On Two-Component Dark-Bright Solitons in Three-dimensional Atomic Bose-Einstein Condensates

Abstract

In the present work, we revisit two-component Bose-Einstein condensates in their fully three-dimensional (3d) form. Motivated by earlier studies of dark-bright solitons in the 1d case, we explore the stability of these structures in their fully 3d form in two variants. In one the dark soliton is planar and trapping a planar bright (disk) soliton. In the other case, a dark spherical shell soliton creates an effective potential in which a bright spherical shell of atoms is trapped in the second component. We identify these solutions as numerically exact states (up to a prescribed accuracy) and perform a Bogolyubov-de Gennes linearization analysis that illustrates that both structures can be dynamically stable in suitable intervals of sufficiently low chemical potentials. We corroborate this finding theoretically by analyzing the stability via degenerate perturbation theory near the linear limit of the system. When the solitary waves are found to be unstable, we explore their dynamical evolution via direct numerical simulations which, in turn, reveal novel waveforms that are more robust. Finally, using the SO$(2)$ symmetry of the model, we produce multi-dark-bright planar or shell solitons involved in pairwise oscillatory motion.

11 pages, 5 figures

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Cited by in corpus (10)

• Ring dark solitons in three-dimensional Bose-Einstein condensates
• Dark-dark soliton breathing patterns in multi-component Bose-Einstein condensates
• Solitons in Nonlinear Systems and Eigen-states in Quantum Wells
• Instabilities of vortex-ring-bright soliton in trapped binary 3D Bose-Einstein condensates
• Dark-bright solitons in spinor polariton condensates under nonresonant pumping
• Vortex precession dynamics in general radially symmetric potential traps in two-dimensional atomic Bose-Einstein condensates
• Controlled engineering of a vortex-bright soliton dynamics using a constant driving force
• Systematic vector solitary waves from their linear limits in one-dimensional $n$-component Bose-Einstein condensates
• Adiabatic invariant analysis of dark and dark-bright soliton stripes in two-dimensional Bose-Einstein condensates
• Probing non-locality of interactions in a Bose-Einstein Condensate using solitons