A quantum particle placed in a disordered potential may be localized thanks to quantum interferences between the various the multiply scattered paths. This phenomenon – known as strong or Anderson localization – is a pure one-body effect. How particle-particle interaction affects Anderson localization is a difficult problem, far from being solved, with lots of open issues and contradictory predictions. Ultra-cold atomic gases can be prepared experimentally in well controlled disordered configurations and/or with tunable atom-atom interaction, opening the way to experimental answers. I will present a brief review of the experimental results obtained so far and will discuss, using quasi-exact numerical simulations, how typical few/many-body one-dimensional excitations, bright and dark solitons, behave in the presence of disorder.

Lab. Kastler-Brossel, UPMC ENS Paris