Quantitative study of 3D and 2D strong localization of matter waves by atomic scatterers

Yvan Castin

Kilian Müller, Fred Jendrzejewski, Alain Bernard +3 more

Mauro Antezza, Yvan Castin, David A. W. Hutchinson

We study the strong localization of atomic matter waves in a disordered potential created by atoms pinned at the nodes of a lattice, for both three-dimensional (3D) and two-dimensional (2D) systems. The localization length of the matter wave, the density of localized states, and the occurrence of energy mobility edges (for the 3D system), are numerically investigated as a function of the effective scattering length between the atomic matter wave and the pinned atoms. Both positive and negative matter wave energies are explored. Interesting features of the density of states are discovered at negative energies, where maxima in the density of bound states for the system can be interpreted in terms of bound states of a matter wave atom with a few pinned atomic scatterers. In 3D we found evidence of up to three mobility edges, one at positive energies, and two at negative energies, the latter corresponding to transitions between extended and localized bound states. In 2D, no mobility edge is found, and a rapid exponential-like increase of the localization length is observed at high energy.

Mauro Antezza

We study the strong localization of atomic matter waves in a disordered potential created by atoms pinnedat the nodes of a lattice, for both three-dimensional (3D) and two-dimensional (2D) systems. The localizationlength of the matter wave, the density of localized states, and the occurrence of energy mobility edges (for the 3Dsystem), are numerically investigated as a function of the effective scattering length between the atomic matterwave and the pinned atoms. Both positive and negative matter wave energies are explored. Interesting featuresof the density of states are discovered at negative energies, where maxima in the density of bound states for thesystem can be interpreted in terms of bound states of a matter wave atom with a few pinned atomic scatterers.In 3D we found evidence of up to three mobility edges, one at positive energies, and two at negative energies,the latter corresponding to transitions between extended and localized bound states. In 2D, no mobility edge isfound, and a rapid exponential-like increase of the localization length is observed at high energy.

Arnaud Landragin, Philippe Bouyer

Marie Piraud, Luca Pezzè, Laurent Sanchez-Palencia

The macroscopic transport properties in a disordered potential, namely diffusion and weak/strong localization, closely depend on the microscopic and statistical properties of the disorder itself.This dependence is rich in counter-intuitive consequences.It can be particularly exploited in matter wave experiments, where the disordered potential can be tailored and controlled, and anisotropies are naturally present.In this work, we apply a perturbative microscopic transport theory and the self-consistent theory of Anderson localization to study the transport properties of ultracold atoms in anisotropic two-dimensional (2D) and three-dimensional (3D) speckle potentials.In particular, we discuss the anisotropy of single-scattering, diffusion and localization.We also calculate disorder-induced shift of the energy states and propose a method to include it, which amounts to renormalizing energies in the standard on-shell approximation.We show that the renormalization of energies strongly affects the prediction for the 3D localization threshold (mobility edge).We illustrate the theoretical findings with examples which are relevant for current matter wave experiments, where the disorder is created with laser speckle.This paper provides a guideline for future experiments aiming at the precise location of the 3D mobility edge and study of anisotropic diffusion and localization effects in 2D and 3D.