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An ultracold gas of coupled two-component atoms in an optical field isstudied. Due to the internal two-level structure of the atoms, three competingenergy terms exist; atomic kinetic, atomic internal, and atom-atom interactionenergies. A novel outcome of this interplay, not present in the regularBose-Hubbard model, is that in the single band and tight binding approximationsfour different phases appear: two superfluid and two Mott phases. When passingthrough the critical point between the two superfluid or the two Mott phases, aswapping of the internal atomic populations takes place. By means of the strongcoupling expansion, we find the full phase diagram for the four differentphases.

Coupling internal atomic states in a two-component Bose-Einstein condensate via an optical lattice: Extended Mott-superfluid transitions