  One of the most intriguing phenomena in physics is the localization of waves
in disordered media. This phenomenon was originally predicted by Anderson,
fifty years ago, in the context of transport of electrons in crystals. Anderson
localization is actually a much more general phenomenon, and it has been
observed in a large variety of systems, including light waves. However, it has
never been observed directly for matter waves. Ultracold atoms open a new
scenario for the study of disorder-induced localization, due to high degree of
control of most of the system parameters, including interaction. Here we employ
for the first time a noninteracting Bose-Einstein condensate to study Anderson
localization. The experiment is performed with a onedimensional quasi-periodic
lattice, a system which features a crossover between extended and exponentially
localized states as in the case of purely random disorder in higher dimensions.
Localization is clearly demonstrated by investigating transport properties,
spatial and momentum distributions. We characterize the crossover, finding that
the critical disorder strength scales with the tunnelling energy of the atoms
in the lattice. Since the interaction in the condensate can be controlled at
will, this system might be employed to solve open questions on the interplay of
disorder and interaction and to explore exotic quantum phases.
