Ultracold atoms in one-dimensional (1D) bichromatic optical lattices constitute a surprisingly simple system for the study of topological insulators. We show that bosons in 1D bichromatic lattices present as a general feature the existence, at equal fractional filling, of Mott-insulator phases with different topological character. These different phases are a direct consequence of the bosonic and interacting nature of the particles and the topological nature of the Bloch bands. We demonstrate that the associated hidden topological transitions may occur both as a function of the superlattice strength and due to intersite interactions. We also discuss the topological character of incommensurate density-wave phases in quasiperiodic superlattices.Ultracold atoms in one-dimensional (1D) bichromatic optical lattices constitute a surprisingly simple system for the study of topological insulators. We show that bosons in 1D bichromatic lattices present as a general feature the existence, at equal fractional filling, of Mott-insulator phases with different topological character. These different phases are a direct consequence of the bosonic and interacting nature of the particles and the topological nature of the Bloch bands. We demonstrate that the associated hidden topological transitions may occur both as a function of the superlattice strength and due to intersite interactions. We also discuss the topological character of incommensurate density-wave phases in quasiperiodic superlattices.

arXiv:1305.5908Physical Review AMar 26, 201445 citations

Topological Insulators with Ultracold Atoms

Indubala I. Satija, Erhai Zhao

arXiv:1201.1458Springer series on atomic, optical, and plasma physicsJan 1, 20130 citations

Topological quantum matter with ultracold gases in optical lattices

Nathan Goldman, Jan Carl Budich, P. Zoller

arXiv:1607.03902Nature PhysicsJun 30, 2016702 citations

Simulating Z2 topological insulators with cold atoms in a one-dimensional optical lattice

Feng Mei, Shi-Liang Zhu, Zhi‐Ming Zhang +2 more

We propose an experimental scheme to simulate and detect the properties of time-reversal invariant topological insulators, using cold atoms trapped in one-dimensional bichromatic optical lattices. This system is described by a one-dimensional Aubry-Andre model with an additional SU(2) gauge structure, which captures the essential properties of a two-dimensional ${Z}_{2}$ topological insulator. We demonstrate that topologically protected edge states, with opposite spin orientations, can be pumped across the lattice by sweeping a laser phase adiabatically. This process is an elegant way to transfer topologically protected quantum states in a highly controllable environment. We discuss how density measurements could provide clear signatures of the topological phases emanating from our one-dimensional system.We propose an experimental scheme to simulate and detect the properties of time-reversal invariant topological insulators, using cold atoms trapped in one-dimensional bichromatic optical lattices. This system is described by a one-dimensional Aubry-Andre model with an additional SU(2) gauge structure, which captures the essential properties of a two-dimensional ${Z}_{2}$ topological insulator. We demonstrate that topologically protected edge states, with opposite spin orientations, can be pumped across the lattice by sweeping a laser phase adiabatically. This process is an elegant way to transfer topologically protected quantum states in a highly controllable environment. We discuss how density measurements could provide clear signatures of the topological phases emanating from our one-dimensional system.

arXiv:1112.3157Physical Review AJan 27, 2012112 citations

{Z}_{2}

topological insulator. We demonstrate that topologically protected edge states, with opposite spin orientations, can be pumped across the lattice by sweeping a laser phase adiabatically. This process is an elegant way to transfer topologically protected quantum states in a highly controllable environment. We discuss how density measurements could provide clear signatures of the topological phases emanating from our one-dimensional system.