  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.
