Atomic three-grating Mach-Zehnder interferometry constitutes an important
tool to probe fundamental aspects of the quantum theory. There is, however, a
remarkable gap in the literature between the oversimplified models and robust
numerical simulations considered to describe the corresponding experiments.
Consequently, the former usually lead to paradoxical scenarios, such as the
wave-particle dual behavior of atoms, while the latter make difficult the data
analysis in simple terms. Here these issues are tackled by means of a simple
grating working model consisting of evenly-spaced Gaussian slits. As is shown,
this model suffices to explore and explain such experiments both analytically
and numerically, giving a good account of the full atomic journey inside the
interferometer, and hence contributing to make less mystic the physics
involved. More specifically, it provides a clear and unambiguous picture of the
wavefront splitting that takes place inside the interferometer, illustrating
how the momentum along each emerging diffraction order is well defined even
though the wave function itself still displays a rather complex shape. To this
end, the local transverse momentum is also introduced in this context as a
reliable analytical tool. The splitting, apart from being a key issue to
understand atomic Mach-Zehnder interferometry, also demonstrates at a
fundamental level how wave and particle aspects are always present in the
experiment, without incurring in any contradiction or interpretive paradox. On
the other hand, at a practical level, the generality and versatility of the
model and methodology presented, makes them suitable to attack analogous
problems in a simple manner after a convenient tuning.Comment: 17 pages, 6 figures (remarkably improved version
