Matter wave interference using two-level atoms and resonant optical   fields
  A theory of matter wave interference is developed in which resonant optical fields interact with two-level atoms. When recoil effects are included, spatial modulation of the atomic density can occur for times that are greater than or comparable with the inverse recoil frequency. In this regime, the atoms exhibit matter-wave interference. Two specific atom field geometries are considered. In the first, atoms characterized by a homogeneous velocity distribution are subjected to a single radiation pulse. The pulse excites the atoms which then decay back to the lower state. The spatial modulation of the total atomic density is calculated as a function of $t$, where $t$ is the time following the pulse. In contrast to the normal Talbot effect, the spatially modulated density is not a periodic function of $ t,$ owing to spontaneous emission; however, after a sufficiently long time, the contribution from spontaneous processes no longer plays a role and the Talbot periodicity is restored. In the second atom-field geometry, there are two pulses separated by an interval $T$. The atomic velocity distribution in this case is assumed to be inhomogeneously broadened. In contrast to the normal Talbot-Lau effect, the spatially modulated density is not a periodic function of $T$, owing to spontaneous emission; however, for sufficiently long time, the contribution from spontaneous processes no longer plays a role and the Talbot periodicity is restored. The structure of the spatially modulated density is studied, and is found to mirror the atomic density following the first pulse. The spatially modulated atomic density serves as an indirect probe of the distribution of spontaneously emitted radiation. 
B. Dubetsky and P. R. Berman