Many-body effects in near-resonant Kapitza-Dirac diffraction: The nonlinear Pendellosung

We investigate the modifications of the Pendello$iuml-sung of near-resonant Kapitza-Dirac diffraction due to many-body effects. For the case of ''two-beam'' doppleron (velocity-tuned) resonances, we find that in the absence of dissipation, the population oscillations between diffraction orders, which are complete in the linear case, can either be decreased in frequency, or become partial, or even be completely suppressed, in which case the system evolves to a quasistationary state where the atoms are in a coherent superposition of their upper and lower excited states. The influence of spontaneous emission on these predictions is then studied by numerically solving the effective single-atom Hartree-Fock master equation of nonlinear atom optics. We find that spontaneous emission is not detrimental in weakly allowed transitions, in which case the predicted effects survive for several spontaneous lifetimes.