Analysis of spontaneous emission of a lattice trapped atom into free space

It has been predicted \footnote{I. de Vega \textit{et al.}, Phys. Rev. Lett. \textbf{101}, 260404 (2008) } that an atom confined in an optical lattice well that is coupled to free space through an internal state transition can exhibit behavior analogous to that of spontaneous emission in a photonic band gap material. We have recently performed a detailed theoretical analysis of such a system in a 1D geometry, including the lattice- confined population evolution, the momentum distribution of the emitted matter waves, and the structure of an evanescent matter-wave state below the continuum boundary \footnote{ M. Stewart \textit{et al.}, Phys. Rev. A \textbf{ 95 }, 013626 (2017) }. We compare our results for the transition from Markovian to non-Markovian behaviors to those previously obtained for three dimensions, and propose an experimental realization of the system.