Symbiotic gap and semigap solitons in Bose-Einstein condensates

Using the variational approximation and numerical simulations, we study one-dimensional gap solitons in a binary Bose-Einstein condensate trapped in an optical-lattice potential. We consider the case of interspecies repulsion, while the intraspecies interaction may be either repulsive or attractive. Several types of gap solitons are found: symmetric or asymmetric; unsplit or split, if centers of the components coincide or separate; intragap (with both chemical potentials falling into a single band gap) or intergap, otherwise. In the case of the intraspecies attraction, a smooth transition takes place between solitons in the semi-infinite gap, those in the first finite band gap, and semigap solitons (with one component in a band gap and the other in the semi-infinite gap).

Dipolar Bose-Einstein condensates with large scattering length

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

Stability of trapped Bose-Einstein condensates

In three-dimensional trapped Bose-Einstein condensate (BEC), described by the time-dependent Gross-Pitaevskii-Ginzburg equation, we study the effect of initial conditions on stability using a Gaussian variational approach and exact numerical simulations. We also discuss the validity of the criterion for stability suggested by Vakhitov and Kolokolov. The maximum initial chirp (initial focusing defocusing of cloud) that can lead a stable condensate to collapse even before the number of atoms reaches its critical limit is obtained for several specific cases. When we consider two- and three-body nonlinear terms, with negative cubic and positive quintic terms, we have the conditions for the existence of two phases in the condensate. In this case, the magnitude of the oscillations between the two phases are studied considering sufficient large initial chirps. The occurrence of collapse in a BEC with repulsive two-body interaction is also shown to be possible.

Numerical study of the coupled time-dependent Gross-Pitaevskii equation: Application to Bose-Einstein condensation

The Bose-Einstein condensate of several types of trapped bosons at ultralow temperature was described using the coupled time dependent Gross-Pitaevskii equation. Both the stationary and time evolution problems were analyzed using this approach. The ground state stationary wave functions were found to be sharply peaked near the origin for attractive interatomic interaction for larger nonlinearity while for a repulsive interatomic interaction the wave function extends over a larger region of space.

Free expansion of attractive and repulsive Bose-Einstein condensed vortex states

A numerical study of the time-dependent Gross-Pitaevskii equation for an axially symmetric trap to obtain insight into the free expansion of vortex states of BEC is presented. As such, the ratio of vortex-core radius to radia rms radius xc/xrms(<1) is found to play an interesting role in the free expansion of condensed vortex states. the larger this ratio, the more prominent is the vortex core and the easier is the possibility of experimental detection of vortex states.

Controlling collapse in Bose-Einstein condensates by temporal modulation of the scattering length

A study was conducted on the dynamics of 2D and 3D Bose-Einstein condensates in the case when the scattering length in the Gross-Pitaevskii (GP) equation which contains constant (dc) and time-variable (ac) parts. Using the variational approximation (VA), simulating the GP equation directly, and applying the averaging procedure to the GP equation without the use of the VA, it was demonstrated that the ac component of the nonlinearity makes it possible to maintain the condensate in a stable self-confined state without external traps.

Mean-field model of interaction between bright vortex solitons in Bose-Einstein condensates

Using the explicit numerical solution of the axially symmetric Gross-Pitaevskii equation we study the dynamics of interaction among vortex solitons in a rotating matter-wave bright soliton train in a radially trapped and axially free Bose-Einstein condensate to understand certain features of the experiment by Strecker et al (2002 Nature 417 150). In a soliton train, solitons of opposite phase (phase δ = π) repel and stay apart without changing shape; solitons with δ = 0 attract, interact and coalesce, but eventually come out; solitons with a general δ usually repel but interact inelastically by exchanging matter. We study this and suggest future experiments with vortex solitons.

Oscilações não-lineares em condensados de Bose-Einstein

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

Dynamics of the corotating vortices in dipolar Bose-Einstein condensates in the presence of dissipation

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

Quantum coherent tunneling between two atomic-molecular Bose-Einstein condensates

We study the quantum coherent tunneling dynamics of two weakly coupled atomic-molecular Bose-Einstein condensates (AMBEC). A weak link is supposed to be provided by a double-well trap. The regions of parameters where the macroscopic quantum localization of the relative atomic population occurs are revealed. The different dynamical regimes are found depending on the value of nonlinearity, namely, coupled oscillations of population imbalance of atomic and molecular condensate, including irregular oscillations regions, and macroscopic quantum self trapping regimes. Quantum means and quadrature variances are calculated for population of atomic and molecular condensates and the possibility of quadrature squeezing is shown via stochastic simulations within P-positive phase space representation method. Linear tunnel coupling between two AMBEC leads to correlations in quantum statistics.

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.

Effects of time-periodic linear coupling on two-component Bose-Einstein condensates in two dimensions

We examine two-component Gross-Pitaevskii equations with nonlinear and linear couplings, assuming self-attraction in one species and self-repulsion in the other, while the nonlinear inter-species coupling is also repulsive. For initial states with the condensate placed in the self-attractive component, a sufficiently strong linear coupling switches the collapse into decay (in the free space). Setting the linear-coupling coefficient to be time-periodic (alternating between positive and negative values, with zero mean value) can make localized states quasi-stable for the parameter ranges considered herein, but they slowly decay. The 2D states can then be completely stabilized by a weak trapping potential. In the case of the high-frequency modulation of the coupling constant, averaged equations are derived, which demonstrate good agreement with numerical solutions of the full equations. (C) 2007 Elsevier B.V. All rights reserved.

Solitons in Bose-Einstein condensates trapped in a double-well potential

We investigate, analytically and numerically, families of bright solitons in a system of two linearly coupled nonlinear Schrodinger/Gross-Pitaevskii equations, describing two Bose-Einstein condensates trapped in an asymmetric double-well potential, in particular, when the scattering lengths in the condensates have arbitrary magnitudes and opposite signs. The solitons are found to exist everywhere where they are permitted by the dispersion law. Using the Vakhitov-Kolokolov criterion and numerical methods, we show that, except for small regions in the parameter space, the solitons are stable to small perturbations. Some of them feature self-trapping of almost all the atoms in the condensate with no atomic interaction or weak repulsion is coupled to the self-attractive condensate. An unusual bifurcation is found, when the soliton bifurcates from the zero solution with vanishing amplitude and width simultaneously diverging but at a finite number of atoms in the soliton. By means of numerical simulations, it is found that, depending on values of the parameters and the initial perturbation, unstable solitons either give rise to breathers or completely break down into incoherent waves (radiation). A version of the model with the self-attraction in both components, which applies to the description of dual-core fibers in nonlinear optics, is considered too, and new results are obtained for this much studied system. (C) 2003 Elsevier B.V. All rights reserved.

Bose-Einstein condensation for general dispersion relations

Bose-Einstein condensation in an ideal (i.e. interactionless) boson gas can be studied analytically, at university-level statistical and solid state physics, in any positive dimensionality (d > 0) for identical bosons with any positive-exponent (s > 0) energy-momentum (i.e. dispersion) relation. Explicit formulae with arbitrary dls are discussed for: the critical temperature (non-zero only if d/s > 1); the condensate fraction; the internal energy; and the constant-volume specific heat (found to possess a jump discontinuity only if d/s > 2) Classical results are recovered at sufficiently high temperatures. Applications to ordinary' Bose-Einstein condensation, as well as to photons, phonons, ferro-and antiferromagnetic magnons, and (very specially) to Cooper pairs in superconductivity, are mentioned.

Liquid-gas phase transition in Bose-Einstein condensates with time evolution

We study the effects of a repulsive three-body interaction on a system of trapped ultracold atoms in a Bose-Einstein condensed state. The stationary solutions of the corresponding s-wave nonlinear Schrödinger equation suggest a scenario of first-order liquid-gas phase transition in the condensed state up to a critical strength of the effective three-body force. The time evolution of the condensate with feeding process and three-body recombination losses has a different characteristic pattern. Also, the decay time of the dense (liquid) phase is longer than expected due to strong oscillations of the mean-squared radius.