Mobility edges in bichromatic optical lattices

Abstract

We investigate the localization properties of single-particle eigenstates in bichromatic one-dimensional optical lattices. Whereas such a lattice with a sufficiently deep primary component and a suitably adjusted incommensurate secondary component provides an approximate realization of the Harper model, the system's self-duality is broken when the lattice is comparatively shallow. As a consequence, the sharp metal-insulator transition exhibited by Harper's model is replaced by a sequence of mobility edges in realistic bichromatic optical lattices that do not reach the tight-binding regime.