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Localization of ultracold atoms in a disordered potential at three dimensions

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Studying disordered systems is of utmost interest: they lie at the heart of many fundamental phenomena, such as Anderson localization in disordered electronic conductors, superfluidity in porous media, and possibly high-Tc superconductivity. In spite of extensive studies, the understanding of such systems remains an exciting but formidable task, many issues still being unresolved or even controversial. Anderson Localization is the most emblematic effect of disorder, describing the appearance of localized states due to interference between many scattering amplitudes associated with the diffusion of a single quantum particle.In fact, Anderson Localization depends strongly on the dimension. A quantum phase transition around a mobility edge is predicted in three dimensions. This mobility edge corresponds to an energy threshold separating localized from extended states. Determining the value of that mobility edge, for which only a scaling law is predicted, and exploring the critical regime around it remains a challenge for microscopic theory, numerical simulations, and experiments. In my talk I will present our recent experimental results on Localization. To investigate the open questions about the transition, we transposed the successful scheme that allowed for the observation of one-dimensional Anderson Localization to the three dimensional case. In our experiments, we monitored the three-dimensional expansion of an initial BEC in the presence of a quasi-isotropic laser speckle disorder and observed an atomic cloud composed of two components: a localized and a diffusive part. These components respectively correspond to energy levels below and above the mobility edge. Altogether, those experiments allowed us to report the first evidence of threedimensional Anderson localization of ultracold atoms in the presence of a well-controlled optical disorder. This marks a first step towards the precise investigation of the critical behavior around the mobility edge with ultracold atoms.

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