  Ultra-cold atoms in 1D bi-chromatic lattices constitute a surprisingly simple
system for the study of topological insulators. We show that topological phase
transitions constitute a general feature of bosons in 1D bi-chromatic lattices,
and that these transitions may occur both as a function of the superlattice
strength and due to inter-site interactions. We discuss in addition the
topological character of incommensurate density wave phases in quasi-periodic
lattices.
