84 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
Multiple atomic dark solitons in cigar-shaped Bose-Einstein condensates
We consider the stability and dynamics of multiple dark solitons in
cigar-shaped Bose-Einstein condensates (BECs). Our study is motivated by the
fact that multiple matter-wave dark solitons may naturally form in such
settings as per our recent work [Phys. Rev. Lett. 101, 130401 (2008)]. First,
we study the dark soliton interactions and show that the dynamics of
well-separated solitons (i.e., ones that undergo a collision with relatively
low velocities) can be analyzed by means of particle-like equations of motion.
The latter take into regard the repulsion between solitons (via an effective
repulsive potential) and the confinement and dimensionality of the system (via
an effective parabolic trap for each soliton). Next, based on the fact that
stationary, well-separated dark multi-soliton states emerge as a nonlinear
continuation of the appropriate excited eigensates of the quantum harmonic
oscillator, we use a Bogoliubov-de Gennes analysis to systematically study the
stability of such structures. We find that for a sufficiently large number of
atoms, multiple soliton states may be dynamically stable, while for a small
number of atoms, we predict a dynamical instability emerging from resonance
effects between the eigenfrequencies of the soliton modes and the intrinsic
excitation frequencies of the condensate. Finally we present experimental
realizations of multi-soliton states including a three-soliton state consisting
of two solitons oscillating around a stationary one.Comment: 17 pages, 11 figure
Rigorous mean-field dynamics of lattice bosons: Quenches from the Mott insulator
We provide a rigorous derivation of Gutzwiller mean-field dynamics for
lattice bosons, showing that it is exact on fully connected lattices. We apply
this formalism to quenches in the interaction parameter from the Mott insulator
to the superfluid state. Although within mean-field the Mott insulator is a
steady state, we show that a dynamical critical interaction exists, such
that for final interaction parameter the Mott insulator is
exponentially unstable towards emerging long-range superfluid order, whereas
for the Mott insulating state is stable. We discuss the implications
of this prediction for finite-dimensional systems.Comment: 6 pages, 3 figures, published versio
Dark solitons in atomic Bose-Einstein condensates: from theory to experiments
This review paper presents an overview of the theoretical and experimental
progress on the study of matter-wave dark solitons in atomic Bose-Einstein
condensates. Upon introducing the general framework, we discuss the statics and
dynamics of single and multiple matter-wave dark solitons in the quasi
one-dimensional setting, in higher-dimensional settings, as well as in the
dimensionality crossover regime. Special attention is paid to the connection
between theoretical results, obtained by various analytical approaches, and
relevant experimental observations.Comment: 82 pages, 13 figures. To appear in J. Phys. A: Math. Theor
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
Quantum transport in ultracold atoms
Ultracold atoms confined by engineered magnetic or optical potentials are
ideal systems for studying phenomena otherwise difficult to realize or probe in
the solid state because their atomic interaction strength, number of species,
density, and geometry can be independently controlled. This review focuses on
quantum transport phenomena in atomic gases that mirror and oftentimes either
better elucidate or show fundamental differences with those observed in
mesoscopic and nanoscopic systems. We discuss significant progress in
performing transport experiments in atomic gases, contrast similarities and
differences between transport in cold atoms and in condensed matter systems,
and survey inspiring theoretical predictions that are difficult to verify in
conventional setups. These results further demonstrate the versatility offered
by atomic systems in the study of nonequilibrium phenomena and their promise
for novel applications.Comment: 24 pages, 7 figures. A revie
Shape Parameterisation Based on Freeform Deformation in Aerodynamic Design Optimization
Shape parameterisation has been identified as an important task for aerodynamic design optimization. A method based on freeform deformation has been established, which enables in combination with grid generation software parameter-controlled variations of given shapes. The applicability and flexibility of the method for aerodynamic wing shape optimization has been demonstrated. For verification of the method airfoil recovery tests have been performed
Einfuerung diskontinuierlicher Blockraender in ein blockstrukturiertes Zelleneckpunkt-Finite-Volumen-Verfahren
Shape Parametrization Using Freeform Deformation
Shape parametrization has been identified as an import issue in aerodynamic design optimization based on high-fidelity CFD-methods. For given shapes, which are available as CAD-models, post-parametrization method, based on freeform deformation, has been established to simplify and to automate the generation of geometrical variants to be used for CFD analyses. To create the necessary deformation lattices, structured grid generation techniques of a grid generation system, developed at DLR, are utilized. As this grid generation system has the salient feature to store and to replay a sequence of processes with different parameter settings, modifications of shapes, given by polygonal curves and surfaces can be performed instantly. The present freeform deformation method has reached a state, where it can be integrated into design loops to handle a variety of shape optimization tasks. In two examples the applicability of the method for aerodynamic wing design and detailed design of a wing tip is demonstrated
Post-Parameterization of Complex CAD-Based Aircraft-Shapes Using Freeform Deformation
A post-parameterization method, based on free-form deformation techniques, has been established to simplify and to automate the generation of geometrical variants from existing CAD-models, to be used for CFD analyses. To create the necessary deformation lattices, structured grid generation techniques of a grid generation system, developed at DLR, are utilized. As this grid generation system has the salient feature to store and to replay a sequence of processes with different parameter settings, modifications of shapes, given by polygonal curves and surfaces, can be controlled quantitatively. Presently strategies and recipes are investigated for routinely use of this method in applied aerodynamics
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