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Nonlinear Dynamics of Bloch Wave Packets in Honeycomb Lattices Read chapter Read first chapter

2013 | OriginalPaper | Chapter

Bright Solitary Matter Waves: Formation, Stability and Interactions

Authors : T. P. Billam, A. L. Marchant, S. L. Cornish, S. A. Gardiner, N. G. Parker

Published in: Spontaneous Symmetry Breaking, Self-Trapping, and Josephson Oscillations

Publisher: Springer Berlin Heidelberg

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Abstract

In recent years, bright soliton-like structures composed of gaseous Bose–Einstein condensates have been generated at ultracold temperature. The experimental capacity to precisely engineer the nonlinearity and potential landscape experienced by these solitary waves offers an attractive platform for fundamental study of solitonic structures. The presence of three spatial dimensions and trapping implies that these are strictly distinct objects to the true soliton solutions. Working within the zero-temperature mean-field description, we explore the solutions and stability of bright solitary waves, as well as their interactions. Emphasis is placed on elucidating their similarities and differences to the true bright soliton. The rich behaviour introduced in the bright solitary waves includes the collapse instability and asymmetric collisions. We review the experimental formation and observation of bright solitary matter waves to date, and compare to theoretical predictions. Finally we discuss some topical aspects, including beyond-mean-field descriptions, symmetry breaking, exotic bright solitary waves, and proposals to exploit bright solitary waves in interferometry and as surface probes.

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previous chapter From Coherent Modes to Turbulence and Granulation of Trapped Gases
next chapter Temporal Quantum Fluctuations in the Fringe-Visibility of Atom Interferometers with Interacting Bose-Einstein Condensate
Footnotes
1
Note that in works that focus specifically on fully trapped condensates, \(k\) is more commonly defined in terms of a geometric average of trap frequencies (e.g. Refs. [11, 15‐24]). The radial harmonic oscillator length here is advantageous as it allows us to readily consider the case of zero axial trapping \((\lambda=0).\)
 
2
Specifically, the criteria \(\hbar \omega_r \gg \mu\) and \(\hbar \omega_r \gg k_{\rm B}T\) are required to ensure that the condensate and thermal energy scales are insufficient to excite the radial modes.
 
3
In contrast to our definition here, a common convention in the literature is to define an amplitude A such that the norm is \(2A\) [59].
 
4
It is also possible to consider solitary waves having the form of higher-energy nonlinear eigenstates; such eigenstates were considered in Ref. [89].
 
5
Such a velocity is imparted numerically by applying a spatially varying phase of \(e^{\pm i m v x/\hbar}.\) Experimentally, this could be achieved by applying a linear external potential to each solitary wave for a short time.
 
6
The GPE is based on the assumption of atomic scattering at low energy and momentum and so by “high velocity” here we refer to a scale relative to the condensate’s natural speed scale of the speed of sound \(c=\sqrt{4 \pi \hbar a_s n/m^2}\) [3].
 
7
Eventually, the effects of the variation in the external trap potential across the collisions could lead to the break-up of solitary waves in the 1D GPE. However, this does not seem to occur on timescales easily accessible to numerical simulation; instead the numerical errors grow faster than the deviation from the soliton-like behaviour.
 
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Metadata
Title
Bright Solitary Matter Waves: Formation, Stability and Interactions
Authors
T. P. Billam
A. L. Marchant
S. L. Cornish
S. A. Gardiner
N. G. Parker
Copyright Year
2013
Publisher
Springer Berlin Heidelberg
Book
Spontaneous Symmetry Breaking, Self-Trapping, and Josephson Oscillations

Print ISBN: 978-3-642-21206-2

Electronic ISBN: 978-3-642-21207-9

Copyright Year: 2013

DOI
https://doi.org/10.1007/10091_2012_20

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