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arXiv:1210.1681 · Applied Sciences

Scattering of Matter Wave Solitons on Localized Potentials

Sidse Damgaard Hansen, Nicolai Gayle Nygaard, Klaus Mølmer

Published Mar 5, 2021• 9 citations
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Abstract

We study the reflection and transmission properties of matter wave solitons impinging on localized scattering potentials in one spatial dimension. By mean field analysis we identify regimes where the solitons behave more like waves or more like particles as a result of the interplay between the dispersive wave propagation and the attractive interactions between the atoms. For a bright soliton propagating together with a dark soliton void in a two-species Bose-Einstein condensate, we find different reflection and transmission properties of the dark and the bright components.

DOI
10.3390/app11052294

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We study the reflection and transmission properties of matter wave solitons impinging on localized scattering potentials in one spatial dimension. By mean field analysis we identify regimes where the solitons behave more like waves or more like particles as a result of the interplay between the dispersive wave propagation and the attractive interactions between the atoms. For a bright soliton propagating together with a dark soliton void in a two-species Bose-Einstein condensate, we find different reflection and transmission properties of the dark and the bright components.
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Adopting a mean-field description for a two-component atomic Bose-Einstein condensate, we study the statics and dynamics of dark-bright solitons in the presence of localized impurities. We use adiabatic perturbation theory to derive an equation of motion for the dark-bright soliton center. We show that, counterintuitively, an attractive (repulsive) delta-like impurity, acting solely on the bright-soliton component, induces an effective localized barrier (well) in the effective potential felt by the soliton; this way, dark-bright solitons are reflected from (transmitted through) attractive (repulsive) impurities. Our analytical results for the small-amplitude oscillations of solitons are found to be in good agreement with results obtained via a Bogoliubov--de Gennes analysis and direct numerical simulations.
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Bright solitons are non-dispersive wave solutions, arising in a diverse range of nonlinear, one-dimensional systems, including atomic Bose-Einstein condensates with attractive interactions. In reality, cold-atom experiments can only approach the idealized one-dimensional limit necessary for the realization of true solitons. Nevertheless, it remains possible to create bright solitary waves, the three-dimensional analogue of solitons, which maintain many of the key properties of their one-dimensional counterparts. Such solitary waves offer many potential applications and provide a rich testing ground for theoretical treatments of many-body quantum systems. Here we report the controlled formation of a bright solitary matter-wave from a Bose-Einstein condensate of (85)Rb, which is observed to propagate over a distance of ∼1.1 mm in 150 ms with no observable dispersion. We demonstrate the reflection of a solitary wave from a repulsive Gaussian barrier and contrast this to the case of a repulsive condensate, in both cases finding excellent agreement with theoretical simulations using the three-dimensional Gross-Pitaevskii equation.
In this work, we examine the collision of an atomic dark–bright soliton, in a two-component Bose–Einstein condensate, with a Gaussian barrier or well. Our study has both an experimental component and a theoretical/computational one. First, we present the results of an experiment, illustrating the classical particle phenomenology (transmission or reflection) in the case of an equal barrier in both components. Then, motivated by the experimental observations, we perform systematic simulations considering not only the case of equal heights of a barrier (or a well), but also the considerably more complex setting, where the potential affects only one of the two components. We systematically classify the ensuing cases within a two-parameter diagram of potential amplitudes in the two components, and provide intuitive explanations for the resulting observations, as well as of their variations as the strength of the potential changes.