Matter-wave gap solitons in atomic band-gap structures

We demonstrate that a Bose-Einstein condensate in an optical lattice forms a reconfigurable matter-wave structure with a band-gap spectrum, which resembles a nonlinear photonic crystal for light waves. We study in detail the case of a two-dimensional square optical lattice and show that this atomic band-gap structure allows nonlinear localization of atomic Bloch waves in the form of two-dimensional matter-wave gap solitons.