Bose-Einstein condensates in optical quasicrystal lattices

We analyze the physics of Bose-Einstein condensates confined in two dimensional (2D) quasiperiodic optical lattices, which offer an intermediate situation between ordered and disordered systems. First, we analyze the time-of-flight interference pattern that reveals quasiperiodic long-range order. Second, we demonstrate localization effects associated with quasidisorder as well as quasiperiodic Bloch oscillations associated with the extended nature of the wave function of a Bose-Einstein condensate in an optical quasicrystal. In addition, we discuss in detail the crossover between diffusive and localized regimes when the quasiperiodic potential is switched on, as well as the effects of interactions.