We analyze the physics of Bose-Einstein condensates confined in 2D quasi-periodic optical lattices, which offer an intermediate situation between ordered and disordered systems. First, we analyze the time-of-flight interference pattern that reveals quasi-periodic long-range order. Second, we demonstrate localization effects associated with quasi-disorder as well as quasiperiodic Bloch oscillations associated with the extended nature of the wavefunction of a Bose-Einstein condensate in an optical quasicrystal. In addition, we discuss in detail the crossover between diffusive and localized regimes when the quasi-periodic potential is switched on, as well as the effects of interactions.
@article{arxiv.cond-mat/0502529,
title = {Bose-Einstein Condensates in Optical Quasicrystal Lattices},
author = {Laurent Sanchez-Palencia and Luis Santos},
journal= {arXiv preprint arXiv:cond-mat/0502529},
year = {2016}
}