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

TL;DR

This study investigates how atomic matter waves become strongly localized in disordered potentials created by pinned atoms, analyzing localization lengths, density of states, and mobility edges in 2D and 3D systems through numerical methods.

Contribution

It provides a detailed numerical analysis of matter wave localization, revealing multiple mobility edges in 3D and the absence of such edges in 2D, with insights into bound state features at negative energies.

Findings

Up to three mobility edges identified in 3D systems.

Density of states shows maxima at negative energies.

Localization length increases rapidly at high energy in 2D.

Abstract

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.