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

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.

17 pages, 10 figures. Revised and extended version, to appear in EJP Special Topic for the special issue on "Novel Quantum Phases and Mesoscopic Physics in Quantum Gases". Extended version of arXiv:1203.1246

References in corpus (20)

• Many-Body Physics with Ultracold Gases
• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• Spin-Injection Spectroscopy of a Spin-Orbit Coupled Fermi Gas
• Tunable gauge potential for neutral and spinless particles in driven lattices
• Non-Abelian gauge fields and topological insulators in shaken optical lattices
• Engineering Time-Reversal Invariant Topological Insulators With Ultra-Cold Atoms
• Realistic Time-Reversal Invariant Topological Insulators With Neutral Atoms
• Fractional Quantum Hall Effect in Optical Lattices
• A General Theorem Relating the Bulk Topological Number to Edge States in Two-dimensional Insulators
• Direct imaging of topological edge states in cold-atom systems
• Wilson Fermions and Axion Electrodynamics in Optical Lattices
• Detecting Chiral Edge States in the Hofstadter Optical Lattice
• Trapped Fermi Gases in Rotating Optical Lattices: Realization and Detection of the Topological Hofstadter Insulator
• Rydberg-Atom Quantum Simulation and Chern Number Characterization of a Topological Mott Insulator
• Optical lattice quantum Hall effect
• Effects of Smooth Boundaries on Topological Edge Modes in Optical Lattices
• Measuring topology in a laser-coupled honeycomb lattice: From Chern insulators to topological semi-metals
• Topology-induced phase transitions in quantum spin Hall lattices
• Quantum Hall-like effect for cold atoms in non-Abelian gauge potentials

Cited by in corpus (1)

• Direct imaging of topological edge states in cold-atom systems