Collapse of attractive Bose-Einstein condensed vortex states in a cylindrical trap

The quantized vortex states of a weakly interacting Bose-Einstein condensate of atoms with attractive interatomic interaction in an axially symmetric harmonic oscillator trap are investigated using the numerical solution of the time-dependent Gross-Pitaevskii equation obtained by the semi-implicit Crank-Nicholson method. The collapse of the condensate is studied in the presence of deformed traps with the larger frequency along either the radial or the axial direction. The critical number of atoms for collapse is calculated as a function of the vortex quantum number L. The critical number increases with increasing angular momentum L of the cortex state but tends to saturate for large L.

Bose-Einstein condensation dynamics from the numerical solution of the Gross-Pitaevskii equation

We study certain stationary and time-evolution problems of trapped Bose-Einstein condensates using the numerical solution of the Gross-Pitaevskii (GP) equation with both spherical and axial symmetries. We consider time-evolution problems initiated by suddenly changing the interatomic scattering length or harmonic trapping potential in a stationary condensate. These changes introduce oscillations in the condensate which are studied in detail. We use a time iterative split-step method for the solution of the time-dependent GP equation, where all nonlinear and linear non-derivative terms are treated separately from the time propagation with the kinetic energy terms. Even for an arbitrarily strong nonlinear term this leads to extremely accurate and stable results after millions of time iterations of the original equation.

General soliton matrices in the Riemann-Hilbert problem for integrable nonlinear equations

We derive the soliton matrices corresponding to an arbitrary number of higher-order normal zeros for the matrix Riemann-Hilbert problem of arbitrary matrix dimension, thus giving the complete solution to the problem of higher-order solitons. Our soliton matrices explicitly give all higher-order multisoliton solutions to the nonlinear partial differential equations integrable through the matrix Riemann-Hilbert problem. We have applied these general results to the three-wave interaction system, and derived new classes of higher-order soliton and two-soliton solutions, in complement to those from our previous publication [Stud. Appl. Math. 110, 297 (2003)], where only the elementary higher-order zeros were considered. The higher-order solitons corresponding to nonelementary zeros generically describe the simultaneous breakup of a pumping wave (u(3)) into the other two components (u(1) and u(2)) and merger of u(1) and u(2) waves into the pumping u(3) wave. The two-soliton solutions corresponding to two simple zeros generically describe the breakup of the pumping u(3) wave into the u(1) and u(2) components, and the reverse process. In the nongeneric cases, these two-soliton solutions could describe the elastic interaction of the u(1) and u(2) waves, thus reproducing previous results obtained by Zakharov and Manakov [Zh. Eksp. Teor. Fiz. 69, 1654 (1975)] and Kaup [Stud. Appl. Math. 55, 9 (1976)]. (C) 2003 American Institute of Physics.

Dynamical classical superfluid-insulator transition in a Bose-Einstein condensate on an optical lattice

We predict a dynamical: classical superfluid-insulator transition in a Bose-Einstein condensate (BEC) trapped in combined optical and axially symmetrical harmonic potentials initiated by the periodic modulation of the radial trapping potential. The transition is marked by a loss of phase coherence in the BEC and a subsequent destruction of the interference pattern upon free:expansion. For a weak modulation of the radial potential the phase coherence is maintained. For a stronger modulation and a longer holding time in the modulated trap, the phase coherence is destroyed thus signalling a classical superfluid-insulator transition. The results are illustrated by a complete numerical solution of the axially symmetrical mean-field Gross-Pitaevskii equation for a repulsive BEC. Suggestions for future experimentation are-made.

On equivalence of Duffin-Kemmer-Petiau and Klein-Gordon equations

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Anisotropic sound and shock waves in dipolar Bose-Einstein condensate

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Measurement of Bose-Einstein correlations in pp collisions at the LHC with CMS

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Realistic equations of state for the primeval universe

Equations of state for the early universe including realistic interactions between constituents are formulated. Under certain hypotheses, these equations are able to generate an inflationary regime prior to the period of the nucleosynthesis. The resulting accelerated expansion is intense enough to solve the flatness and horizon problems. In the cases of a curvature parameter. equal to 0 or + 1, the model is able to avoid the initial singularity and offers a natural explanation for why the universe is in expansion. All the results are valid only for a matter-antimatter symmetric universe.

Two-dimensional dipolar Bose-Einstein condensate bright and vortex solitons on a one-dimensional optical lattice

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Numerical and variational solutions of the dipolar Gross-Pitaevskii equation in reduced dimensions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Dynamics of quasi-one-dimensional bright and vortex solitons of a dipolar Bose-Einstein condensate with repulsive atomic interaction

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

DM particles: how warm they can be?

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Dynamics of Bose-Einstein condensates with atomic pumping and dissipative processes

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

NOISE and ULTRAVIOLET DIVERGENCES IN SIMULATIONS of GINZBURG-LANDAU-LANGEVIN TYPE of EQUATIONS

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Gap solitons in a dipolar Bose-Einstein condensate on a three-dimensional optical lattice

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)