Effects of Smooth Boundaries on Topological Edge Modes in Optical Lattices

TL;DR

This paper demonstrates that smooth boundaries in optical lattices can support topological edge states, which are robust against disorder and detectable via Bragg spectroscopy, expanding the understanding of topological phases in cold atom systems.

Contribution

It shows that sharp boundaries are not necessary for topological edge states in optical lattices and explores their properties and detection methods.

Findings

Edge states exist with smooth confinement potentials.

Edge states are robust against disorder.

Bragg spectroscopy can detect topological edge states.

Abstract

Since the experimental realization of synthetic gauge fields for neutral atoms, the simulation of topologically non-trivial phases of matter with ultracold atoms has become a major focus of cold atom experiments. However, several obvious differences exist between cold atom and solid state systems, for instance the finite size of the atomic cloud and the smooth confining potential. In this article we show that sharp boundaries are not required to realize quantum Hall or quantum spin Hall physics in optical lattices and, on the contrary, that edge states which belong to a smooth confinement exhibit additional interesting properties, such as spatially resolved splitting and merging of bulk bands and the emergence of robust auxiliary states in bulk gaps to preserve the topological quantum numbers. In addition, we numerically validate that these states are robust against disorder. Finally, we analyze possible detection methods, with a focus on Bragg spectroscopy, to demonstrate that the edge states can be detected and that Bragg spectroscopy can reveal how topological edge states are connected to the different bulk bands.