Three-dimensional gap solitons in Bose-Einstein condensates supported by one-dimensional optical lattices

Abstract

We study fundamental and compound gap solitons (GSs) of matter waves in one-dimensional (1D) optical lattices (OLs) in a three-dimensional (3D) weak-radial-confinement regime, which corresponds to realistic experimental conditions in Bose-Einstein condensates (BECs). In this regime GSs exhibit nontrivial radial structures. Associated with each 3D linear spectral band exists a family of fundamental gap solitons that share a similar transverse structure with the Bloch waves of the corresponding linear band. GSs with embedded vorticity $m$ may exist \emph{inside} bands corresponding to other values of $m$. Stable GSs, both fundamental and compound ones (including vortex solitons), are those which originate from the bands with lowest axial and radial quantum numbers. These findings suggest a scenario for the experimental generation of robust GSs in 3D settings.

5 pages, 5 figures; v2: matches published version

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• Fully Localized Two-dimensional Embedded Solitons
• Spontaneous symmetry breaking of photonic and matter waves in two-dimensional pseudopotentials
• Effective equations for matter-wave gap solitons in higher-order transversal states
• Accurate one-dimensional effective description of realistic matter-wave gap solitons
• A nonpolynomial Schroedinger equation for resonantly absorbing gratings
• Stable symmetry-protected 3D embedded solitons in Bose-Einstein condensates
• Stable single light bullets and vortices and their active control in cold Rydberg gases