  An ultracold gas of coupled two-component atoms in an optical field is
studied. Due to the internal two-level structure of the atoms, three competing
energy terms exist; atomic kinetic, atomic internal, and atom-atom interaction
energies. A novel outcome of this interplay, not present in the regular
Bose-Hubbard model, is that in the single band and tight binding approximations
four different phases appear: two superfluid and two Mott phases. When passing
through the critical point between the two superfluid or the two Mott phases, a
swapping of the internal atomic populations takes place. By means of the strong
coupling expansion, we find the full phase diagram for the four different
phases.
