  We study the transverse expansion of arrays of ultracold $^{87}$Rb atoms
weakly confined in tubes created by a 2D optical lattice, and observe that
transverse expansion is delayed because of mutual atom interactions. A
mean-field model of a coupled array shows that atoms become localized within a
roughly square fort-like self-trapping barrier with time-evolving edges. But
the observed dynamics is poorly described by the mean-field model. Theoretical
introduction of random phase fluctuations among tubes improves the agreement
with experiment, but does not correctly predict the density at which the atoms
start to expand with larger lattice depths. Our results suggest a new type of
self-trapping, where quantum correlations suppress tunneling even when there
are no density gradients.
