Dissipative dynamics of an open Bose Einstein condensate

As an atomic Bose Einstein condensate BEC.is coupled to a source of uncondensed atoms at the same temperature and to a sink extraction towards an atom laser.the idealized description in terms of a Gross–Pitaevsky equation GP. no longer holds. Under suitable physical assumptions we show that the dissipative BEC obeys a Complex Ginzburg Landau equation CGL.and for some parameter range it undergoes a space time patterning. As a consequence, the density of BEC atoms within the trap displays non trivial space time correlations, which can be detected by monitoring the density profile of the outgoing atom laser. The patterning condition requires a negative scattering length, as e.g. in 7Li. In such a case we expect a many domain collapsed regime, rather than a single one as reported for a closed BEC. q2000 Elsevier Science B.V. All rights reserved

Controlling and synchronizating space time chaos

Control and synchronization of continuous space-extended systems is realized by means of a finite number of local tiny perturbations. The perturbations are selected by an adaptive technique, and they are able to restore each of the independent unstable patterns present within a space time chaotic regime, as well as to synchronize two space time chaotic states. The effectiveness of the method and the robustness against external noise is demonstrated for the amplitude and phase turbulent regimes of the one-dimensional complex Ginzburg-Landau equation. The problem of the minimum number of local perturbations necessary to achieve control is discussed as compared with the number of independent spatial correlation lengths

Characterization of synchronization spatiotemporal states in coupled non identical complex Ginzburg-Landau equations.

We characterize the synchronization of two nonidentical spatially extended elds ruled by onedimensional Complex Ginzburg{Landau equations, in the two regimes of phase and amplitude turbulence. If two elds display the same dynamical regime, the coupling induces a transition to a completely synchronized state. When, instead, the two elds are in di erent dynamical regimes, the transition to complete synchronization is mediated by defect synchronization. In the former case, the synchronized manifold is dynamically equivalent to that of the unsynchronized systems, while in the latter case the synchronized state substantially di ers from the unsynchronized one, and it is mainly dictated by the synchronization process of the space-time defects

Fragment formation in the break up of a drop falling in a miscible liquid

When falling in a lighter miscible solvent, a drop of liquid deforms to a torus which then breaks up into several fragments or just disappears by diffusion. By using liquids of different compositions we show the universal behaviour of the phenomenon, and its dependence on two nondimensional numbers, the fragmentation number F, and the Schmidt number S. While F marks the transition from diffusion to splitting, here we show the role of S in controlling the number of horizontal fragments after the first break-up. The process is explained in terms of competitions of different time scales

Order parameter fragmentation after a symmetry-breaking transition

As a nonlinear optical system consisting of a Kerr medium inserted in a feedback loop is exposed to a light intensity growing linearly from below to above the threshold for pattern formation, the critical slowing down around threshold freezes the defect population. The measured number of defects immediately after the transition scales with the quench time as predicted by Zurek for a two-dimensional Ginzburg-Landau model. The further temporal evolution of the defect number is in agreement with a simple annihilation model, once the drift of defects specific for our system is taken into account

Synchronization in nonidentical extended systems

We report the synchronization of two nonidentical spatially extended fields, ruled by one-dimensional complex Ginzburg-Landau equations, both in the phase and in the amplitude turbulence regimes. In the case of small parameter mismatches, the coupling induces a transition to a completely synchronized state. For large parameter mismatches, the transition is mediated by phase synchronization. In the former case, the synchronized state is not qualitatively different from the unsynchronized one, while in the latter case the synchronized state may substantially differ from the unsynchronized one, and it is mainly dictated by the synchronization process of the space-time defects

Domain segregation in a two-dimensional system in the presence of drift

Motivated by experiments on optical patterns we analyze two-dimensional extended bistable systems with drift after a quench above threshold. The evolution can be separated into successive stages: linear growth and diffusion, coarsening, and transport, leading finally to a quasi-one-dimensional kink-antikink state. The phenomenon is general and occurs when the bistability relates to uniform phases or two different patterns

Control of defects and spacelike structures in delayed dynamical systems

In many nonequilibrium dynamical situations delays are crucial in inducing chaotic scenarios. In particular, a delayed feedback in an oscillator can break the regular oscillation into trains mutually uncorrelated in phase, whereby the phase jumps are localized as defects in an extended system. We show that an adaptive control procedure is effective in suppressing these defects and stabilizing the regular oscillations. The analysis of the transient times for achieving control demonstrates that stabilization is obtained within an amplitude turbulent regime, analogous to what is present in spatially distributed systems. The control technique is robust against the presence of large amounts of noise

Time interval distributions of atoms in atomic beams

We report on the experimental investigation of two-particle correlations between neutral atoms in a Hanbury Brown and Twiss experiment. Both an atom laser beam and a pseudo-thermal atomic beam are extracted from a Bose-Einstein condensate and the atom flux is measured with a single atom counter. We determine the conditional and the unconditional detection probabilities for the atoms in the beam and find good agreement with the theoretical predictions.Comment: 4 pages, 3 figure

Contracting the Wigner kernel of a spin to the Wigner kernel of a particle

A general relation between the Moyal formalisms for a spin and a particle is established. Once the formalism has been set up for a spin, the phase-space description of a particle is obtained from contracting the group of rotations to the oscillator group. In this process, turn into a spin Wigner kernel turns into the Wigner kernel of a particle. In fact, only one out of 22s different possible kernels for a spin shows this behavior