Coupled oscillators as models of phantom and scalar field cosmologies

We study a toy model for phantom cosmology recently introduced in the literature and consisting of two oscillators, one of which carries negative kinetic energy. The results are compared with the exact phase space picture obtained for similar dynamical systems describing, respectively, a massive canonical scalar field conformally coupled to the spacetime curvature, and a conformally coupled massive phantom. Finally, the dynamical system describing exactly a minimally coupled phantom is studied and compared with the toy model.Comment: 18 pages, LaTeX, to appear in Physical Review

Photonic Cavity Synchronization of Nanomechanical Oscillators

Synchronization in oscillatory systems is a frequent natural phenomenon and is becoming an important concept in modern physics. Nanomechanical resonators are ideal systems for studying synchronization due to their controllable oscillation properties and engineerable nonlinearities. Here we demonstrate synchronization of two nanomechanical oscillators via a photonic resonator, enabling optomechanical synchronization between mechanically isolated nanomechanical resonators. Optical backaction gives rise to both reactive and dissipative coupling of the mechanical resonators, leading to coherent oscillation and mutual locking of resonators with dynamics beyond the widely accepted phase oscillator (Kuramoto) model. Besides the phase difference between the oscillators, also their amplitudes are coupled, resulting in the emergence of sidebands around the synchronized carrier signal.Comment: 23 pages including supplementary materia

Nano-optomechanical measurement in the photon counting regime

Optically measuring in the photon counting regime is a recurrent challenge in modern physics and a guarantee to develop weakly invasive probes. Here we investigate this idea on a hybrid nano-optomechanical system composed of a nanowire hybridized to a single Nitrogen-Vacancy (NV) defect. The vibrations of the nanoresonator grant a spatial degree of freedom to the quantum emitter and the photon emission event can now vary in space and time. We investigate how the nanomotion is encoded on the detected photon statistics and explore their spatio-temporal correlation properties. This allows a quantitative measurement of the vibrations of the nanomechanical oscillator at unprecedentedly low light intensities in the photon counting regime when less than one photon is detected per oscillation period, where standard detectors are dark-noise-limited. These results have implications for probing weakly interacting nanoresonators, for low temperature experiments and for investigating single moving markers

Identifying stochastic oscillations in single-cell live imaging time series using Gaussian processes

Multiple biological processes are driven by oscillatory gene expression at different time scales. Pulsatile dynamics are thought to be widespread, and single-cell live imaging of gene expression has lead to a surge of dynamic, possibly oscillatory, data for different gene networks. However, the regulation of gene expression at the level of an individual cell involves reactions between finite numbers of molecules, and this can result in inherent randomness in expression dynamics, which blurs the boundaries between aperiodic fluctuations and noisy oscillators. Thus, there is an acute need for an objective statistical method for classifying whether an experimentally derived noisy time series is periodic. Here we present a new data analysis method that combines mechanistic stochastic modelling with the powerful methods of non-parametric regression with Gaussian processes. Our method can distinguish oscillatory gene expression from random fluctuations of non-oscillatory expression in single-cell time series, despite peak-to-peak variability in period and amplitude of single-cell oscillations. We show that our method outperforms the Lomb-Scargle periodogram in successfully classifying cells as oscillatory or non-oscillatory in data simulated from a simple genetic oscillator model and in experimental data. Analysis of bioluminescent live cell imaging shows a significantly greater number of oscillatory cells when luciferase is driven by a {\it Hes1} promoter (10/19), which has previously been reported to oscillate, than the constitutive MoMuLV 5' LTR (MMLV) promoter (0/25). The method can be applied to data from any gene network to both quantify the proportion of oscillating cells within a population and to measure the period and quality of oscillations. It is publicly available as a MATLAB package.Comment: 36 pages, 17 figure

Inhomogeneous mechanical losses in micro-oscillators with high reflectivity coating

We characterize the mechanical quality factor of micro-oscillators covered by a highly reflective coating. We test an approach to the reduction of mechanical losses, that consists in limiting the size of the coated area to reduce the strain and the consequent energy loss in this highly dissipative component. Moreover, a mechanical isolation stage is incorporated in the device. The results are discussed on the basis of an analysis of homogeneous and non-homogeneous losses in the device and validated by a set of Finite-Element models. The contributions of thermoelastic dissipation and coating losses are separated and the measured quality factors are found in agreement with the calculated values, while the absence of unmodeled losses confirms that the isolation element integrated in the device efficiently uncouples the dynamics of the mirror from the support system. Also the resonant frequencies evaluated by Finite-Element models are in good agreement with the experimental data, and allow the estimation of the Young modulus of the coating. The models that we have developed and validated are important for the design of oscillating micro-mirrors with high quality factor and, consequently, low thermal noise. Such devices are useful in general for high sensitivity sensors, and in particular for experiments of quantum opto-mechanics