Edge states and topological phases in one-dimensional optical   superlattices
  We show that one-dimensional quasi-periodic 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. The butterfly-like spectrum of the superlattice system can be also determined from the finite-temperature density profiles of the trapped fermion system. This finding opens an alternative avenue to study the topological phases and Hofstadter-like spectrum in one-dimensional optical lattices. 
Li-Jun Lang, Xiaoming Cai, Shu Chen
cond-mat.quant-gas quant-ph