Trajectory-probed instability and statistics of desynchronization events in coupled chaotic systems.

Complex systems, such as financial markets, earthquakes, and neurological networks, exhibit extreme events whose mechanisms of formation are not still completely understood. These mechanisms may be identified and better studied in simpler systems with dynamical features similar to the ones encountered in the complex system of interest. For instance, sudden and brief departures from the synchronized state observed in coupled chaotic systems were shown to display non-normal statistical distributions similar to events observed in the complex systems cited above. The current hypothesis accepted is that these desynchronization events are influenced by the presence of unstable object(s) in the phase space of the system. Here, we present further evidence that the occurrence of large events is triggered by the visitation of the system's phase-space trajectory to the vicinity of these unstable objects. In the system studied here, this visitation is controlled by a single parameter, and we exploit this feature to observe the effect of the visitation rate in the overall instability of the synchronized state. We find that the probability of escapes from the synchronized state and the size of those desynchronization events are enhanced in attractors whose shapes permit the chaotic trajectories to approach the region of strong instability. This result shows that the occurrence of large events requires not only a large local instability to amplify noise, or to amplify the effect of parameter mismatch between the coupled subsystems, but also that the trajectories of the system wander close to this local instability.

Casimir-Polder interactions in the presence of thermally excited surface modes.

The temperature dependence of the Casimir-Polder interaction addresses fundamental issues for understanding vacuum and thermal fluctuations. It is highly sensitive to surface waves, which, in the near field, govern the thermal emission of a hot surface. Here we use optical reflection spectroscopy to monitor the atom-surface interaction potential between a Cs*(7D3/2) atom and a hot sapphire surface at distances of ~100 nm. In our experiments, that explore a large range of temperatures (500-1,000 K), the surface is at thermal equilibrium with the vacuum. The observed increase of the interaction with temperature, by up to 50%, relies on the coupling between atomic virtual transitions in the infrared range and thermally excited surface-polariton modes. We extrapolate our findings to a broad distance range, from the isolated atom to the short distances relevant to physical chemistry. Our work also opens the prospect of controlling atom-surface interactions by engineering thermal fields.

Tunable power law in the desynchronization events of coupled chaotic electronic circuits.

We study the statistics of the amplitude of the synchronization error in chaotic electronic circuits coupled through linear feedback. Depending on the coupling strength, our system exhibits three qualitatively different regimes of synchronization: weak coupling yields independent oscillations; moderate to strong coupling produces a regime of intermittent synchronization known as attractor bubbling; and stronger coupling produces complete synchronization. In the regime of moderate coupling, the probability distribution for the sizes of desynchronization events follows a power law, with an exponent that can be adjusted by changing the coupling strength. Such power-law distributions are interesting, as they appear in many complex systems. However, most of the systems with such a behavior have a fixed value for the exponent of the power law, while here we present an example of a system where the exponent of the power law is easily tuned in real time.

Two-beam nonlinear Kerr effect to stabilize laser frequency with sub-Doppler resolution.

Avoiding laser frequency drifts is a key issue in many atomic physics experiments. Several techniques have been developed to lock the laser frequency using sub-Doppler dispersive atomic lineshapes as error signals in a feedback loop. We propose here a two-beam technique that uses nonlinear properties of an atomic vapor around sharp resonances to produce sub-Doppler dispersivelike lineshapes that can be used as error signals. Our simple and robust technique has the advantage of not needing either modulation or magnetic fields.

Temperature dependence of the dielectric permittivity of CaF(2), BaF(2) and Al(2)O(3): application to the prediction of a temperature-dependent van der Waals surface interaction exerted onto a neighbouring Cs(8P(3/2)) atom.

The temperature behaviour in the range 22-500 °C of the dielectric permittivity in the infrared range is investigated for CaF(2), BaF(2) and Al(2)O(3) through reflectivity measurements. The dielectric permittivity is retrieved by fitting reflectivity spectra with a model taking into account multiphonon contributions. The results extrapolated from the measurements are applied to predict a temperature-dependent atom-surface van der Waals interaction. We specifically consider as the atom of interest Cs(8P(3/2)), the most relevant virtual couplings of which fall in the range of thermal radiation and are located in the vicinity of the reststrahlen band of fluoride materials.