Topological Insulators and Metals in Atomic Optical Lattices

TL;DR

This paper proposes a method to realize and observe topological quantum states using cold atoms in an optical lattice, specifically implementing the Haldane model and enabling direct visualization and control of topological features.

Contribution

It introduces a feasible experimental setup for creating topological states with cold atoms, including conditions for observation and control of edge states.

Findings

Conditions for observing topological states are identified.

Cold atom topological states can be directly visualized.

Control over topological properties is achievable.

Abstract

We propose the realization of topological quantum states with cold atoms trapped in an optical lattice. We discuss an experimental setup that generates a two-dimensional hexagonal lattice in the presence of a light-induced periodic vector potential, which represents a realization of the Haldane model with cold atoms. We determine theoretically the conditions necessary for observing the topological states and show that two of the key conditions are: 1) the realization of sharp boundaries and 2) the minimization of any smoothly varying component of the confining potential. We argue that, unlike their condensed matter counterparts, cold atom topological quantum states can be i) "seen", by mapping out the characteristic chiral edge states, and ii) controlled, by controlling the periodic vector potential and the properties of the confining potential.