Direct Measurement of the Zak phase in Topological Bloch Bands

Abstract

Geometric phases that characterize the topological properties of Bloch bands play a fundamental role in the modern band theory of solids. Here we report on the direct measurement of the geometric phase acquired by cold atoms moving in one-dimensional optical lattices. Using a combination of Bloch oscillations and Ramsey interferometry, we extract the Zak phase - the Berry phase acquired during an adiabatic motion of a particle across the Brillouin zone - which can be viewed as an invariant characterizing the topological properties of the band. For a dimerized optical lattice, which models polyacetylene, we measure a difference of the Zak phase equal to phi_Zak=0.97(2)pi for the two possible polyacetylene phases with different dimerization. This indicates that the two dimerized phases belong to different topological classes, such that for a filled band, domain walls have fractional quantum numbers. Our work establishes a new general approach for probing the topological structure of Bloch bands in optical lattices.

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• Hermitian chiral boundary states in non-Hermitian topological insulators
• Intrinsic topological magnons in arrays of magnetic dipoles
• Topologically Protected Edge States in Triangular Lattices
• Topological phonon polariton enhanced radiative heat transfer in bichromatic nanoparticle arrays mimicking Aubry-André-Harper model
• Chirality Dependent Photon Transport and Helical Superradiance
• Transport signatures of symmetry protection in 1D Floquet topological insulators
• Non-adiabatic extension of the Zak phase and charge pumping in the Rice--Mele model
• Mobile Kink Solitons in a Van der Waals Charge-Density-Wave Layer
• Calculating the polarization in bi-partite lattice models: application to an extended Su-Schrieffer-Heeger model
• Topologically trivial and nontrivial edge bands in graphene induced by irradiation
• Multiparticle interactions for ultracold atoms in optical tweezers: Cyclic ring-exchange terms
• Wannier functions using a discrete variable representation for optical lattices
• Dynamics of noisy quantum systems in the Heisenberg picture: application to the stability of fractional charge
• Observation of dynamical topology in 1D
• Geometrical phase shift in Friedel oscillations
• Topological states and interplay between spin-orbit and Zeeman interactions in a spinful Su-Schrieffer-Heeger nanowire
• Three-body constrained bosons in double-well optical lattice
• Topological nodal chains in optical lattices
• Delocalization of edge states in topological phases
• Topological gap solitons in Rabi Su-Schrieffer-Heeger lattices
• Dirac fermions in graphene and analogues: magnetic field and topological properties
• Synthetic non-Abelian topological charges in ultracold atomic gases
• Topology, Holonomy, and Quantum Walks
• Berry Curvature and Bulk-Boundary Correspondence from Transport Measurement for Photonic Chern Bands
• Landau-Zener tunneling problem for Bloch states
• Band engineering and study of disorder using topology in compact high kinetic inductance cavity arrays
• Real-space effects of a quench in the Su-Schrieffer-Heeger model and elusive dynamical appearance of the topological edge states
• PC-symmetry-protected edge states in interacting driven-dissipative bosonic systems
• Probing the Topological Anderson Transition in Quasiperiodic Photonic Lattices via Chiral Displacement and Wavelength Tuning
• Light-induced odd-parity altermagnets on dimerized lattices
• Topological quantum interference in a pumped Su-Schrieffer-Heeger lattice
• A numerically exact study of Weyl superconductivity
• Weyl Nodal-Ring Semimetallic Behavior and Topological Superconductivity in Crystalline Forms of Su-Schrieffer-Heeger Chains
• Nonparaxiality-triggered Landau-Zener transition in topological photonic waveguides
• Boundary-induced dynamics in 1D topological systems and memory effects of edge modes
• Corroborating the bulk-edge correspondence in weakly interacting 1D topological insulators
• Interaction driven topological phase transitions of hardcore bosons on a two-leg ladder
• Measuring geometric phases with a dynamical quantum Zeno effect in a Bose-Einstein condensate
• Exact scaling of geometric phase and fidelity susceptibility and their breakdown across the critical points
• Bloch Oscillations of Hybrid Light-Matter Particles in a Waveguide Array
• Selection Rule for Topological Amplifiers in Bogoliubov de Gennes Systems
• Topological study of a Bogoliubov-de Gennes system of pseudo spin-$1/2$ bosons with conserved magnetization in a honeycomb lattice
• Protocols for dynamically probing topological edge states and dimerization with fermionic atoms in optical potentials
• Controllable simulation of topological phases and edge states with quantum walk
• Hidden-symmetry-protected Z_2 topological insulator in a cubic lattice
• Self-interaction corrected SCAN functional for molecules and solids in the numeric atom-center orbital framework
• Programmable Hamiltonian engineering with quadratic quantum Fourier transform
• Hidden-symmetry-protected quantum pseudo-spin Hall effect in optical lattices
• Two-Dimensional Thouless Pumping of Ultracold Fermions in Obliquely Introduced Optical Superlattice
• Bloch Oscillations, Landau-Zener Transition, and Topological Phase Evolution in a Pendula Array
• Light-matter correlations in Quantum Floquet engineering of cavity quantum materials
• Topological properties of a class of generalized Su-Schrieffer-Heeger networks: chains and meshes
• Universal Scaling Theory of the Boundary Geometric Tensor in Disordered Metals
• An SU(2) geometric phase induced by periodically driven Raman process in an ultracold dilute Bose gas
• Exotic odd-even parity effects in transmission phase, (Andreev) conductance, and shot noise of a dimer atomic chain by topology
• Soliton metacrystals: topology and chirality
• Wannier center spectroscopy to identify boundary-obstructed topological insulators
• Topologically nontrivial states in one-dimensional nonlinear bichromatic superlattices
• One-dimensional s-p superlattice
• Particle and thermal transport through one dimensional topological systems via Lindblad formalism
• Uhlmann holonomy against Lindblad dynamics of topological systems at finite temperatures
• Quantum phase transition without gap opening
• Artificial Magnetic Fields in Momentum Space in Spin-Orbit Coupled Systems
• Energy polarization and energy pumping in Rice-Mele chains
• Weak topological insulating phases of hard-core-bosons on the honeycomb lattice
• Entanglement and particle fluctuations of one-dimensional chiral topological insulators
• Observation of average topological phase in disordered Rydberg atom array
• Modification of the Optical Properties of Molecular Chains upon Coupling to Adatoms
• Topological electronic properties of silicon
• Emergence of Floquet edge states in the coupled Su-Schrieffer-Heeger model
• Introduction to Topological Phases and Electronic Interactions in (2+1) Dimensions
• Quantum Dissipation at Conical Intersections of Quasienergies
• Uncover band topology via quantized drift in two-dimensional Bloch oscillations
• Artificial topological models based on a one-dimensional spin-dependent optical lattice
• Topologically compatible non-Hermitian skin effect
• Exotic Topological States with Raman-Induced Spin-Orbit Coupling
• Tunable topological phases with fermionic atoms in a one-dimensional flux lattice
• Elementary models of 3D topological insulators with chiral symmetry
• Distinguishing trivial and topological quadrupolar insulators by Wannier-Stark ladders
• Topological optical Raman superlattices
• Realization of geometric phase topology induced by multiple exceptional points
• Topological Rice-Mele model in an emergent lattice: Exact diagonalization approach
• Intrinsic anomalous Hall effect across the magnetic phase transition of a spin-orbit-coupled Bose-Einstein condensate
• Topological phase and lattice structures in spin chain models
• Topological quantum thermometry
• Efficiently measuring $d$-wave pairing and beyond in quantum gas microscopes
• Quasi-edge states and topological Bloch oscillation in the synthetic space
• Individually tunable tunnelling coefficients in optical lattices using local periodic driving
• Spectroscopy and topological properties of a Haldane light system
• Yang monopoles and emergent three-dimensional topological defects in interacting bosons
• Adiabatic charge transport in extended SSH models
• Multiparticle quantum walk: a dynamical probe of topological many-body excitations
• Signature of edge states in resonant wave scattering
• Quantum sensing with ultracold simulators in lattice and ensemble systems: a review
• Structure-dynamics relation in shaken optical lattices
• Probing entanglement dynamics and topological transitions on noisy intermediate-scale quantum computers
• Symmetry-Protected Solitons and Bulk-Boundary Correspondence in Generalized Jackiw-Rebbi Models
• The $\pi$ Berry Phase and Topological Excitation in Interacting Boson-Fermion Mixtures
• 2D Topological Edge States in Periodic Space-Time Interfaces
• Tunable symmetry-protected higher-order topological states with fermionic atoms in bilayer optical lattices
• Berry phase, entanglement entropy, and algebraic properties of ground states of BCS and BEC superfluids
• Synthesizing the Quantum Spin Hall Phase for Ultracold Atoms in Bichromatic Chiral Optical Ladders
• Single-shot measurement of photonic topological invariant
• Topologically protected quantization of work
• Cumulants associated with geometric phases
• Direct Measurement of a Non-Hermitian Topological Invariant in a Hybrid Light-Matter System
• Universality of Abelian and non-Abelian Wannier functions in one dimension
• Floquet control of interactions and edge states in a programmable quantum simulator
• Characterizing Floquet topological phases by quench dynamics: A multiple-subsystem approach
• Characterizing topological pumping of charges in exactly solvable Rice-Mele chains of the non-Hermitian variety
• Fermionic Quantum Simulation on Andreev Bound State Superlattices
• Topological bosonic states on ribbons of honeycomb lattice
• Density-Dependent Gauge Field with Raman Lattices
• Majorana stellar representation for mixed-spin $(s,\frac{1}{2})$ systems
• Resonant edge-site pumping of polaritonic Su-Schrieffer-Heeger lattices
• Topological Phases in Coupled Polyyne Chains
• Dynamical detection of mean-field topological phases in an interacting Chern insulator
• Jackiw-Rebbi-type bound state carrying fractional fermion parity
• Dynamical signatures of symmetry protected topology following symmetry breaking
• Su-Schrieffer-Heeger-Hubbard model at quarter filling: effects of magnetic field and non-local interactions
• Exploring Thouless Pumping in the Generalized Creutz Model: A Graphical Method and Modulation Schemes
• Interaction-induced phases in the half-filled Bernevig-Hughes-Zhang model in one dimension
• Unusual behavior of sound velocity of a Bose gas in an optical superlattice at quasi-one-dimension
• One-dimensional Dexter-type excitonic topological phase transition
• Collective Oscillations of Bose-Einstein Condensates in a Synthetic Magnetic Field
• Exceptional points in SSH-like models with hopping amplitude gradient
• Few-particle dynamics of fractional quantum Hall lattice models
• Accelerated and Airy-Bloch oscillations
• On the complex behaviour of the density in composite quantum systems
• Revealing the topological nature of the bond order wave in a strongly correlated quantum system
• Comparison of entangling protocols in ABC-type spin chains
• Critical phase boundary and finite-size fluctuations in Su-Schrieffer-Heeger model with random inter-cell couplings
• Preparation of edge states by shaking boundaries
• Emerging (2+1)D massive graviton in graphene-like systems
• Connecting Topological Anderson and Mott Insulators in Disordered Interacting Fermionic Systems
• Non-Superconducting Non-Abelian Statistics in One-Dimensional Topological Insulators
• Tunable zero modes and quantum interferences in flat-band topological insulators
• Quantum emulation of topological magneto-optical effects using ultracold atoms
• Scattering description of edge states in Aharonov-Bohm triangle chains
• Flat bands and topological phase transition in entangled Su-Schrieffer-Heeger chains
• Anomalous Topological Bloch Oscillations under Non-Abelian Gauge Fields
• Adiabatic charge transport through non-Bloch bands
• Landau-Stark states and edge-induced Bloch oscillations in topological lattices
• Emergent topological phases in an extended Su-Schrieffer-Heeger model with Rashba spin-orbit interaction, higher order hopping and domain wall
• Absence of gapless Majorana edge modes in few-leg bosonic flux ladders
• Phase diagrams of bosonic $A{B}_n$ chains
• Topological analog of the magnetic bit within the Su-Schrieffer-Heeger-Holstein model
• Simulating a Topological Transition in a Superconducting Phase Qubit by Fast Adiabatic Trajectories
• Topological boundary states in engineered quantum-dot molecules on the InAs(111)A surface
• Anomalous Bloch oscillation and electrical switching of edge magnetization in bilayer graphene nanoribbon
• Probing the topology of the two-photon bands via time-dependent quantum walks
• Topological edge states in bowtie ladders with different cutting edges
• Revealing inverted chirality of hidden domain wall states in multiband systems without topological transition
• Low-frequency tunable topological interface states in soft phononic crystal cylinders
• Inter-species topological phases via a dynamical gauge field
• A symmetry-protected topological optical lattice clock
• Using superlattice potentials to probe long-range magnetic correlations in optical lattices
• Hidden chiral symmetry protected $\mathbb{Z}\oplus \mathbb{Z}$ topological insulators in a ladder dimer model
• One-dimensional superlattices with s-p resonance
• Devil's staircase of topological Peierls insulators and Peierls supersolids
• Nutation dynamics and multifrequency resonance in a many-body seesaw
• Seeing Topological Order and Band Inversion in Optical Diatomic Chain
• Pancharatnam-Zak phase
• Influence of anisotropy, tilt and pairing of Weyl nodes: The Weyl semimetals TaAs, TaP, NbAs and NbP
• Photoinduced intradomain dynamics and nonthermal switching of metastable states in the one-dimensional extended Peierls-Hubbard model
• Engineering the Bogoliubov Modes through Geometry and Interaction: From Collective Edge Modes to Flat-band Excitations
• Topological edge states in dipolar zig-zag stripes
• Interplay of Kekulé distortions and laser fields in graphene
• Spinor bosons in optical superlattices: a numerical study
• Glide-resolved photoemission spectroscopy: Measuring topological invariants in nonsymmorphic space groups
• Zak Phase Dislocations in Trimer Lattices
• Correlated disorder induced anomalous transport in magnetically doped topological insulators
• Topological edge states and disorder robustness in one-dimensional off-diagonal mosaic lattices
• Observation of the topological edge state in X-ray band
• Fluctuational susceptibility of ultracold bosons in the vicinity of condensation
• Topological Molecules and Topological Localization of a Rydberg Electron on a Classical Orbit
• Mott-insulating phases of the Bose-Hubbard model on quasi-1D ladder lattices
• Evolution of quantum geometric tensor of 1D periodic systems after a quench
• Shot noise signatures identifying non-Abelian properties of Jackiw-Rebbi zero modes
• Topological phases of bosons with local parity coupling on a dimerized lattice
• Third quantization with Hartree approximation for open-system bosonic transport
• Detecting degenerate bands topological invariants in optical lattice
• Emergence of Imaginary Time Crystals in the non-Hermitian Su-Schrieffer-Heeger model
• Interferometric detection of Chern numbers in topological optical lattices
• A Universal Quantum Computing Virtual Machine
• Exploiting $\vartheta -$functions for the identification of topological materials
• Characterizing Real-space Topology in Rice-Mele Model by Thermodynamics
• Higher-order topological quantum paramagnets
• Preparation and observation of anomalous counterpropagating edge states in a periodically driven optical Raman lattice