  We introduce a simple set--up corresponding to the matter-wave analogue of
impurity atoms embedded in an infinite photonic crystal and interacting with
the radiation field. Atoms in a given internal level are trapped in an optical
lattice, and play the role of the impurities. Atoms in an untrapped level play
the role of the radiation field. The interaction is mediated by means of lasers
that couple those levels. By tuning the lasers parameters, it is possible to
drive the system through different regimes, and observe phenomena like matter
wave superradiance, non-Markovian atom emission, and the appearance of bound
atomic states.
