2 research outputs found
Experimental observation of oscillating and interacting matter wave dark solitons
We report on the generation, subsequent oscillation and interaction of a pair
of matter wave dark solitons. These are created by releasing a Bose-Einstein
condensate from a double well potential into a harmonic trap in the crossover
regime between one dimension (1D) and three dimensions (3D). The oscillation of
the solitons is observed and the frequency is in quantitative agreement with
simulations using the Gross-Pitaevskii equation. An effective particle picture
is developed and reveals that the deviation of the observed frequencies from
the asymptotic prediction , where is the
longitudinal trapping frequency, results from the dimensionality of the system
and the interaction between the solitons.Comment: 5 pages, 3 figure
Nonlinear Waves in Bose-Einstein Condensates: Physical Relevance and Mathematical Techniques
The aim of the present review is to introduce the reader to some of the
physical notions and of the mathematical methods that are relevant to the study
of nonlinear waves in Bose-Einstein Condensates (BECs). Upon introducing the
general framework, we discuss the prototypical models that are relevant to this
setting for different dimensions and different potentials confining the atoms.
We analyze some of the model properties and explore their typical wave
solutions (plane wave solutions, bright, dark, gap solitons, as well as
vortices). We then offer a collection of mathematical methods that can be used
to understand the existence, stability and dynamics of nonlinear waves in such
BECs, either directly or starting from different types of limits (e.g., the
linear or the nonlinear limit, or the discrete limit of the corresponding
equation). Finally, we consider some special topics involving more recent
developments, and experimental setups in which there is still considerable need
for developing mathematical as well as computational tools.Comment: 69 pages, 10 figures, to appear in Nonlinearity, 2008. V2: new
references added, fixed typo