Interferometric approach to measuring band topology in 2D optical lattices

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.

7 pages, 5 figures

References in corpus (10)

• The electronic properties of graphene
• Topological characterization of periodically-driven quantum systems
• 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
• Multi-Component Quantum Gases in Spin-Dependent Hexagonal Lattices
• Optical Flux Lattices for Ultracold Atomic Gases
• Staggered-Vortex Superfluid of Ultracold Bosons in an Optical Lattice
• Quantum Spin Dynamics of Mode-Squeezed Luttinger Liquids in Two-Component Atomic Gases
• Competing Superconducting States for Ultracold Atoms in Optical Lattices with Artificial Staggered Magnetic Field

Cited by in corpus (30)

• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
• An Aharonov-Bohm interferometer for determining Bloch band topology
• Two-Dimensional Density-Matrix Topological Fermionic Phases: Topological Uhlmann Numbers
• Topological indices for open and thermal systems via Uhlmann's phase
• Quantum correlations and entanglement in far-from-equilibrium spin systems
• Correlation Length, Universality Classes, and Scaling Laws Associated with Topological Phase Transitions
• Realization of Fractional Chern Insulators in the Thin-Torus-Limit with Ultracold Bosons
• Universality classes of topological phase transitions with higher-order band crossing
• Quantum simulation of non-trivial topology
• Phase spectroscopy of topological invariants in photonic crystals
• Direct Probe of Topological Order for Cold Atoms
• Symmetry-protected Topological Phases at Finite Temperature
• Signatures of topological phase transition on a quantum critical line
• Anomalous charge pumping in a one-dimensional optical superlattice
• Bloch-Landau-Zener dynamics induced by a synthetic field in a photonic quantum walk
• Generalized Bloch theorem and topological characterization
• 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
• Michelson Interferometry of High-order Harmonic Generation in Solids
• Realizing and detecting Stiefel-Whitney insulators in an optical Raman lattice
• Multidimensional Spectroscopy of Time-Dependent Impurities in Ultracold Fermions
• Geometric phase in Stückelberg interferometry
• Chirality Dependent Photon Transport and Helical Superradiance
• Berry Curvature and Bulk-Boundary Correspondence from Transport Measurement for Photonic Chern Bands
• Velocity Scanning Tomography for Room-Temperature Quantum Simulation
• Hidden-symmetry-protected Z_2 topological insulator in a cubic lattice
• Detecting degenerate bands topological invariants in optical lattice