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arXiv:1001.4835 · Physical Review Letters

Stable Vortex–Bright-Soliton Structures in Two-Component Bose-Einstein Condensates

Kody J. H. Law, P. G. Kevrekidis, Laurette S. Tuckerman

Published Oct 15, 2010• 115 citations
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Abstract

We report the numerical realization of robust two-component structures in 2D and 3D Bose-Einstein condensates with nontrivial topological charge in one component. We identify a stable symbiotic state in which a higher-dimensional bright soliton exists even in a homogeneous setting with defocusing interactions, due to the effective potential created by a stable vortex in the other component. The resulting vortex-bright-solitons, generalizations of the recently experimentally observed dark-bright solitons, are found to be very robust both in the homogeneous medium and in the presence of external confinement.

DOI
10.1103/physrevlett.105.160405

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We report the numerical realization of robust two-component structures in 2D and 3D Bose-Einstein condensates with nontrivial topological charge in one component. We identify a stable symbiotic state in which a higher-dimensional bright soliton exists even in a homogeneous setting with defocusing interactions, due to the effective potential created by a stable vortex in the other component. The resulting vortex-bright-solitons, generalizations of the recently experimentally observed dark-bright solitons, are found to be very robust both in the homogeneous medium and in the presence of external confinement.
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In this work, we employ the SO(2)\mathrm{SO}(2)SO(2) rotations of a two-component, one-, two-, and three-dimensional nonlinear Schr\"odinger system at and near the Manakov limit to construct vector solitons and vortex structures. In this way, stable stationary dark-bright solitons and their higher-dimensional siblings are transformed into robust oscillatory dark-dark solitons (and generalizations thereof) with and without a harmonic confinement. By analogy to the one-dimensional case, vector higher-dimensional structures take the form of vortex-vortex states in two dimensions and, e.g., vortex-ring--vortex-ring ones in three dimensions. We consider the effects of unequal (self- and cross-) interaction strengths, where the SO(2)\mathrm{SO}(2)SO(2) symmetry is only approximately satisfied, showing the dark-dark soliton oscillation is generally robust. Similar features are found in higher dimensions too, although our examples suggest that phenomena such as phase separation may contribute to the associated dynamics. These results, in connection with the experimental realization of one-dimensional variants of such states in optics and Bose-Einstein condensates, suggest the potential observability of the higher-dimensional bound states proposed herein.
Motivated by recent experimental results, we present a systematic theoretical analysis of dark-bright-soliton interactions and multiple-dark-bright-soliton complexes in atomic two-component Bose-Einstein condensates. We study analytically the interactions between two dark-bright solitons in a homogeneous condensate and then extend our considerations to the presence of the trap. We illustrate the existence of robust stationary dark-bright-soliton ``molecules,'' composed of two or more solitons, which are formed due to the competition of the interaction forces between the dark- and bright-soliton components and the trap force. Our analysis is based on an effective equation of motion, derived for the distance between two dark-bright solitons. This equation provides equilibrium positions and characteristic oscillation frequencies of the solitons, which are found to be in good agreement with the eigenfrequencies of the anomalous modes of the system.
We study dark–bright (DB) ring solitons in two-component Bose–Einstein condensates. In the limit of large densities of the dark component, we describe the soliton dynamics by means of an equation of motion for the ring radius. The presence of the bright, 'filling' species is demonstrated to have a stabilizing effect on the ring dark soliton. Near the linear limit, we discuss the symmetry-breaking bifurcations of DB soliton stripes and vortex-bright soliton clusters from the DB ring and relate the stabilizing effect of filling to changes in the bifurcation diagram. Finally, we show that the stabilization by means of a second component is not limited to the radially symmetric structures, but can also be observed in a cross-like DB soliton configuration.
We have created spatial dark solitons in two-component Bose-Einstein condensates in which the soliton exists in one of the condensate components and the soliton nodal plane is filled with the second component. The filled solitons are stable for hundreds of milliseconds. The filling can be selectively removed, making the soliton more susceptible to dynamical instabilities. For a condensate in a spherically symmetric potential, these instabilities cause the dark soliton to decay into stable vortex rings. We have imaged the resulting vortex rings.
In this work we study spherical shell dark soliton states in three-dimensional atomic Bose-Einstein condensates. Their symmetry is exploited in order to analyze their existence, as well as that of topologically charged variants of the structures, and, importantly, to identify their linear stability Bogoliubov--de Gennes spectrum. We compare our effective one-dimensional spherical and two-dimensional cylindrical computations with the full three-dimensional numerics. An important conclusion is that such spherical shell solitons can be stable sufficiently close to the linear limit of the isotropic condensates considered herein. We have also identified their instabilities leading to the emergence of vortex line and vortex ring cages. In addition, we generalize effective particle pictures of lower-dimensional dark solitons and ring dark solitons to the spherical shell solitons concerning their equilibrium radius and effective dynamics around it. In this case too, we favorably compare, qualitatively and quantitatively, the resulting predictions such as the shell equilibrium radius with full numerical solutions in three dimensions.