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

TL;DR

This study explores how next-nearest-neighbor hopping influences localization and Bose-Einstein condensation of non-interacting bosons in quasi-disordered optical lattices, revealing sign-dependent effects and the impact of boundary conditions.

Contribution

It provides a detailed analysis of the role of NNN hopping on localization and condensation, including analytical support and the effects of experimental parameters.

Findings

Sign of $t_2$ significantly affects localization.

Positive $t_2$ enhances condensate depletion at low temperatures.

Quasi-disorder strength influences condensate fraction differently in extended and localized regimes.

Abstract

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-Andr\'{e} 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. We find 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 quasi-disorder 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.