Three-dimensional strong localization of matter waves by scattering from atoms in a lattice with a confinement-induced resonance

The possibility of using ultracold atoms to observe strong localization of matter waves is now a subject of great interest, as undesirable decoherence and interactions can be made negligible in these systems. It was proposed that a static-disordered potential can be realized by trapping atoms of a given species in randomly chosen sites of a deep three-dimensional (3D) optical lattice with no multiple occupation. We analyze in detail the prospects of this scheme for observing localized states in 3D for a matter wave of a different atomic species that interacts with the trapped particles and that is sufficiently far detuned from the optical lattice to be insensitive to it. We demonstrate that at low energy a large number of 3D strongly localized states can be produced for the matter wave, if the effective scattering length describing the interaction of the matter wave with a trapped atom is of the order of the mean distance between the trapped particles. Such high values of the effective scattering length can be obtained by using a Feshbach resonance to adjust the free-space interspecies scattering length and by taking advantage of confinement-induced resonances induced by the trapping of the scatterers in the lattice.