Generalized Aubry-Andre-Harper Models in Optical Superlattices

Ultracold atoms trapped in optical superlattices provide a simple platform for realizing the seminal Aubry-Andr\'{e}-Harper (AAH) model. However, the periodic modulations on the nearest-neighbour hoppings have been ignored in this model. In this paper, we find that optical superlattice system actually can be approximately described by a generalized AAH model in the case of $V_1\gg V_2$, with periodic modulations on both on-site energies and nearest-neighbour hoppings, supporting much richer topological properties that are absent in the standard AAH model. Specifically, by calculating Chern numbers and topological edge states, we show that the generalized AAH model possesses multifarious topological phases and topological phase transitions, as compared to the standard AAH model only supporting a single topological phase. Our findings can open up more opportunities for using optical superlattices to study topological and localization physics.