Control of entanglement dynamics in a system of three coupled quantum oscillators.

Dynamical control of entanglement and its connection with the classical concept of instability is an intriguing matter which deserves accurate investigation for its important role in information processing, cryptography and quantum computing. Here we consider a tripartite quantum system made of three coupled quantum parametric oscillators in equilibrium with a common heat bath. The introduced parametrization consists of a pulse train with adjustable amplitude and duty cycle representing a more general case for the perturbation. From the experimental observation of the instability in the classical system we are able to predict the parameter values for which the entangled states exist. A different amount of entanglement and different onset times emerge when comparing two and three quantum oscillators. The system and the parametrization considered here open new perspectives for manipulating quantum features at high temperatures.

Mixed-mode oscillations via canard explosions in light-emitting diodes with optoelectronic feedback.

Chaotically spiking attractors in semiconductor lasers with optoelectronic feedback have been recently observed to be the result of canard phenomena in three-dimensional phase space (incomplete homoclinic scenarios). Since light-emitting diodes display the same dynamics and are much more easily controllable, we use one of these systems to complete the attractor analysis demonstrating experimentally and theoretically the occurrence of complex sequences of periodic mixed-mode oscillations. In particular, we investigate the transition between periodic and chaotic mixed-mode states and analyze the effects of the unavoidable experimental noise on these transitions.

Granularity and inhomogeneity are the joint generators of optical rogue waves.

In the presence of many waves, giant events can occur with a probability higher than expected for random dynamics. By studying linear light propagation in a glass fiber, we show that optical rogue waves originate from two key ingredients: granularity, or a minimal size of the light speckles at the fiber exit, and inhomogeneity, that is, speckles clustering into separate domains with different average intensities. These two features characterize also rogue waves in nonlinear systems; thus, nonlinearity just plays the role of bringing forth the two ingredients of granularity and inhomogeneity.

Non-Gaussian statistics and extreme waves in a nonlinear optical cavity.

A unidirectional optical oscillator is built by using a liquid crystal light valve that couples a pump beam with the modes of a nearly spherical cavity. For sufficiently high pump intensity, the cavity field presents complex spatiotemporal dynamics, accompanied by the emission of extreme waves and large deviations from the Gaussian statistics. We identify a mechanism of spatial symmetry breaking, due to a hypercycle-type amplification through the nonlocal coupling of the cavity field.

Control of stochastic multistable systems: experimental demonstration.

Stochastic disturbances and spikes (sudden sharp fluctuations of any system parameter), commonly observed among natural and laboratory-scale systems, can perturb the multistable dynamics significantly and become a serious impediment when the device is designed for a certain dynamical behavior. We experimentally demonstrate that suitable periodic modulation of any system parameter may efficiently control such stochastic multistability related problems. The control mechanism is verified individually with two standard models (namely, an analog circuit of Lorenz equations and a cavity-loss modulated CO2 laser), against three externally introduced disturbing signals, (namely, white Gaussian noise, pink noise, and train of spikes). Indeed, with both the systems, it has been observed that the modulation is capable to significantly control untoward jumps to coexisting attractors that otherwise would have occurred due to either of the disturbances. These results establish the robustness and wide applicability of this control mechanism in resolving stochastic multistability related problems.

Spatiotemporal dynamics of the electrical network activity in the root apex.

The study of electrical network systems, integrated with chemical signaling networks, is becoming a common trend in contemporary biology. Classical techniques are limited to the assessment of signals from doublets or triplets of cells at a fixed temporal bin width. At present, full characteristics of the electrical network distribution and dynamics in plant cells and tissues has not been established. Here, a 60-channels multielectrode array (MEA) is applied to study spatiotemporal characteristics of the electrical network activity of the root apex. Both intense spontaneous electrical activities and stimulation-elicited bursts of locally propagating electrical signals have been observed. Propagation of the spikes indicates the existence of excitable traveling waves in plants, similar to those observed in non-nerve electrogenic tissues of animals. Obtained data reveal synchronous electric activities of root cells emerging in a specific root apex region. The dynamic electrochemical activity of root apex cells is proposed to continuously integrate internal and external signaling for developmental adaptations in a changing environment.

Spike synchronization of chaotic oscillators as a phase transition.

We study how a locally coupled array of spiking chaotic systems synchronizes to an external driving in a short time. Synchronization means spike separation at adjacent sites much shorter than the average inter-spike interval; a local lack of synchronization is called a defect. The system displays sudden spontaneous defect disappearance at a critical coupling strength suggesting an existence of a phase transition. Below critical coupling, the system reaches order at a definite amplitude of an external input; this order persists for a fixed time slot. Thus, the array behaves as an excitable-like system, even though the single element lacks such a property.

Comparison of single neuron models in terms of synchronization propensity.

A plausible model for coherent perception is the synchronization of chaotically distributed neural spike trains over wide cortical areas. A recently introduced propensity criterion provides a tool for a quantitative comparison of different neuron models in terms of their ability to synchronize to an applied perturbation. We explore the propensity of several systems and indicate the requirements to be satisfied by a plausible candidate for modeling neuronal activity. Our results show that the conflicting requirements of stability and sensitivity leading to high propensity to synchronization can be satisfied by a strongly nonuniform attractor made of two distinct regions: a saddle focus plus a sufficiently separated saddle node.

Sharp versus smooth synchronization transition of locally coupled oscillators.

We provide a general condition for the occurrence of a sudden transition to synchronization in an array of oscillators mutually coupled via the nearest neighbors. At the onset of synchronization a specific constraint must be fulfilled: precisely, the response time of a single system to signals from the adjacent sites must be smaller than the refractory period. We verify this criterion in some models for neuronal dynamics, namely, in excitable systems driven by noise as well as in chaotic oscillators.

Avoiding escapes in open dynamical systems using phase control.

In this paper we study how to avoid escapes in open dynamical systems in the presence of dissipation and forcing, as it occurs in realistic physical situations. We use as a prototype model the Helmholtz oscillator, which is the simplest nonlinear oscillator with escapes. For some parameter values, this oscillator presents a critical value of the forcing for which all particles escape from its single well. By using the phase control technique, weakly changing the shape of the potential via a periodic perturbation of suitable phase varphi , we avoid the escapes in different regions of the phase space. We provide numerical evidence, heuristic arguments, and an experimental implementation in an electronic circuit of this phenomenon. Finally, we expect that this method might be useful for avoiding escapes in more complicated physical situations.

Continuous wavelet transform in the analysis of burst synchronization in a coupled laser system.

The transition to synchronization of a pair of coupled chaotic CO2 lasers is investigated numerically in a model system. This system displays episodes of bursting of different predominant frequencies. Due to the multiple time scales present in this system, we use a complex continuous wavelet transform to perform the synchronization analysis. Thus it enables us to resolve the time of occurrence as well as the frequency of an event in a given time series up to an intrinsic uncertainty. Furthermore, due to the complex nature of that wavelet transform, it yields a direct estimate of the system's phase. We show that, as the coupling strength of the laser system is increased, the mutual coherency increases differently for different frequencies. Additionally we test our method with experimental data.

Quantum decoherence reduction by increasing the thermal bath temperature.

The well-known increase of the decoherence rate with the temperature, for a quantum system coupled to a linear thermal bath, no longer holds for a different bath dynamics. This is shown by means of a simple classical nonlinear bath, as well as a quantum spin-boson model. The anomalous effect is due to the temperature dependence of the bath spectral profile. In the case of the second model, a link with the quantum Zeno effect is provided. The decoherence reduction via the temperature increase can be relevant for the design of quantum computers.

Spatiotemporal pulses in a liquid crystal optical oscillator.

A nonlinear optical medium results by the collective orientation of liquid crystal molecules tightly coupled to a transparent photoconductive layer. We show that such a medium can give a large gain; thus, if inserted in a ring cavity, it results in an unidirectional optical oscillator. We report new dynamical regimes characterized by the generation of spatiotemporal pulses, localized in three dimensions and arising from the random superposition of many longitudinal and transverse modes with different frequencies.

Role of refractory period in homoclinic models of neural synchronization.

We study the properties of a homoclinic model of neuron by introducing a suitable one-dimensional map. We show that the system is characterized by a response time to external signals which is a decreasing function of the signal strength, in contrast to excitable models whose response time is signal-independent. In a one-dimensional array of these systems with bidirectional coupling, we observe a sudden transition to a synchronized state at a certain value of the coupling strength. The transition occurs when the response time of a site to the signals of the adjacent sites is of the order of refractory time. Near the transition, we find an intermittent behavior due to the competition between a turbulent and a synchronized state. The observed behavior distinguishes homoclinic systems from excitable systems.

Phase control of intermittency in dynamical systems.

We present a nonfeedback method to tame or enhance crisis-induced intermittency in dynamical systems. By adding a small harmonic perturbation to a parameter of the system, the intermittent behavior can be suppressed or enhanced depending on the value of the phase difference between the main driving and the perturbation. The validity of the method is shown both in the model and in an experiment with a CO2 laser. An analysis of this scheme applied to the quadratic map near crisis illustrates the role of phase control in nonlinear dynamical systems.

Neural coding for the retrieval of multiple memory patterns.

We investigate the retrieval dynamics in a feature-based semantic memory model, in which the features are coded by neurons of the Hindmarsh-Rose type in the chaotic regime. We consider the retrieval process as consisting of the synchronized firing activity of the neurons coding for the same memory pattern. The retrieval dynamics is investigated for multiple patterns, with particular attention to the case of overlapping memories. In this case, we hypothesize a dynamical nontransitive mechanism based on synchronization, that allows for a shared feature to participate in multiple memory representations. The problem of the choice of a cognitive plausible time-scale for the retrieval analysis is investigated by analyzing the information that can be inferred from finite-time analyses. Different types of indicators are proposed in order to evaluate the temporal dynamics of the neurons engaged in the retrieval process. We interpret the simulation results as suggestive of a role for chaotic dynamics in allowing for flexible composition of elementary meaningful units in memory representations.

Attractor selection in chaotic dynamics.

For different settings of a control parameter, a chaotic system can go from a region with two separate stable attractors (generalized bistability) to a crisis where a chaotic attractor expands, colliding with an unstable orbit. In the bistable regime jumps between independent attractors are mediated by external perturbations; above the crisis, the dynamics includes visits to regions formerly belonging to the unstable orbits and this appears as random bursts of amplitude jumps. We introduce a control method which suppresses the jumps in both cases by filtering the specific frequency content of one of the two dynamical objects. The method is tested both in a model and in a real experiment with a CO2 laser.

Dynamics of narrow bright solitons in an array of attractive atoms in a Bose-Einstein condensate.

We study the dynamics of a narrow bright soliton in a one-dimensional lattice of condensed attractive atoms when the soliton width is comparable to the lattice spacing. If a momentum is imprinted to a stationary state, the soliton can have oscillations around a site or it can undergo a random motion along the array. The motion is very sensitive to the atomic background distribution, and a thermal cloud or quantum field fluctuations can induce a random motion of the soliton.

Fragmentation instability of a liquid drop falling inside a heavier miscible fluid.

We report a different type of drop instability, where the density difference between the drop and the solvent is negative. We show that the drop falls inside the solvent down to a minimum height, then fragmentation takes place and secondary droplets rise up to the surface. We have developed a theoretical model that captures the essentials of the phenomenon and predicts the correct scalings for the rise-up time and the minimum height.

A programmable electronic circuit for modelling CO2 laser dynamics.

We introduce a programmable electronic circuit implementing the rich dynamics of CO2 laser models. The design and the implementation of the circuit are accomplished by using a programmable analog device, which permits an experimental characterization of the laser dynamics. The experimental results shown in the paper demonstrate that the circuit exhibits homoclinic chaos typical of CO2 laser with feedback modulation of cavity losses. Moreover, experimental results showing that noise regularizes the dynamical time scales of the system are reported.