Topological Quantum Matter with Ultracold Gases in Optical Lattices

Abstract

Since the discovery of topological insulators, many topological phases have been predicted and realized in a range of different systems, providing both fascinating physics and exciting opportunities for devices. And although new materials are being developed and explored all the time, the prospects for probing exotic topological phases would be greatly enhanced if they could be realized in systems that were easily tuned. The flexibility offered by ultracold atoms could provide such a platform. Here, we review the tools available for creating topological states using ultracold atoms in optical lattices, give an overview of the theoretical and experimental advances and provide an outlook towards realizing strongly correlated topological phases.

10 pages, 4 figures. Author-produced version of a Progress Article published in Nature Physics

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• Many-Body Physics with Ultracold Gases
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• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• Topological characterization of periodically-driven quantum systems
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Single-Spin Addressing in an Atomic Mott Insulator
• Non-Abelian gauge potentials for ultra-cold atoms with degenerate dark states
• Measuring entanglement growth in quench dynamics of bosons in an optical lattice
• $p_x+i{p}_y$ superfluid from s-wave interactions of fermionic cold atoms
• Non-Abelian gauge fields and topological insulators in shaken optical lattices
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• Engineering Time-Reversal Invariant Topological Insulators With Ultra-Cold Atoms
• Fractional Quantum Hall Effect in Optical Lattices
• Quantum Computation Using Vortices and Majorana Zero Modes of a $p_x$ + $i{p}_y$ Superfluid of Fermionic Cold Atoms
• An Aharonov-Bohm interferometer for determining Bloch band topology
• Designing Frustrated Quantum Magnets with Laser-Dressed Rydberg Atoms
• Direct imaging of topological edge states in cold-atom systems
• Optical Flux Lattices for Ultracold Atomic Gases
• Wilson Fermions and Axion Electrodynamics in Optical Lattices
• Composite Fermion Theory for Bosonic Atoms in Optical Lattices
• Detecting Chiral Edge States in the Hofstadter Optical Lattice
• Topology of density matrices
• Dissipative preparation of Chern insulators
• Rydberg-Atom Quantum Simulation and Chern Number Characterization of a Topological Mott Insulator
• Floquet Edge States with Ultracold Atoms
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Cited by in corpus (81)

• Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump
• Topological phase transition in non-Hermitian quasicrystals
• Tools for quantum simulation with ultracold atoms in optical lattices
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Topological quantum matter in synthetic dimensions
• Topological photonic crystals: physics, designs and applications
• Synthetic dimensions and spin-orbit coupling with an optical clock transition
• Topological characterizations of an extended Su-Schrieffer-Heeger model
• Two-terminal transport measurements with cold atoms
• A perspective on topological nanophotonics: current status and future challenges
• Experimentally Detecting Quantized Zak Phases without Chiral Symmetry in Photonic Lattices
• Symmetry-broken states in a system of interacting bosons on a two-leg ladder with a uniform Abelian gauge field
• Nano-Scale `Dark State' Optical Potentials for Cold Atoms
• Semi-synthetic zigzag optical lattice for ultracold bosons
• Topological Anderson insulators in two-dimensional non-Hermitian disordered systems
• Type-II Weyl Points in Three-Dimensional Cold Atom Optical Lattices
• Stability of fractional Chern insulators in the effective continuum limit of Harper-Hofstadter bands with Chern number $|C|>1$
• Second-order topological corner states with ultracold atoms carrying orbital angular momentum in optical lattices
• Tunable axial gauge fields in engineered Weyl semimetals: Semiclassical analysis and optical lattice implementations
• Helical Floquet Channels in 1D Lattices
• Floquet Engineering of Haldane Chern Insulators and Chiral bosonic phase transitions
• Interaction-induced topological properties of two bosons in flat-band systems
• Measurement of spin Chern numbers in quantum simulated topological insulators
• Boson-mediated quantum spin simulators in transverse fields: XY model and spin-boson entanglement
• Quantum dynamics of bosons in a two-ring ladder: dynamical algebra, vortex-like excitations and currents
• Non-equilibrium Fractional Hall Response After a Topological Quench
• Topological Anderson insulators induced by random binary disorders
• Bosonic Pfaffian State in the Hofstadter-Bose-Hubbard Model
• Space, matter and topology
• Nonlinear Dirac Cones
• Topological features of ground states and topological solitons in generalized Su-Schrieffer-Heeger models using generalized time-reversal, particle-hole, and chiral symmetries
• Pretopological fractional excitations in the two-leg flux ladder
• Enhancing Kondo Coupling in Alkaline-Earth Atomic Gases with Confinement-induced Resonances in Mixed Dimensions
• Quantum Simulation of Competing Orders with Fermions in Quantum Optical Lattices
• Flat band induced by the interplay of synthetic magnetic flux and non-Hermiticity
• Simulating bosonic Chern insulators in one-dimensional optical superlattices
• Robust localized zero-energy modes from locally embedded PT-symmetric defects
• Topology-dependent quantum dynamics and entanglement-dependent topological pumping in superconducting qubit chains
• Preparing Atomic Topological Quantum Matter by Adiabatic Nonunitary Dynamics
• Topological superfluidity of lattice fermions inside a Bose-Einstein condensate
• Light-matter interactions near photonic Weyl points
• Optically induced topological spin-valley Hall effect for exciton polaritons
• On the observability of Pauli crystals
• Chiral magnetic effect in three-dimensional optical lattices
• Group theory study of the vibrational modes and magnetic order in the topological antiferromagnet MnBi${}_2$Te${}_4$
• Realising Type II Weyl Points in an Optical Lattice
• Finite-temperature properties of interacting bosons on a two-leg flux ladder
• Synthetic Hall ladder with tunable magnetic flux
• Topological Protection and Control of Quantum Markovianity
• Dynamics and Control of Edge States in Laser-driven Graphene Nanoribbons
• Spectroscopic determination of magnetic-field-dependent interactions in an ultracold Yb(3P2)-Li mixture
• Feasible model for photo-induced interband pairing
• Experimental realization of a high precision tunable hexagonal optical lattice
• Topological nodal chains in optical lattices
• Detecting topological transitions in two dimensions by Hamiltonian evolution
• Observing a topological phase transition with deep neural networks from experimental images of ultracold atoms
• Binary Bose-Einstein condensates in a disordered time-dependent potential
• Exact Topological Flat Bands from Continuum Landau Levels
• Hidden-symmetry-protected Z_2 topological insulator in a cubic lattice
• Many-body delocalization with random vector potentials
• Effects of Boundary on Orbital Magnetization for a Bilayer System with Different Chern Numbers
• Robust Identification of Topological Phase Transition by Self-Supervised Machine Learning Approach
• Tunability of Spin-Dependent Secondary Topological Interface States Induced in an Optical Complex Superlattice
• Entangled Cloning of Stabilizer Codes and Free Fermions
• Enhanced Directional Quantum Emission by Tunable Topological Doubly-Resonant Cavities
• Emergence of asymmetric fermionic order in interacting birefringent fermions
• Fractional quantum Hall states of dipolar fermions in a strained optical lattice
• Topological Quantum Phase Transition from Fermionic Integer Quantum Hall Phase to Bosonic Fractional Quantum Hall Phase through P-Wave Feshbach Resonance
• Topologically protected quantization of work
• Transport through Quantum Anomalous Hall Bilayers with Lattice Mismatch
• Thermometry for Laughlin States of Ultracold Atoms
• Simulating a Topological Transition in a Superconducting Phase Qubit by Fast Adiabatic Trajectories
• Bosonic Quantum Dynamics Following Colliding Potential Wells
• New Frontiers in Multidimensional Self-Trapping of Nonlinear Fields and Matter
• Non-Hermitian Aharonov-Bohm Cage
• Analytical solutions of topological surface states in a series of lattice models
• Metal-insulator phase transition and topology in a three-component system
• Three-nodal surface phonons in solid-state materials: Theory and material realization
• Digital Quantum Simulation of Floquet Topological Phases with a Solid-State Quantum Simulator
• Nonlinear optical response of Type-II Weyl fermions in two dimensions
• Giant synthetic gauge field for spinless microcavity polaritons in crossed electric and magnetic fields