Hyper-transport of light and stochastic acceleration by evolving disorder

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.

Nonlinear periodic lattices occur in a large variety of systems, such as biological molecules, nonlinear optical waveguides, solid-state systems and Bose-Einstein condensates. The underlying dynamics in these systems is dominated by the interplay between tunnelling between adjacent potential wells and nonlinearity. A balance between these two effects can result in a self-localized state: a lattice or 'discrete' soliton. Direct observation of lattice solitons has so far been limited to one-dimensional systems, namely in arrays of nonlinear optical waveguides. However, many fundamental features are expected to occur in higher dimensions, such as vortex lattice solitons, bright lattice solitons that carry angular momentum, and three-dimensional collisions between lattice solitons. Here, we report the experimental observation of two-dimensional (2D) lattice solitons. We use optical induction, the interference of two or more plane waves in a photosensitive material, to create a 2D photonic lattice in which the solitons form. Our results pave the way for the realization of a variety of nonlinear localization phenomena in photonic lattices and crystals. Finally, our observation directly relates to the proposed lattice solitons in Bose-Einstein condensates, which can be observed in optically induced periodic potentials.