos. The control of the dynamics by external periodic forcing is demonstrated by numerical simulations. It is shown that one-cluster and multi-cluster chimeras can be achieved by adjusting the external forcing frequency to appropriate resonance conditions. If a stochastic component is superimposed to the determin- istic external forcing, chimera states can be induced in a way similar to stochastic resonance, they appear, therefore, in regimes where they do not exist without noise.Comment: 6 pages of paper with references + tex style file + 5 figure

Time evolution and squeezing of the field amplitude in cavity QED

We present the conditional time evolution of the electromagnetic field produced by a cavity QED system in the strongly coupled regime. We obtain the conditional evolution through a wave-particle correlation function that measures the time evolution of the field after the detection of a photon. A connection exists between this correlation function and the spectrum of squeezing which permits the study of squeezed states in the time domain. We calculate the spectrum of squeezing from the master equation for the reduced density matrix using both the quantum regression theorem and quantum trajectories. Our calculations not only show that spontaneous emission degrades the squeezing signal, but they also point to the dynamical processes that cause this degradation.Comment: 12 pages. Submitted to JOSA

Detection of synchronization from univariate data using wavelet transform

A method is proposed for detecting from univariate data the presence of synchronization of a self-sustained oscillator by external driving with varying frequency. The method is based on the analysis of difference between the oscillator instantaneous phases calculated using continuous wavelet transform at time moments shifted by a certain constant value relative to each other. We apply our method to a driven asymmetric van der Pol oscillator, experimental data from a driven electronic oscillator with delayed feedback and human heartbeat time series. In the latest case, the analysis of the heart rate variability data reveals synchronous regimes between the respiration and slow oscillations in blood pressure.Comment: 10 pages, 9 figure

Noise-induced inhibitory suppression of malfunction neural oscillators

Motivated by the aim to find new medical strategies to suppress undesirable neural synchronization we study the control of oscillations in a system of inhibitory coupled noisy oscillators. Using dynamical properties of inhibition, we find regimes when the malfunction oscillations can be suppressed but the information signal of a certain frequency can be transmitted through the system. The mechanism of this phenomenon is a resonant interplay of noise and the transmission signal provided by certain value of inhibitory coupling. Analyzing a system of three or four oscillators representing neural clusters, we show that this suppression can be effectively controlled by coupling and noise amplitudes.Comment: 10 pages, 14 figure