Nonlinear Schrodinger equation with chaotic, random, and nonperiodic nonlinearity

In this Letter we deal with a nonlinear Schrodinger equation with chaotic, random, and nonperiodic cubic nonlinearity. Our goal is to study the soliton evolution, with the strength of the nonlinearity perturbed in the space and time coordinates and to check its robustness under these conditions. Here we show that the chaotic perturbation is more effective in destroying the soliton behavior, when compared with random or nonperiodic perturbation. For a real system, the perturbation can be related to, e.g., impurities in crystalline structures, or coupling to a thermal reservoir which, on the average, enhances the nonlinearity. We also discuss the relevance of such random perturbations to the dynamics of Bose-Einstein condensates and their collective excitations and transport. (C) 2010 Elsevier B.V. All rights reserved.

Fortran programs for the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Equação de Schrödinger não linear com coeficientes modulados

Pós-graduação em Física - FEG

Stability and collapse of a coupled Bose-Einstein condensate

The dynamics of a coupled Bose-Einstein condensate involving trapped atoms in two quantum states is studied using the time-dependent Gross-Pitaevskii equation including an interaction which can transform atoms from one state to the other. We find interesting oscillation of the number of atoms in each of the states. For all repulsive interactions, stable condensates are formed. When some of the atomic interactions are attractive, the possibility of collapse is studied by including an absorptive contact interaction and a quartic three-body recombination term. One or both components of the condensate may undergo collapse when one or more of the nonlinear terms are attractive in nature. (C) 2001 Elsevier B.V. B.V. All rights reserved.

Dynamics of a collapsing and exploding Bose-Einstein condensed vortex state

The dynamics of small repulsive Bose-Einstein condensed vortex states of 85Rb atoms in a cylindrical traps with low angular momentum was studied. The time-dependent mean-field Gross-Pitaevskii equation was used for the study. The condensates collapsed and atoms ejected via explosion and a remnant condensate with a smaller number of atoms emerges that survived for a long time.

The dynamics of bright matter wave solitons in a quasi one-dimensional Bose-Einstein condensate with a rapidly varying trap

The dynamics of a bright matter wave soliton in a quasi one-dimensional Bose-Einstein condensate (BEC) with a periodically rapidly varying time trap is considered. The governing equation is based on averaging the fast modulations of the Gross-Pitaevskii (GP) equation. This equation has the form of a GP equation with an effective potential of a more complicated structure than an unperturbed trap. In the case of an inverted (expulsive) quadratic trap corresponding to an unstable GP equation, the effective potential can be stable. For the bounded space trap potential it is showed that bifurcation exists, i.e. the single-well potential bifurcates to the triple-well effective potential. The stabilization of a BEC cloud on-site state in the temporary modulated optical lattice is found. This phenomenon is analogous to the Kapitza stabilization of an inverted pendulum. The analytical predictions of the averaged GP equation are confirmed by numerical simulations of the full GP equation with rapid perturbations.

Bright solitons in a quasi-one-dimensional reduced model of a dipolar Bose-Einstein condensate with repulsive short-range interactions

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Self-similar Expansion of the Density Profile in a Turbulent Bose-Einstein Condensate

In a recent study we demonstrated the emergence of turbulence in a trapped Bose-Einstein condensate of Rb-87 atoms. An intriguing observation in such a system is the behavior of the turbulent cloud during free expansion. The aspect ratio of the cloud size does not change in the way one would expect for an ordinary non-rotating (vortex-free) condensate. Here we show that the anomalous expansion can be understood, at least qualitatively, in terms of the presence of vorticity distributed throughout the cloud, effectively counteracting the usual reversal of the aspect ratio seen in free time-of-flight expansion of non-rotating condensates.

Computational Methods for Studies of Quantum Dots and Boson Condensates

This thesis presents ab initio studies of two kinds of physical systems, quantum dots and bosons, using two program packages of which the bosonic one has mainly been developed by the author. The implemented models, \emph{i.e.}, configuration interaction (CI) and coupled cluster (CC) take the correlated motion of the particles into account, and provide a hierarchy of computational schemes, on top of which the exact solution, within the limit of the single-particle basis set, is obtained. The theory underlying the models is presented in some detail, in order to provide insight into the approximations made and the circumstances under which they hold. Some of the computational methods are also highlighted. In the final sections the results are summarized. The CI and CC calculations on multiexciton complexes in self-assembled semiconductor quantum dots are presented and compared, along with radiative and non-radiative transition rates. Full CI calculations on quantum rings and double quantum rings are also presented. In the latter case, experimental and theoretical results from the literature are re-examined and an alternative explanation for the reported photoluminescence spectra is found. The boson program is first applied on a fictitious model system consisting of bosonic electrons in a central Coulomb field for which CI at the singles and doubles level is found to account for almost all of the correlation energy. Finally, the boson program is employed to study Bose-Einstein condensates confined in different anisotropic trap potentials. The effects of the anisotropy on the relative correlation energy is examined, as well as the effect of varying the interaction potential.}

Annihilation of vortex dipoles in an oblate Bose-Einstein condensate

We theoretically explore the annihilation of vortex dipoles, generated when an obstacle moves through an oblate Bose-Einstein condensate, and examine the energetics of the annihilation event. We show that the grey soliton, which results from the vortex dipole annihilation, is lower in energy than the vortex dipole. We also investigate the annihilation events numerically and observe that annihilation occurs only when the vortex dipole overtakes the obstacle and comes closer than the coherence length. Furthermore, we find that noise reduces the probability of annihilation events. This may explain the lack of annihilation events in experimental realizations.

Coherent scattering of light by Bose-Einstein condensation in a tight confinement

We have observed strong scattering of a probe light by dilute Bose-Einstein condensate (BEC) Rb-87 gas in a tight magnetic trap. The scattering light forms fringes at the image plane. It is found that we can infer the real size of the condensation and the number of the atoms by modelling the imaging system. We present a quantitative calculation of light scattering by the condensed atoms. The calculation shows that the experimental results agree well with the prediction of the generalized diffraction theory, and thus we can directly observe the phase transition of BEC in a tight trap.

Second-harmonic generation of Bogoliubov excitations in a two-component Bose-Einstein condensate

A second-harmonic generation (SHG) is predicted for the Bogoliubov excitations in a two-component Bose-Einstein condensate. It is shown that, because the linear dispersion curve of the excitations displays two branches, the phase-matching condition for the SHG can be fulfilled if the wave vectors and frequencies of fundamental and second-harmonic waves are selected suitably from different branches. The nonlinearly coupled envelope equations for the SHG are derived by using a method of multiple scales. The explicit solutions of these envelope equations are provided and the conversion efficiency of the SHG is also discussed.

Josephson dynamics of a Bose-Einstein condensate trapped in a double-well potential

The Josephson equations for a Bose-Einstein Condensate gas trapped in a double-well potential are derived with the two-mode approximation by the Gross-Pitaevskii equation. The dynamical characteristics of the equations are obtained by the numerical phase diagrams. The nonlinear self-trapping effect appeared in the phase diagrams are emphatically discussed, and the condition EcN > 4E(J) is presented.