  We experimentally study one-dimensional, lattice-modulated Bose gases in the
presence of an uncorrelated disorder potential formed by localized impurity
atoms, and compare to the case of correlated quasi-disorder formed by an
incommensurate lattice. While the effects of the two disorder realizations are
comparable deeply in the strongly interacting regime, both showing signatures
of Bose glass formation, we find a dramatic difference near the
superfluid-to-insulator transition. In this transition region, we observe that
random, uncorrelated disorder leads to a shift of the critical lattice depth
for the breakdown of transport as opposed to the case of correlated
quasi-disorder, where no such shift is seen. Our findings, which are consistent
with recent predictions for interacting bosons in one dimension, illustrate the
important role of correlations in disordered atomic systems.
