Interferometric approach to measuring band topology in 2D optical lattices
arXiv:1212.0562 · doi:10.1103/PhysRevLett.110.165304
Abstract
Recently, optical lattices with non-zero Berry's phases of Bloch bands have been realized. New approaches for measuring Berry's phases and topological properties of bands with experimental tools appropriate for ultracold atoms need to be developed. In this paper, we propose an interferometric method for measuring Berry's phases of two dimensional Bloch bands. The key idea is to use a combination of Ramsey interference and Bloch oscillations to measure Zak phases, i.e. Berry's phases for closed trajectories corresponding to reciprocal lattice vectors. We demonstrate that this technique can be used to measure Berry curvature of Bloch bands, the π-Berry's phase of Dirac points, and the first Chern number of topological bands. We discuss several experimentally feasible realizations of this technique, which make it robust against low-frequency magnetic noise.
arXiv comment7 pages, 5 figures
References in corpus (29)
- The electronic properties of graphene
- Topological Insulators
- Berry Phase Effects on Electronic Properties
- A spin-orbit coupled Bose-Einstein condensate
- Topological characterization of periodically-driven quantum systems
- Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice
- Nonlinear atom interferometer surpasses classical precision limit
- Spin-Injection Spectroscopy of a Spin-Orbit Coupled Fermi Gas
- Matter-wave interferometry in a double well on an atom chip
- Creation of effective magnetic fields in optical lattices: The Hofstadter butterfly for cold neutral atoms
- Berry Curvature on the Fermi Surface: Anomalous Hall Effect as a Topological Fermi-Liquid Property
- Atom interferometry with Bose-Einstein condensates in a double-well potential
- Cold atoms in non-Abelian gauge potentials: From the Hofstadter "moth" to lattice gauge theory
- Multi-Component Quantum Gases in Spin-Dependent Hexagonal Lattices
- Gauge fields for ultracold atoms in optical superlattices
- Berry phase, hyperorbits, and the Hofstadter spectrum
- Atom interferometry with trapped Fermi gases
- Ultracold quantum gases in triangular optical lattices
- Seeing topological order in time-of-flight measurements
- Mapping the Berry Curvature from Semiclassical Dynamics in Optical Lattices
- Artificial electromagnetism for neutral atoms: Escher staircase and Laughlin liquids
- Optical Flux Lattices for Ultracold Atomic Gases
- Creating artificial magnetic fields for cold atoms by photon-assisted tunneling
- Staggered-Vortex Superfluid of Ultracold Bosons in an Optical Lattice
- Quantum Spin Dynamics of Mode-Squeezed Luttinger Liquids in Two-Component Atomic Gases
- Chern numbers hiding in time-of-flight images
- Optical Flux Lattices for Two-Photon Dressed States
- Observation of off-diagonal geometric phase in polarized neutron interferometer experiments
- Competing Superconducting States for Ultracold Atoms in Optical Lattices with Artificial Staggered Magnetic Field
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- Topological phases of non-Hermitian systems
- Light-induced gauge fields for ultracold atoms
- Direct Measurement of the Zak phase in Topological Bloch Bands
- Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
- Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
- Probing topological invariants in the bulk of a non-Hermitian optical system
- Fractional Quantum Hall Physics in Topological Flat Bands
- Topological quantum matter with cold atoms
- An Aharonov-Bohm interferometer for determining Bloch band topology
- Topological semimetals with double-helix nodal link
- Bloch state tomography using Wilson lines
- Exploring Interacting Topological Insulators with Ultracold Atoms: the Synthetic Creutz-Hubbard Model
- Spin-orbit coupling and spin Hall effect for neutral atoms without spin-flips
- 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
- Anomalous and Quantum Hall Effects in Lossy Photonic Lattices
- Two-Dimensional Density-Matrix Topological Fermionic Phases: Topological Uhlmann Numbers
- Observing Topological Invariants Using Quantum Walk in Superconducting Circuits
- Density Matrix Topological Insulators
- Unified bulk-boundary correspondence for band insulators
- Direct Probe of Topological Invariants Using Bloch Oscillating Quantum Walks
- Topological indices for open and thermal systems via Uhlmann's phase
- Measuring topological invariants in photonic systems
- Quantum correlations and entanglement in far-from-equilibrium spin systems
- Detecting Topological Phases in Cold Atoms
- Interferometric Measurements of Many-body Topological Invariants using Mobile Impurities
- Measurement of Chern numbers through center-of-mass responses
- Correlation Length, Universality Classes, and Scaling Laws Associated with Topological Phase Transitions
- Hidden-Symmetry-Protected Topological Semimetals on a Square Lattice
- Zak phase of photons in optical waveguide lattices
- Realization of Fractional Chern Insulators in the Thin-Torus-Limit with Ultracold Bosons
- Topological Bloch oscillations
- Measuring Z2 topological invariants in optical lattices using interferometry
- Simulating and exploring Weyl semimetal physics with cold atoms in a two-dimensional optical lattice
- Universality classes of topological phase transitions with higher-order band crossing
- Quantum simulation of non-trivial topology
- Experimental realization of strong effective magnetic fields in optical superlattice potentials
- Dynamic Optical Superlattices with Topological Bands
- Phase spectroscopy of topological invariants in photonic crystals
- Direct Probe of Topological Order for Cold Atoms
- Scaling Theory of Topological Phase Transitions
- Symmetry-protected Topological Phases at Finite Temperature
- Fidelity susceptibility near topological phase transitions in quantum walks
- Bulk detection of time-dependent topological transitions in quenched chiral models
- Realizing non-Abelian gauge potentials in optical square lattices: Application to atomic Chern insulators
- Characterizing Topological Excitations of a Long-Range Heisenberg Model with Trapped Ions
- Topological polarons, quasiparticle invariants and their detection in 1D symmetry-protected phases
- Mass and chirality inversion of a Dirac cone pair in Stückelberg interferometry
- Solitons in one-dimensional lattices with a flat band
- Anomalous charge pumping in a one-dimensional optical superlattice
- Signatures of topological phase transition on a quantum critical line
- Bloch-Landau-Zener dynamics induced by a synthetic field in a photonic quantum walk
- Detection of Chern numbers and entanglement in topological two-species systems through subsystem winding numbers
- Direct manifestation of band topology in the winding number of the Wannier-Stark ladder
- Generalized Bloch theorem and topological characterization
- Design of laser-coupled honeycomb optical lattices supporting Chern insulators
- Chiral Topological Orders in an Optical Raman Lattice
- Moving and merging of Dirac points on a square lattice and hidden symmetry protection
- Synthetic Hall ladder with tunable magnetic flux
- Spontaneous magnetization and anomalous Hall effect in an emergent Dice lattice
- Topological flat bands in optical checkerboard-like lattices
- Demonstration of Hopf-link semimetal bands with superconducting circuits
- Michelson Interferometry of High-order Harmonic Generation in Solids
- Geometric phase in Stückelberg interferometry
- Multidimensional Spectroscopy of Time-Dependent Impurities in Ultracold Fermions
- Realizing and detecting Stiefel-Whitney insulators in an optical Raman lattice
- Generating and detecting topological phases with higher Chern number
- Chirality Dependent Photon Transport and Helical Superradiance
- Dirac fermions in graphene and analogues: magnetic field and topological properties
- Seeing Hofstadter's Butterfly in Atomic Fermi Gases
- Berry Curvature and Bulk-Boundary Correspondence from Transport Measurement for Photonic Chern Bands
- Hidden-symmetry-protected Z_2 topological insulator in a cubic lattice
- Hidden-symmetry-protected quantum pseudo-spin Hall effect in optical lattices
- Velocity Scanning Tomography for Room-Temperature Quantum Simulation
- Beyond the Spin Model Approximation for Ramsey Spectroscopy
- Efficient algorithm to compute the Berry conductivity
- Finite size effects and Hofstadter butterfly in a bosonic Mott insulator with relativistic dispersion background
- Detecting degenerate bands topological invariants in optical lattice
- Interferometric detection of Chern numbers in topological optical lattices
- Simulating topological phases and topological phase transitions with classical strings