  The coherence effects induced by external photons coupled to matter waves
inside a Mach-Zehnder three-grating interferometer are analyzed. Alternatively
to atom-photon entanglement scenarios, the model considered here only relies on
the atomic wave function and the momentum shift induced in it by the photon
scattering events. A functional dependence is thus found between the
observables, namely the fringe visibility and the phase shift, and the
transversal momentum transfer distribution. A good quantitative agreement is
found when comparing the results obtained from our model with the experimental
data.
