  We study the two-body bound and scattering states of two particles in a one
dimensional optical lattice in the presence of a coherent coupling between two
internal atomic levels. Due to the interplay between periodic potential,
interactions and coherent coupling, the internal structure of the bound states
depends on their center of mass momentum. This phenomenon corresponds to an
effective momentum-dependent magnetic field for the dimer pseudo-spin, which
could be observed in a chirping of the precession frequency during Bloch
oscillations. The essence of this effect can be easily interpreted in terms of
an effective bound state Hamiltonian. Moreover for indistinguishable bosons,
the two-body eigenstates can present simultaneously attractive and repulsive
bound-state nature or even bound and scattering properties.
