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We characterize the disorder induced localization in momentum space forultracold atoms in one-dimensional incommensurate lattices, according to thedual Aubry-Andr\'e model. For low disorder the system is localized in momentumspace, and the momentum distribution exhibits time-periodic oscillations of therelative intensity of its components. The behavior of these oscillations isexplained by means of a simple three-mode approximation. We predict theirfrequency and visibility by using typical parameters of feasible experiments.Above the transition the system diffuses in momentum space, and theoscillations vanish when averaged over different realizations, offering a clearsignature of the transition.

Localization in momentum space of ultracold atoms in incommensurate lattices