Coherent atomic deflection by resonant standing waves

We extend the previous theoretical treatment of standing-wave deflection of two-level atoms to include nonresonant excitation, nonorthogonal laser and atomic beams, and excitation duration upper bounded only by atomic relaxation times. Numerically solving equations analogous to those of abruptly initiated multilevel atomic excitation, we find bounds on the maximum deflection fixed by balancing acquired kinetic energy against interaction energy. We find that frequency detuning or nonorthogonal orientation of laser and atomic beams can enhance the deflection and, given sufficiently long interaction time, one can observe deflections at larger discrete angles. We comment on the connection between these Bragg scatterings and multiphoton resonances.