Quantum motion effects in an ultracold-atom Mach-Zehnder interferometer

We study the effect of quantum motion in a Mach-Zehnder interferometer where ultracold, two-level atoms cross a $\pi/2$-$\pi$-$\pi/2$ configuration of separated, laser illuminated regions. Explicit and exact expressions are obtained for transmission amplitudes of monochromatic, incident atomic waves using recurrence relations which take into account all possible paths: the direct ones usually considered in the simple semiclassical treatment, but including quantum motion corrections, and the paths in which the atoms are repeatedly reflected at the fields.