Cold-atom optical lattices as quantum analog simulators for aperiodic one-dimensional localization without disorder

Cold-atom optical lattices allow for the study of quantum localization and mobility edges in a disorder-free environment. We predict the existence of an Anderson-like insulator with sharp mobility edges in a one-dimensional nearly periodic optical lattice. We show that the mobility edge manifests itself as the early onset of pinning in center of mass dipole oscillations in the presence of a magnetic trap, which should be observable in optical lattices.