Self-Trapping dynamics in a 2D optical lattice

We present a variational mean field model used to characterize our recent experiments on the expansion dynamics of an ultra cold gas of $^{87}$Rb atoms initially trapped in a two dimensional optical lattice. The expansion is driven by suddenly turning off the harmonic confinement potentials in all directions. \textit{In situ} measurements of the density profile vs time were performed for different lattice depths. The observed dynamics are characterized by an initial suppression of the transverse dynamics, followed by a ballistic expansion across the lattice after the initial interaction energy is converted into kinetic energy along the free expanding axial direction. The slow initial expansion is predicted to be a manifestation of macroscopic self-trapping. We present comparisons between our variational model and the measured profiles.