Computational studies of dipole-dipole interactions among Stark manifold states

In our experiment, we excite ultra-cold atoms in a magneto-optical trap to Rydberg states in a Stark manifold ($n \sim 35$). An external electric field tunes the states such that a pair of atoms can resonantly exchange energy. One atom transitions to the $(n+1)$ manifold and the other to the $(n-1)$ manifold. We present the results of a computational model of this interaction which includes as many as 6 atoms. We examine many-body effects and redistribution of initial atomic population among the densely packed manifold states.