报告摘要：

　　We show that one-dimensional quasiperiodic optical lattice systems can exhibit edge states and topological phases which are generally believed to appear in two-dimensional systems. When the Fermi energy lies in gaps, the Fermi system on the optical superlattice is a topological insulator characterized by a nonzero topological invariant. The topological nature can be revealed by observing the density profile of a trapped fermion system, which displays plateaus with their positions uniquely determined by the ration of wavelengths of the bichromatic optical lattice. This finding provides us an alternative way to study the topological phases and Hofstadterlike spectrum in onedimensional optical lattices. The cases with longrange interactions or onsite interactions are also discussed, where fractional topological states or Mott topological states can be found.