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Bose-Einstein condensates loaded in one-dimensional bichromatic opticallattices with constituent sublattices having incommensurate periods isconsidered. Using the rational approximations for the incommensurate periods,we show that below the mobility edge the localized states are distributednearly homogeneously in the space and explore the versatility of suchpotentials. We show that superposition of symmetric and anti-symmetriclocalized can be used to simulate various physical dynamical regimes, known tooccur in double-well and multi-well traps. As examples, we obtain analternative realization of a bosonic Josephson junction, whose coherentoscillations display beatings or switching in the weakly nonlinear regime,describe selftrapping and four-mode dynamics, mimicking coherent oscillationsand self-trapping in four-well potentials. These phenomena can be observed fordifferent pairs of modes, which are localized due to the interference ratherthan due to a confining trap. The results obtained using few-modeapproximations are compared with the direct numerical simulations of theone-dimensional Gross-Pitaevskii equation. The localized states and the relateddynamics are found to persist for long times even in the repulsive condensates.We also described bifurcations of the families of nonlinear modes, the symmetrybreaking and stable minigap solitons.

Bose-Einstein condensates in quasi-periodic lattices: bosonic Josephson junction, self-trapping, and multi-mode dynamics