  We report the first experimental observation of nonlinear self-trapping of
Bose-condensed 87Rb atoms in a one dimensional waveguide with a superimposed
deep periodic potential . The trapping effect is confirmed directly by imaging
the atomic spatial distribution. Increasing the nonlinearity we move the system
from the diffusive regime, characterized by an expansion of the condensate, to
the nonlinearity dominated self-trapping regime, where the initial expansion
stops and the width remains finite. The data are in quantitative agreement with
the solutions of the corresponding discrete nonlinear equation. Our results
reveal that the effect of nonlinear self-trapping is of local nature, and is
closely related to the macroscopic self-trapping phenomenon already predicted
for double-well systems.
