Identifying topological edge states in 2D optical lattices using light scattering
arXiv:1209.2051 · doi:10.1140/epjst/e2013-01762-x
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 (46)
- Topological Insulators
- Topological insulators and superconductors
- Many-Body Physics with Ultracold Gases
- Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
- A spin-orbit coupled Bose-Einstein condensate
- Artificial gauge potentials for neutral atoms
- A quantum gas microscope - detecting single atoms in a Hubbard regime optical lattice
- Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
- Synthetic magnetic fields for ultracold neutral atoms
- Spin-Orbit Coupled Degenerate Fermi Gases
- Spin-Injection Spectroscopy of a Spin-Orbit Coupled Fermi Gas
- Creation of effective magnetic fields in optical lattices: The Hofstadter butterfly for cold neutral atoms
- Bragg spectroscopy of a Bose-Einstein condensate
- Rapidly Rotating Atomic Gases
- Tunable gauge potential for neutral and spinless particles in driven lattices
- Fractional quantum Hall states of atoms in optical Lattices
- Non-Abelian gauge fields and topological insulators in shaken optical lattices
- The Excitation Spectrum of a Bose-Einstein Condensate
- Engineering Time-Reversal Invariant Topological Insulators With Ultra-Cold Atoms
- Realistic Time-Reversal Invariant Topological Insulators With Neutral Atoms
- Conduction of Ultracold Fermions Through a Mesoscopic Channel
- Gauge fields for ultracold atoms in optical superlattices
- Fractional Quantum Hall Effect in Optical Lattices
- The Peierls substitution in an engineered lattice potential
- A General Theorem Relating the Bulk Topological Number to Edge States in Two-dimensional Insulators
- Seeing topological order in time-of-flight measurements
- Mapping the Berry Curvature from Semiclassical Dynamics in Optical Lattices
- 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
- Topological states in two-dimensional optical lattices
- Quantum Anomalous Hall Effect with Cold Atoms Trapped in a Square Lattice
- Topological Flat Bands from Dipolar Spin Systems
- 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
- Chern numbers hiding in time-of-flight images
- 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
- Probing Atomic Majorana Fermions in Optical Lattices
- Topology-induced phase transitions in quantum spin Hall lattices
- Topological phase transitions between chiral and helical spin textures in a lattice with spin-orbit coupling and a magnetic field
- Quantum Hall-like effect for cold atoms in non-Abelian gauge potentials
- Photon Counting for Bragg Spectroscopy of Quantum Gases
- Imaging topologically protected transport with quantum degenerate gases
- Simulating and detecting artificial magnetic fields in trapped atoms
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- Direct imaging of topological edge states in cold-atom systems
- Probing topology by "heating": Quantized circular dichroism in ultracold atoms
- Floquet Edge States with Ultracold Atoms
- Detecting fractional Chern insulators through circular dichroism
- Creating topological interfaces and detecting chiral edge modes in a 2D optical lattice
- Charge excitation dynamics in bosonic fractional Chern insulators
- Realizing and detecting a topological insulator in the AIII symmetry class
- Realizing non-Abelian gauge potentials in optical square lattices: Application to atomic Chern insulators
- Quantized Rabi Oscillations and Circular Dichroism in Quantum Hall Systems
- Anomalous charge pumping in a one-dimensional optical superlattice
- Topological phase transitions driven by non-Abelian gauge potentials in optical square lattices
- Quantum particle in a parabolic lattice in the presence of a gauge field
- Anisotropic Quantum Hall Droplets
- Pseudo-time-reversal-symmetry-protected topological Bogoliubov excitations of Bose-Einstein condensates in optical lattices
- Landau-Stark states and cyclotron-Bloch oscillations of a quantum particle