We present an ab initio study of the ground state of an ideal coupled
two-component gas of ultracold atoms in a one dimensional optical lattice,
either bosons or fermions. Due to the internal two-level structure of the
atoms, the Brillouin zone is twice as large as imposed by the periodicity of
the lattice potential. This is reflected in the Bloch dispersion curves, where
the energy bands regularly possess several local minima. As a consequence, when
the system parameters are tuned across a resonance condition, a non-zero
temperature phase transition occurs which arises from an interplay between
internal and kinetic atomic energies. For fermions, this phase transition is of
topological character since the structure of the Fermi surface is changed
across the critical value. It is shown that these phenomena are also expected
to occur for two and three dimensional optical lattices.Comment: 10 pages, 7 figure