  Behavior analogous to that of spontaneous emission in photonic band gap
materials has been predicted for an atom-optical system consisting of an atom
confined in a well of a state-dependent optical lattice that is coupled to free
space through an internal-state transition [de Vega et al., Phys. Rev. Lett.
101, 260404 (2008)]. Using the Weisskopf-Wigner approach and considering a
one-dimensional geometry, we analyze the properties of this system in detail,
including the evolution of the lattice-trapped population, the momentum
distribution of emitted matter waves, and the detailed structure of an
evanescent matter-wave state below the continuum boundary. We compare and
contrast our findings for the transition from Markovian to non-Markovian
behaviors to those previously obtained for three dimensions.
