Dark spherical shell solitons in three-dimensional Bose-Einstein condensates: Existence, stability and dynamics

Abstract

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 Bogolyubov-de Gennes spectrum. We compare our effective 1D spherical and 2D cylindrical computations with the full 3D 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 the resulting predictions such as the shell equilibrium radius, qualitatively and quantitatively, with full numerical solutions in 3D.

10 pages, 7 figures, for movie go to: http://nonlinear.sdsu.edu/~carreter/DSS.html

References in corpus (8)

• Oscillations and interactions of dark and dark-bright solitons in Bose-Einstein condensates
• Formation of bright matter-wave solitons during the collapse of Bose-Einstein condensates
• Experimental observation of oscillating and interacting matter wave dark solitons
• Stationary and non-stationary fluid flow of a Bose-Einstein condensate through a penetrable barrier
• Observation of Solitonic Vortices in Bose-Einstein Condensates
• Symmetry Breaking in Symmetric and Asymmetric Double-Well Potentials
• Dynamics of ring dark solitons in Bose-Einstein condensates and nonlinear optics
• Robust Vortex Lines, Vortex Rings and Hopfions in 3D Bose-Einstein Condensates

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• Single and Multiple Vortex Rings in Three-Dimensional Bose-Einstein Condensates: Existence, Stability and Dynamics
• Ring dark solitons in three-dimensional Bose-Einstein condensates
• Two infinite families of resonant solutions for the Gross-Pitaevskii equation
• Deflation-based Identification of Nonlinear Excitations of the 3D Gross--Pitaevskii equation
• Instabilities of vortex-ring-bright soliton in trapped binary 3D Bose-Einstein condensates
• Spectral and dynamical analysis of a single vortex ring in anisotropic harmonically trapped three-dimensional Bose-Einstein condensates
• On Two-Component Dark-Bright Solitons in Three-dimensional Atomic Bose-Einstein Condensates
• Vortex precession dynamics in general radially symmetric potential traps in two-dimensional atomic Bose-Einstein condensates
• Planar and Radial Kinks in Nonlinear Klein-Gordon Models: Existence, Stability and Dynamics
• Pairwise Interactions of Ring Dark Solitons with Vortices and other Rings: Stationary States, Stability Features and Nonlinear Dynamics
• Controlled engineering of a vortex-bright soliton dynamics using a constant driving force
• Dynamics of interacting dark soliton stripes
• Adiabatic invariant analysis of dark and dark-bright soliton stripes in two-dimensional Bose-Einstein condensates
• Stability of dark solitons in a bubble Bose-Einstein condensate
• Variational Approach to the Snake Instability of a Bose-Einstein Condensate Soliton