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

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.

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Cited by in corpus (11)

• Non-Hermitian Euclidean random matrix theory
• Eigenvalue distributions of large Euclidean random matrices for waves in random media
• Localization of Bogoliubov quasiparticles in interacting Bose gases with correlated disorder
• Transport regimes of cold gases in a two-dimensional anisotropic disorder
• Confinement-induced p-wave resonances from s-wave interactions
• Random matrix ensembles with column/row constraints: part I
• Quantum state engineering with a trapped atom and a set of static impurities
• Optical lattices with large scattering length: Using few-body physics to simulate an electron-phonon system
• Statistical analysis of chiral structured ensembles: role of matrix constraints
• Matter waves in two-dimensional arbitrary atomic crystals
• Matter Waves in Atomic Artificial Graphene