Optimal Phase-Control Strategy for Damped-Driven Duffing Oscillators.

Phase-control techniques of chaos aim to extract periodic behaviors from chaotic systems by applying weak harmonic perturbations with a suitably chosen phase. However, little is known about the best strategy for selecting adequate perturbations to reach desired states. Here we use experimental measures and numerical simulations to assess the benefits of controlling individually the three terms of a Duffing oscillator. Using a real-time analog indicator able to discriminate on-the-fly periodic behaviors from chaos, we reconstruct experimentally the phase versus perturbation strength stability areas when periodic perturbations are applied to different terms governing the oscillator. We verify the system to be more sensitive to perturbations applied to the quadratic term of the double-well Duffing oscillator and to the quartic term of the single-well Duffing oscillator.

Mid-infrared digital holography and holographic interferometry with a tunable quantum cascade laser.

Mid-infrared digital holography based on CO2 lasers has proven to be a powerful coherent imaging technique due to reduced sensitivity to mechanical vibrations, increased field of view, high optical power, and possible vision through scattering media, e.g., smoke. Here we demonstrate a similar and more compact holographic system based on an external cavity quantum cascade laser emitting at 8 µm. Such a setup, which includes a highly sensitive microbolometric camera, allows the acquisition of speckle holograms of scattering objects, which can be processed in real time. In addition, by exploiting the broad laser tunability, we can acquire holograms at different wavelengths, from which we extract phase images not subjected to phase wrapping, at synthetic wavelengths ranging from hundreds of micrometers to several millimeters.

Imaging live humans through smoke and flames using far-infrared digital holography.

The ability to see behind flames is a key challenge for the industrial field and particularly for the safety field. Development of new technologies to detect live people through smoke and flames in fire scenes is an extremely desirable goal since it can save human lives. The latest technologies, including equipment adopted by fire departments, use infrared bolometers for infrared digital cameras that allow users to see through smoke. However, such detectors are blinded by flame-emitted radiation. Here we show a completely different approach that makes use of lensless digital holography technology in the infrared range for successful imaging through smoke and flames. Notably, we demonstrate that digital holography with a cw laser allows the recording of dynamic human-size targets. In this work, easy detection of live, moving people is achieved through both smoke and flames, thus demonstrating the capability of digital holography at 10.6 µm.

An automatic method for assembling a large synthetic aperture digital hologram.

A major issue so far for digital holography is the low spatial resolution generally achieved. The numerical aperture is limited by the area of currently available detectors, such as CCD sensors, which is significantly lower than that of a holographic plate. This is an even more severe constraint when IR sensors such as microbolometers are taken into account. In order to increase the numerical aperture of such systems, we developed an automatic technique which is capable of recording several holograms and of stitching them together, obtaining a digital hologram with a synthetic but larger numerical aperture. In this way we show that more detail can be resolved and a wider parallax angle can be achieved. The method is demonstrated for visible as well IR digital holography, recording and displaying large size objects.

Visible reconstruction by a circular holographic display from digital holograms recorded under infrared illumination.

A circular holographic display that consists of phase-only spatial light modulators is used to reconstruct images in visible light from digital holograms recorded under infrared (10.6 µm) illumination. The reconstruction yields a holographic digital video display of a three-dimensional ghostlike image of an object floating in space where observers can move and rotate around it.

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.

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.

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.

Coherence resonance in excitable electronic circuits in the presence of colored noise.

We give evidence of coherence resonance in an excitable electronic circuit whose dynamics obeys the FitzHugh-Nagumo model system, under the application of different noise sources, ranging from Gaussian white noise to colored 1/f2 noises. The resonance behavior can be significantly reinforced when experimental parameters are tuned in order to place the stable fixed point closer to the excitability threshold of spiking behavior, as well as when the time scales of the circuit are properly modified. A quantitative description of the effects of noise correlations in inducing the resonant behavior is provided.

Dynamics and stabilization of the Elettra storage-ring free-electron laser.

The ultimate performance of a storage-ring free-electron laser in terms of light stability and extracted power depends on the possibility of simultaneously controlling the electron-beam and laser dynamics. As a preliminary requirement, the level of longitudinal and transverse electron-beam stability must be high enough to guarantee the laser start-up and growth. This is usually obtained by means of dedicated feedback systems. Once such a requirement is satisfied, the possibility of establishing and maintaining a continuous-wave operation mode finally resides in a deep understanding of the strongly coupled laser-electrons dynamics. For this purpose, we have developed a simple theoretical model which has been proved to be able to provide insight into the evolution of the laser intensity. In this framework, we have also proposed the possibility of utilizing a derivative closed-loop feedback to create or enlarge the region of stable signal. A feedback of this type has been implemented on the Elettra storage-ring free-electron laser. The obtained results, which fully confirm our predictions, are discussed in this paper.

Generation of entanglement in quantum parametric oscillators using phase control.

The control of quantum entanglement in systems in contact with environment plays an important role in information processing, cryptography and quantum computing. However, interactions with the environment, even when very weak, entail decoherence in the system with consequent loss of entanglement. Here we consider a system of two coupled oscillators in contact with a common heat bath and with a time dependent oscillation frequency. The possibility to control the entanglement of the oscillators by means of an external sinusoidal perturbation applied to the oscillation frequency has been theoretically explored. We demonstrate that the oscillators become entangled exactly in the region where the classical counterpart is unstable, otherwise when the classical system is stable, entanglement is not possible. Therefore, we can control the entanglement swapping from stable to unstable regions by adjusting amplitude and phase of our external controller. We also show that the entanglement rate is approximately proportional to the real part of the Floquet coefficient of the classical counterpart of the oscillators. Our results have the intriguing peculiarity of manipulating quantum information operating on a classical system.

Whole optical wavefields reconstruction by digital holography.

In this paper, we have investigated on the potentialities of digital holography for whole reconstruction of wavefields. We show that this technique can be efficiently used for obtaining quantitative information from the intensity and the phase distributions of the reconstructed field at different locations along the propagation direction. The basic concept and procedure of wavefield reconstruction for digital in-line holography is discussed. Numerical reconstructions of the wavefield from digitally recorded in-line hologram patterns and from simulated test patterns are presented. The potential of the method for analysing aberrated wave front has been exploited by applying the reconstruction procedure to astigmatic hologram patterns.

Experimental control of coherence of a chaotic oscillator.

We give experimental evidence that a delayed feedback control strategy is able to efficiently enhance the coherence of an experimental self-sustained chaotic oscillator obtained from a CO2 laser with electro-optical feedback. We demonstrate that coherence control is achieved for various choices of the delay time in the feedback control, including values that would lead to the stabilization of an unstable periodic orbit embedded within the chaotic attractor. The relationship between the two processes is discussed.

Chaotic function generator: complex dynamics and its control in a loss-modulated Nd:YAG laser.

The complex dynamics resulting from electronic feedback of a laser's intensity are explored and characterized. Distinct stable and chaotic regimes can be elicited from the laser by tuning the bias of the feedback loop. An additional branch of the feedback loop, containing a derivative filter, provides access to new kinds of dynamics, including a more gradual transition to chaos. The whole feedback network together allows the laser dynamics to be selected from among a wide range of chaotic wave forms distinguished by statistical or spectral information. In other words, this laser system can be used as a tunable generator of chaotic functions.

Identifying physical properties of a CO2 laser by dynamical modeling of measured time series.

We estimate internal parameters of a Q-switched CO2 laser by fitting trajectories of the four-level model to measured scalar time series. The four-level model is a five-dimensional nonlinear system of ordinary differential equations. A multiple shooting technique is used to construct the unobserved time courses of the population densities and to reveal the dependence of the parameters on the excitation current. For excitations barely above the laser threshold large pulse variations are identified as an effect of small variations of the pump parameter.

Constructive effects of noise in homoclinic chaotic systems.

Many chaotic oscillators have coherent phase dynamics but strong fluctuations in the amplitudes. At variance with such a behavior, homoclinic chaos is characterized by quite regular spikes but strong fluctuation in their time intervals due to the chaotic recurrence to a saddle point. We study influences of noise on homoclinic chaos. We demonstrate both numerically and experimentally on a CO2 laser various constructive effects of noise, including coherence resonance, noise-induced synchronization in uncoupled systems and noise-enhanced phase synchronization, deterministic resonance with respect to signal frequency, and stochastic resonance versus noise intensity in response to weak signals. The peculiar sensitivity of the system along the weak unstable manifold of the saddle point underlines the unified mechanism of these nontrivial and constructive noise-induced phenomena.

Delayed self-synchronization in homoclinic chaos.

The chaotic spike train of a homoclinic dynamical system is self-synchronized by applying a time-delayed correction proportional to the laser output intensity. Due to the sensitive nature of the homoclinic chaos to external perturbations, stabilization of very long-periodic orbits is possible. On these orbits, the dynamics appears chaotic over a finite time, but then it repeats with a recurrence time that is slightly longer than the delay time. The effect, called delayed self-synchronization, displays analogies with neurodynamic events that occur in the buildup of long-term memories.

Noise-enhanced synchronization of homoclinic chaos in a CO2 laser.

Many chaotic oscillators have rather coherent phase dynamics but strong fluctuation in the amplitudes. Conversely, homoclinic chaos is characterized by quite regular spikes but strong fluctuation in their time intervals. We study the effects of noise on the synchronization of homoclinic chaos to a weak periodic signal and demonstrate numerically and experimentally in a CO2 laser system that noise enhances synchronization of homoclinic chaos. The system exhibits both conventional resonance versus driving frequency and stochastic resonance with respect to noise intensity.

Coupling scheme for complete synchronization of periodically forced chaotic CO2 lasers.

We present a way of coupling two nonautonomous, periodically forced, chaotic C O2 lasers in a master-slave configuration in order to achieve complete synchronization. The method consists of modulating the forcing of the slave laser by means of the difference between the intensities of the two lasers, and lends itself to a simple physical implementation. Experimental evidence of complete synchronization induced by a suitable coupling strength is shown, and a numerical model is used to achieve further insight of the synchronization phenomena. Finally, we describe a possible application of the investigated technique to the design of a digital communication system.