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

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 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.