Anderson localization of matterwaves in optical speckle

Anderson localization is ubiquitous in wave physics as it originates from the interference between multiple scattering paths, and this has prompted an intense activity to observe it with light waves, microwaves, sound waves, and electron gases, but there was no direct observation of exponential spatial localization of matter-waves (electrons or others). We will present recent theoretical prospects as well as experiments demonstrating directly exponential localization of the wave function using ultracold atoms released into a one-dimensional wave-guide for matter waves, in the presence of a controlled disorder created by laser speckle. We will also discuss possibilities to extend this study to quantum gases in higher dimensions (2D and 3D) and with controlled interactions. We will show that random potentials resulting from laser speckle form an original class of disorder and we will discuss the impact of their original properties on the behavior of localization in 1D geometry.