Lattice bosons in a quasi-disordered environment: The effects of next-nearest-neighbor hopping on localization and Bose-Einstein condensation

摘要

We present a theoretical study of the effects of the next-nearest-neighbor (NNN) hopping (t_2) on the properties of non-interacting bosons in optical lattices in the presence of an Aubry-André quasi-disorder. First we investigate, employing exact diagonalization, the effects of t_2 on the localization properties of a single boson. The localization is monitored using an entanglement measure as well as with inverse participation ratio.Wefind that the sign of t_2 has a significant influence on the localization effects. We also provide analytical results in support of the trends found in the localization behavior. Further, we extend these results including the effects of a harmonic potential which obtains in experiments. Next, we study the effects of t_2 on Bose-Einstein condensation. We find that, a positive t_2 strongly enhances the low temperature thermal depletion of the condensate while a negative t_2 reduces it. It is also found that, for a fixed temperature, increasing the quasidisorder strength reduces the condensate fraction in the extended regime while enhancing it in the localized regime. We also investigate the effects of boundary conditions and that of the phase of the AA potential on the condensate. These are found to have significant effects on the condensate fraction in the localization transition region.