Direct measurement of topological invariants in optical lattices

Abstract

We propose an experimental technique for classifying the topology of band structures realized in optical lattices, based on a generalization of topological charge pumping in quantum Hall systems to cold atom in optical lattices. Time-of-flight measurement along one spatial direction combined with in situ detection along the transverse direction provide a direct measure of the system's Chern number, as we illustrate by calculations for the Hofstadter lattice. Based on an analogy with Wannier functions techniques of topological band theory, the method is very general and also allows the measurement of other topological invariants, such as the $Z_2$ topological invariant of time-reversal symmetric insulators.

arXiv comment4.5 pages, 5 figures

References in corpus (27)

• Topological Insulators
• Maximally-localized generalized Wannier functions for composite energy bands
• Maximally localized Wannier functions: Theory and applications
• Synthetic magnetic fields for ultracold neutral atoms
• Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice
• Spin-Orbit Coupled Degenerate Fermi Gases
• Spin-Injection Spectroscopy of a Spin-Orbit Coupled Fermi Gas
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• An equivalent expression of Z2 Topological Invariant for band insulators using Non-Abelian Berry's connection
• The Quantum-Mechanical Position Operator in Extended Systems
• Quantum Spin Hall Effect and Topologically Invariant Chern Numbers
• Tunable gauge potential for neutral and spinless particles in driven lattices
• Direct Observation of Second Order Atom Tunnelling
• Computing topological invariants without inversion symmetry
• Robustness of the Spin-Chern number
• Conduction of Ultracold Fermions Through a Mesoscopic Channel
• A synthetic electric force acting on neutral atoms
• The Peierls substitution in an engineered lattice potential
• Seeing topological order in time-of-flight measurements
• Electron localization in the insulating state: application to crystalline semiconductors
• Detecting Chiral Edge States in the Hofstadter Optical Lattice
• Expansion of a quantum gas released from an optical lattice
• Smooth gauge for topological insulators
• Electric polarization in a Chern insulator
• Chern numbers hiding in time-of-flight images
• Effects of Smooth Boundaries on Topological Edge Modes in Optical Lattices
• Entanglement spectrum and Wannier center flow of the Hofstadter problem

Cited by in corpus (51)

• Light-induced gauge fields for ultracold atoms
• A Thouless Quantum Pump with Ultracold Bosonic Atoms in an Optical Superlattice
• Z2Pack: Numerical Implementation of Hybrid Wannier Centers for Identifying Topological Materials
• Topological quantum matter with cold atoms
• Quantum simulation of 2d topological physics using orbital-angular-momentum-carrying photons in a 1d array of cavities
• Tomography of band insulators from quench dynamics
• Extracting the Chern number from the dynamics of a Fermi gas: Implementing a quantum Hall bar for cold atoms
• Dynamical quantum phase transitions: Role of topological nodes in wavefunction overlaps
• Detecting Topological Phases in Cold Atoms
• Floquet Edge States with Ultracold Atoms
• Topological insulator and particle pumping in a one-dimensional shaken optical lattice
• Emergent pseudospin-1 Maxwell fermions with a threefold degeneracy in optical lattices
• Measuring Z2 topological invariants in optical lattices using interferometry
• Constructing a Weyl semimetal by stacking one dimensional topological phases
• Simulating and exploring Weyl semimetal physics with cold atoms in a two-dimensional optical lattice
• Quantum simulation of non-trivial topology
• Quantum Simulation of a Topological Mott Insulator with Rydberg Atoms in a Lieb Lattice
• Phase spectroscopy of topological invariants in photonic crystals
• Direct Probe of Topological Order for Cold Atoms
• Fractional charge pumping of interacting bosons in one-dimensional superlattice
• Dissipation-induced topological insulators: A no-go theorem and a recipe
• Single-site-resolved measurement of the current statistics in optical lattices
• $p$-wave chiral superfluidity from an $s$-wave interacting atomic Fermi gas
• Tunable Band Topology Reflected by Fractional Quantum Hall States in Two-Dimensional Lattices
• Interacting Hofstadter Interface
• Bulk detection of time-dependent topological transitions in quenched chiral models
• Topological Mott insulators of ultracold atomic mixtures induced by interactions in one-dimensional optical superlattices
• Imaging topology of Hofstadter ribbons
• Realizing non-Abelian gauge potentials in optical square lattices: Application to atomic Chern insulators
• Interacting bosonic flux ladders with a synthetic dimension: Ground-state phases and quantum quench dynamics
• Mass and chirality inversion of a Dirac cone pair in Stückelberg interferometry
• Exploring topological double-Weyl semimetals with cold atoms in optical lattices
• Simulating bosonic Chern insulators in one-dimensional optical superlattices
• Measuring Chern numbers in Hofstadter strips
• Topological phase transitions driven by non-Abelian gauge potentials in optical square lattices
• Quench Dynamics of Josephson Current in a Topological Josephson Junction
• Critical integer quantum Hall topology and the integrable Maryland model as a topological quantum critical point
• Chiral Topological Orders in an Optical Raman Lattice
• Tunable Flux through a Synthetic Hall Tube of Neutral Fermions
• Topological metal bands with double-triple-point fermions in optical lattices
• Generating and detecting topological phases with higher Chern number
• Hall response of interacting bosonic atoms in strong gauge fields: from condensed to FQH states
• Synthetic gauge field in two interacting ultracold atomic gases without an optical lattice
• Seeing Hofstadter's Butterfly in Atomic Fermi Gases
• Dimerization, Trimerization and Quantum pumping
• Velocity Scanning Tomography for Room-Temperature Quantum Simulation
• Determination of Chern numbers with a phase retrieval algorithm
• Quantum emulation of topological magneto-optical effects using ultracold atoms
• Proposal for realizing unpaired Weyl points in a three-dimensional periodically driven optical Raman lattice
• Interferometric detection of Chern numbers in topological optical lattices
• Propagation in media as a probe for topological properties