Matter wave beam splitters in gravito-inertial and trapping potentials: generalized ttt scheme for atom interferometry

I present a strong field theory of matter wave splitting in the presence of various gravitational, inertial and trapping potentials. The effect of these potentials on both the resonance condition (between the splitting potential and considered effective two-level systems) and the atomic Borrmann effect is investigated in detail. Then I express this triple interaction "matter - splitting potential - gravito-inertial and trapping potentials" as an equivalent instantaneous interaction (generalized ttt scheme) which turns out to be a very efficient tool for the modeling of atom interferometers. Finally, I detail this beam splitter modeling for the particular case of a uniform and constant acceleration, and I bring to light some non-trivial corrections to the usual atom gravimeters phase shift expression.