Quantitative study of two- and three-dimensional strong localization of matter waves by atomic scatterers

Mauro Antezza (1) , Yvan Castin (1) , David Hutchinson (2)

1 LKB (Lhomond) - Laboratoire Kastler Brossel
2 The Jack Dodd Center for Quantum Technology

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.

Mots clés: Anderson localization; strong localization; ultracold atoms; optical lattices; localization length; matter waves; disorder; 2D systems

Domaines: Gaz Quantiques [cond-mat.quant-gas]; Mécanique statistique [cond-mat.stat-mech]; Systèmes désordonnés et réseaux de neurones [cond-mat.dis-nn]

Mauro Antezza, Yvan Castin, David Hutchinson. Quantitative study of two- and three-dimensional strong localization of matter waves by atomic scatterers. Physical Review A : Atomic, molecular, and optical physics [1990-2015], 2010, 82, pp.043602. ⟨10.1103/PhysRevA.82.043602⟩. ⟨hal-00494324v2⟩