Dynamical formation and interaction of bright solitary waves and solitons in the collapse of Bose-Einstein condensates with attractive interactions

We model the dynamics of formation of multiple, long-lived, bright solitary waves in the collapse of Bose-Einstein condensates with attractive interactions as studied in the experiment of Cornish et al. [Phys. Rev. Lett. 96 (2006) 170401]. Using both mean-field and quantum field simulation techniques, we find that while a number of separated wave packets form as observed in the experiment, they do not have a repulsive \pi phase difference that has been previously inferred. We observe that the inclusion of quantum fluctuations causes soliton dynamics to be predominantly repulsive in one dimensional simulations independent of their initial relative phase. However, indicative three-dimensional simulations do not support this conclusion and in fact show that quantum noise has a negative impact on bright solitary wave lifetimes. Finally, we show that condensate oscillations, after the collapse, may serve to deduce three-body recombination rates, and that the remnant atom number may still exceed the critical number for collapse for as long as three seconds independent of the relative phases of the bright solitary waves.Comment: 14 pages, 5 figure

Orbital Josephson effect and interactions in driven atom condensates on a ring

In a system of ac-driven condensed bosons we study a new type of Josephson effect occurring between states sharing the same region of space and the same internal atom structure. We first develop a technique to calculate the long time dynamics of a driven interacting many-body system. For resonant frequencies, this dynamics can be shown to derive from an effective time-independent Hamiltonian which is expressed in terms of standard creation and annihilation operators. Within the subspace of resonant states, and if the undriven states are plane waves, a locally repulsive interaction between bosons translates into an effective attraction. We apply the method to study the effect of interactions on the coherent ratchet current of an asymmetrically driven boson system. We find a wealth of dynamical regimes which includes Rabi oscillations, self-trapping, and chaotic behavior. In the latter case, a full many-body calculation deviates from the mean-field results by predicting large quantum fluctuations of the relative particle number.Comment: Published versio

Finite Temperature Models of Bose-Einstein Condensation

The theoretical description of trapped weakly-interacting Bose-Einstein condensates is characterized by a large number of seemingly very different approaches which have been developed over the course of time by researchers with very distinct backgrounds. Newcomers to this field, experimentalists and young researchers all face a considerable challenge in navigating through the `maze' of abundant theoretical models, and simple correspondences between existing approaches are not always very transparent. This Tutorial provides a generic introduction to such theories, in an attempt to single out common features and deficiencies of certain `classes of approaches' identified by their physical content, rather than their particular mathematical implementation. This Tutorial is structured in a manner accessible to a non-specialist with a good working knowledge of quantum mechanics. Although some familiarity with concepts of quantum field theory would be an advantage, key notions such as the occupation number representation of second quantization are nonetheless briefly reviewed. Following a general introduction, the complexity of models is gradually built up, starting from the basic zero-temperature formalism of the Gross-Pitaevskii equation. This structure enables readers to probe different levels of theoretical developments (mean-field, number-conserving and stochastic) according to their particular needs. In addition to its `training element', we hope that this Tutorial will prove useful to active researchers in this field, both in terms of the correspondences made between different theoretical models, and as a source of reference for existing and developing finite-temperature theoretical models.Comment: Detailed Review Article on finite temperature theoretical techniques for studying weakly-interacting atomic Bose-Einstein condensates written at an elementary level suitable for non-experts in this area (e.g. starting PhD students). Now includes table of content