Exponential localization in one-dimensional quasi-periodic optical lattices

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We investigate the localization properties of a one-dimensional bichromatic optical lattice in the tight-binding regime, by discussing how exponentially localized states emerge upon changing the degree of commensurability. We also review the mapping onto the discrete Aubry–André model, and provide evidence on how the momentum distribution gets modified in the crossover from extended to exponentially localized states. This analysis is relevant to the recent experiment on the Anderson localization of a noninteracting Bose–Einstein condensate in a quasi-periodic optical lattice (Roati et al 2008 Nature 453 895).