Identifying topological edge states in 2D optical lattices using light scattering

TL;DR

This paper demonstrates a method to detect and visualize topological edge states in a 2D optical lattice using light scattering, revealing their dispersion and chiral properties in cold atom systems.

Contribution

It introduces a detailed scheme combining Bragg spectroscopy and a shelving method to identify and visualize topological edge states in optical lattices.

Findings

Existence of robust topological edge states in Hofstadter optical lattices.

Bragg spectra reveal the dispersion and chirality of edge states.

A shelving technique enables direct visualization of edge states.

Abstract

We recently proposed in a Letter [Physical Review Letters 108 255303] a novel scheme to detect topological edge states in an optical lattice, based on a generalization of Bragg spectroscopy. The scope of the present article is to provide a more detailed and pedagogical description of the system - the Hofstadter optical lattice - and probing method. We first show the existence of topological edge states, in an ultra-cold gas trapped in a 2D optical lattice and subjected to a synthetic magnetic field. The remarkable robustness of the edge states is verified for a variety of external confining potentials. Then, we describe a specific laser probe, made from two lasers in Laguerre-Gaussian modes, which captures unambiguous signatures of these edge states. In particular, the resulting Bragg spectra provide the dispersion relation of the edge states, establishing their chiral nature. In order to make the Bragg signal experimentally detectable, we introduce a "shelving method", which simultaneously transfers angular momentum and changes the internal atomic state. This scheme allows to directly visualize the selected edge states on a dark background, offering an instructive view on topological insulating phases, not accessible in solid-state experiments.