Detecting Chiral Edge States in the Hofstadter Optical Lattice

TL;DR

The paper presents a feasible method using Bragg spectroscopy and a shelving technique to detect and visualize chiral topological edge states in optical lattices with synthetic magnetic fields, enhancing experimental accessibility.

Contribution

It introduces a novel detection scheme combining Bragg spectroscopy and Raman-based shelving to unambiguously identify and image topological edge states in optical lattices.

Findings

Bragg spectra reveal unambiguous signatures of chiral edge states.

The shelving method enhances detectability of weak signals.

The approach enables direct in situ imaging of topological edge states.

Abstract

We propose a realistic scheme to detect topological edge states in an optical lattice subjected to a synthetic magnetic field, based on a generalization of Bragg spectroscopy sensitive to angular momentum. We demonstrate that using a well-designed laser probe, the Bragg spectra provide an unambiguous signature of the topological edge states that establishes their chiral nature. This signature is present for a variety of boundaries, from a hard wall to a smooth harmonic potential added on top of the optical lattice. Experimentally, the Bragg signal should be very weak. To make it detectable, we introduce a "shelving method", based on Raman transitions, which transfers angular momentum and changes the internal atomic state simultaneously. This scheme allows to detect the weak signal from the selected edge states on a dark background, and drastically improves the detectivity. It also leads to the possibility to directly visualize the topological edge states, using in situ imaging, offering a unique and instructive view on topological insulating phases.