Non-Abelian gauge fields and topological insulators in shaken optical lattices

Abstract

Time-periodic driving like lattice shaking offers a low-demanding method to generate artificial gauge fields in optical lattices. We identify the relevant symmetries that have to be broken by the driving function for that purpose and demonstrate the power of this method by making concrete proposals for its application to two-dimensional lattice systems: We show how to tune frustration and how to create and control band touching points like Dirac cones in the shaken kagomé lattice. We propose the realization of a topological and a quantum spin Hall insulator in a shaken spin-dependent hexagonal lattice. We describe how strong artificial magnetic fields can be achieved for example in a square lattice by employing superlattice modulation. Finally, exemplified on a shaken spin-dependent square lattice, we develop a method to create strong non-Abelian gauge fields.

5 pages, 4 figures + supplemental material (2 pages, 1 figure). Accepted for publication in Phys. Rev. Lett.. Minor changes with respect to version 2 to improve presentation

References in corpus (19)

• Non-Abelian Anyons and Topological Quantum Computation
• Topological characterization of periodically-driven quantum systems
• An Open-System Quantum Simulator with Trapped Ions
• Dynamical control of matter-wave tunneling in periodic potentials
• Tunable gauge potential for neutral and spinless particles in driven lattices
• Engineering Time-Reversal Invariant Topological Insulators With Ultra-Cold Atoms
• Realistic Time-Reversal Invariant Topological Insulators With Neutral Atoms
• Multi-Component Quantum Gases in Spin-Dependent Hexagonal Lattices
• Coherent control of dressed matter waves
• Observation of photon-assisted tunneling in optical lattices
• Bose condensation in flat bands
• Non-Abelian optical lattices: Anomalous quantum Hall effect and Dirac Fermions
• Staggered-Vortex Superfluid of Ultracold Bosons in an Optical Lattice
• Periodically driven Quantum Ratchets: Symmetries and Resonances
• AC-induced superfluidity
• Quantum Phases of Trapped Ions in an Optical Lattice
• Avoided level crossing spectroscopy with dressed matter waves
• Non-abelian anyons from degenerate Landau levels of ultracold atoms in artificial gauge potentials
• Competing Superconducting States for Ultracold Atoms in Optical Lattices with Artificial Staggered Magnetic Field

Cited by in corpus (59)

• Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
• Topological Quantum Matter with Ultracold Gases in Optical Lattices
• Non-standard Hubbard models in optical lattices: a review
• Chiral symmetry and bulk--boundary correspondence in periodically driven one-dimensional systems
• Topological invariants of Floquet systems: General formulation, special properties, and Floquet topological defects
• Topological index for periodically driven time-reversal invariant 2D systems
• Anisotropic dynamics of a spin-orbit coupled Bose-Einstein condensate
• Periodically-driven quantum matter: the case of resonant modulations
• Scattering Theory for Floquet-Bloch States
• Time-Reversal-Invariant Hofstadter-Hubbard Model with Ultracold Fermions
• Anomalous Hall Effects of Light and Chiral Edge Modes on the Kagome Lattice
• Floquet Edge States with Ultracold Atoms
• Superradiance Lattice
• Topological insulator and particle pumping in a one-dimensional shaken optical lattice
• Sum rules, dipole oscillation and spin polarizability of a spin-orbit coupled quantum gas
• Spin Orbit Coupling in Periodically Driven Optical Lattices
• Stability of a Floquet Bose-Einstein condensate in a one-dimensional optical lattice
• Floquet analysis of a quantum system with modulated periodic driving
• Quantum simulation of non-trivial topology
• Meissner-like effect for synthetic gauge field in multimode cavity QED
• Floquet control of quantum dissipation in spin chains
• The role of real-space micromotion for bosonic and fermionic Floquet fractional Chern insulators
• Floquet edge states in a harmonically driven integer quantum Hall system
• Shaping topological properties of the band structures in a shaken optical lattice
• Chains with loops - synthetic magnetic fluxes and topological order in one-dimensional spin systems
• Transverse collisional instabilities of a Bose-Einstein condensate in a driven one-dimensional lattice
• Stroboscopic versus non-stroboscopic dynamics in the Floquet realization of the Harper-Hofstadter Hamiltonian
• Boson-mediated quantum spin simulators in transverse fields: XY model and spin-boson entanglement
• Quantum disorder in the spatially completely anisotropic triangular lattice II: frustrated hard-core bosons
• The fate of dynamical many-body localization in the presence of disorder
• Quantum disorder in the spatially completely anisotropic triangular lattice I: Heisenberg $S=1/2$ antiferromagnet
• Dimensional crossover and cold-atom realization of topological Mott insulators
• Disordered Chern insulator with a two step Floquet drive
• Identifying topological edge states in 2D optical lattices using light scattering
• Spiral spin textures of bosonic Mott insulator with SU(3) spin-orbit coupling
• Mimicking interacting relativistic theories with stationary pulses of light
• Time-of-flight patterns of ultra-cold bosons in optical lattices in various Abelian artificial magnetic field gauges
• Preparing Atomic Topological Quantum Matter by Adiabatic Nonunitary Dynamics
• Excitation of atoms in an optical lattice driven by polychromatic amplitude modulation
• Floquet FFLO superfluids and Majorana fermions in a shaken fermionic optical lattice
• Ultracold fermions in a one-dimensional bipartite optical lattice: metal-insulator transitions driven by shaking
• Breakdown of the Peierls substitution for the Haldane model with ultracold atoms
• Topological Floquet states on a Möbius band irradiated by circularly polarised light
• Spontaneous magnetization and anomalous Hall effect in an emergent Dice lattice
• Simulating Dirac models with ultracold atoms in optical lattices
• Transport signatures in topological systems coupled to AC fields
• Simulation of frustrated classical XY models with ultra-cold atoms in 3D triangular optical lattices
• Topological defect dynamics of vortex lattices in Bose--Einstein condensates
• Dimerized Mott insulators in hexagonal optical lattices
• Spontaneous quantum Hall effect in an atomic spinor Bose-Fermi mixture
• Rapidly-oscillating scatteringless non-Hermitian potentials and the absence of Kapitza stabilization
• Single atom edge-like states via quantum interference
• Quantum crystal growing: Adiabatic preparation of a bosonic antiferromagnet in the presence of a parabolic inhomogeneity
• Directed motion of doublons and holes in periodically driven Mott insulators
• Symmetry-enriched Bose-Einstein condensates in spin-orbit coupled bilayer system
• Topological spin models in Rydberg lattices
• Correspondence between a shaken honeycomb lattice and the Haldane model
• Topological orbital superfluid with chiral d-wave order in a rotating optical lattice
• Kaluza-Klein Reduction of the 6 Dimensional \\ Dirac Equation on ${\mathbb{S}}^3\cong SU(2)$ and \\ Non-abelian Topological Insulators