Creation of effective magnetic fields in optical lattices: The Hofstadter butterfly for cold neutral atoms

Abstract

We investigate the dynamics of neutral atoms in a 2D optical lattice which traps two distinct internal states of the atoms in different columns. Two Raman lasers are used to coherently transfer atoms from one internal state to the other, thereby causing hopping between the different columns. By adjusting the laser parameters appropriately we can induce a non vanishing phase of particles moving along a closed path on the lattice. This phase is proportional to the enclosed area and we thus simulate a magnetic flux through the lattice. This setup is described by a Hamiltonian identical to the one for electrons on a lattice subject to a magnetic field and thus allows us to study this equivalent situation under very well defined controllable conditions. We consider the limiting case of huge magnetic fields -- which is not experimentally accessible for electrons in metals -- where a fractal band structure, the Hofstadter butterfly, characterizes the system.

6 pages, RevTeX

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• Adiabatic preparation of vortex lattices
• Hall conductivity beyond the linear response regime
• Chiral orbital order of interacting bosons without higher bands
• Hall response of interacting bosonic atoms in strong gauge fields: from condensed to FQH states
• Bose-Einstein condensates in rotating ring-shaped lattices: a multimode model
• Evidence of spin liquid with hard-core bosons in a square lattice
• Controlled parity switch of persistent currents in quantum ladders
• Harnessing synthetic gauge fields for maximally entangled state generation
• Seeing Hofstadter's Butterfly in Atomic Fermi Gases
• Ultracold bosons in a synthetic periodic magnetic field: Mott phases and re-entrant superfluid-insulator transitions
• Floquet analysis of pulsed Dirac systems: A way to simulate rippled graphene
• Single atom edge-like states via quantum interference
• Geometric quantum phase for displaced states for a particle with an induced electric dipole moment
• Strongly Interacting Two-component Coupled Bose Gas in Optical Lattices
• Simulation of two-flavors symmetry-locking phases in ultracold fermionic mixtures
• Degeneracy of Many-body Quantum States in an Optical Lattice with a Uniform Magnetic Field
• Mott-Insulator Transition for Ultracold Fermions in Two-Dimensional Optical Lattices
• Exact diagonalization of cubic lattice models in commensurate Abelian magnetic fluxes and translational invariant non-Abelian potentials
• Simulating and detecting artificial magnetic fields in trapped atoms
• Tunable quantum switcher and router of cold atom matter waves using artificial magnetic fields
• Dynamically Generated Synthetic Electric Fields for Photons
• Synthetic Gauge Fields for Lattices with Multi-Orbital Unit Cells: Routes towards a $\pi$-flux Dice Lattice with Flat Bands
• Synthetic topological Kondo insulator in a pumped optical cavity
• Spin-Orbit Coupling and Topological States in $F=\frac{3}{2}$ Cold Fermi Gas
• Microscopic Study of the Coupled-Wire Construction and Plausible Realization in Spin-Dependent Optical Lattices
• Quantum walks accompanied by spin flipping in one-dimensional optical lattices
• Topological transitions in a model with Particle-Hole symmetry, Pancharatnam-Berry Curvature and Dirac Points
• Universal spatiotemporal dynamics of spontaneous superfluidity breakdown in the presence of synthetic gauge fields
• Simulation of gauge transformations on systems of ultracold atoms
• Quantized electromagnetic response of three-dimensional chiral topological insulators
• Energy Spectrum of Bloch Electrons Under Checkerboard Field Modulations
• Layered Quantum Hall Insulators with Ultracold Atoms
• Fractional Excitations in Cold Atomic Gases
• Non-Abelian gauge potential driven localization transition in quasiperiodic optical lattices
• Cyclotron dynamics of a Bose-Einstein condensate in a quadruple-well potential with synthetic gauge fields
• Finite-temperature phase structures of hard-core bosons in an optical lattice with an effective magnetic field
• Elementary Excitations of a Bose-Einstein Condensate in an Effective Magnetic Field
• Spin-1 bosons in an external magnetic field and a three body interaction potential
• Valley-dependent gauge fields for ultracold atoms in square optical superlattices
• Exciton condensation in an extended spinless Falicov Kimball model in the presence of orbital magnetic fields
• Generalized Interaction-Free Evolutions
• Effective field theory for two-species bosons in an optical lattice: Multiple order, the Nambu-Goldstone bosons, the Higgs mode and vortex lattice
• Faithful Simulation and Detection of Quantum Spin Hall Effect on Superconducting Circuits
• Symmetry-enriched Bose-Einstein condensates in spin-orbit coupled bilayer system
• A method of state-selective transfer of atoms between microtraps based on the Franck-Condon Principle
• Electron structure of the Falicov-Kimball model with a magnetic field
• Topological spin models in Rydberg lattices
• Light-Matter interactions in Hofstadter lattice with the next-nearest neighbor couplings
• Topological spin-orbit-coupled fermions beyond rotating wave approximation
• Floquet Flux Attachment in Cold Atomic Systems
• Synthetic magneto-hydrodynamics in Bose-Einstein condensates and routes to vortex nucleation
• Engineering flux-controlled flat bands and topological states in a Stagome lattice
• Fragility of the Laughlin state in an anharmonically-trapped Bose-Einstein condensate
• Artificial topological models based on a one-dimensional spin-dependent optical lattice
• Quantum Zeno-based Detection and State Engineering of Ultracold Polar Molecules
• Topological-Fermi-Liquid to Quantum-Hall-Liquid Transitions: $p$-Band and $d$-Band Fermions in a Magnetic Field
• Topological multiferroic phases in the extended Kane-Mele-Hubbard Model in the Hofstadter regime
• Emergence of non-Abelian SU(2) invariance in Abelian frustrated fermionic ladders
• Efficient algorithm to compute the Berry conductivity
• Landau-Zener tunneling in 2D periodic structures in the presence of a gauge field I: Tunneling rates
• Single-branch theory of ultracold Fermi gases with artificial Rashba spin-orbit coupling
• Topological spinor vortex matter on spherical surface induced by non-Abelian spin-orbital-angular-momentum coupling
• Transport Enhancement of Irregular Optical Lattices with Polychromatic Amplitude Modulation
• Determination of Chern numbers with a phase retrieval algorithm
• Non-equilibrium $8\pi$ Josephson Effect in Atomic Kitaev Wires
• Dynamics of fermions in an amplitude modulated lattice
• Phase diagram and non-Abelian symmetry locking for fermionic mixtures with unequal interactions
• Finite Temperature Phase Diagram in Rotating Bosonic Optical Lattice
• Fulde-Ferrell superfluids in spinless ultracold Fermi gases
• Topological lattice using multi-frequency radiation
• Solid-state magnetic traps and lattices
• Surveying structural complexity in quantum many-body systems
• Circulating Current States in Bilayer Fermionic and Bosonic Systems
• Cold atoms in U(3) gauge potentials
• Chiral excitation flows of a multinode network based on synthetic gauge fields
• Abelian and non-Abelian quantum spin liquids in a three-component Bose gas on optical Kagome lattices
• Exact diagonalization using hierarchical wave functions and calculation of topological entanglement entropy
• Fractionalization via ${\mathbb{Z}}_2$ Gauge Fields at a Cold Atom Quantum Hall Transition
• Laser assisted tunneling in a Tonks-Girardeau gas
• Bose-Einstein Condensates in Non-abelian Gauge Fields
• Measurement and Significance of Wilson Loops in Synthetic Gauges Fields
• Nonreciprocal microwave transmission based on Gebhard-Ruckenstein hopping
• Non-invasive measurement of currents in analog quantum simulators
• Bosonic Fractional Quantum Hall States in Rotating Optical Lattices: Projective Symmetry Group Analysis
• Dynamical Generation of Synthetic Electric Fields for Photons in the Quantum Regime
• Homogeneous Magnetic Flux in Rydberg Lattices
• Stability of superfluids in tilted optical lattices with periodic driving
• Generating topological optical flux lattices for ultracold atoms by modulated Raman and radio-frequency couplings
• Chiral Gravitons on the Lattice
• Momentum-space dynamics of Dirac quasiparticles in correlated random potentials: Interplay between dynamical and Berry phases
• Stability of Fractional Quantum Hall States in Disordered Photonic Systems
• Transition from the mean-field to the bosonic Laughlin state in a rotating Bose-Einstein condensate
• Electron cloud design for Rydberg multi-qubit gates
• Quantum science with arrays of metastable helium-3 atoms
• Quantum Hall states for $\alpha =1/3$ in optical lattices
• Superpositions in Atomic Quantum Rings
• Interacting fermions in two dimension in simultaneous presence of disorder and magnetic field
• Two-dimensional imaging of gauge fields in optical lattices
• Transient Oscillation of Currents in Quantum Hall Effect of Bloch Electrons
• Topological bands in the continuum using Rydberg states
• Vortices in rotating optical lattices: commensurability, hysteresis, and proximity to the Mott State
• Waveguide QED toolboxes for universal quantum matter
• Landau Quantization for $\Lambda$-Type Neutral Atoms in an Homogeneous Spin-Dependent Gauge Potential
• The attractive Hubbard model as an $SO(3)$ system of competing phases: supersolid order and its thermal melting
• Generation, manipulation and detection of snake state trajectories of a neutral atom in a ring-cavity
• Semiclassical asymptotics of the Aharonov-Bohm interference process
• Quantum Hall-like effect for neutral particles with magnetic dipole moments in a quantum dot
• The Sagnac Effect in Optical Lattices with Laser-Assisted Tunneling
• Quantum States and Spectra of Small Cylindrical and Toroidal Lattices
• Competition of light- and phonon-dressing in microwave-dressed Bose polarons
• Ultracold atomic lattice systems for simulating topological phases: A review
• Proposal for realizing and probing topological crystalline insulators in optical lattices
• Orbital Optical Raman Lattice
• Synthetic gauge field and pseudospin-orbit interaction in a stacked two-dimensional ring-network lattice
• Geometric Phases generated by the non-trivial spatial topology of static vector fields coupled to a neutral spin-endowed particle. Application to 171Yb atoms trapped in a 2D optical lattice
• Detecting degenerate bands topological invariants in optical lattice
• Emergence of caustics in dynamics of the Kitaev model
• Exact Parent Hamiltonians for All Landau Level States in a Half-flux Lattice
• Entanglement Spectroscopy and probing the Li-Haldane Conjecture in Topological Quantum Matter
• Emergent dipole field theory in atomic ladders
• Chiral Graviton Modes in Fermionic Fractional Chern Insulators
• Finite size effects and Hofstadter butterfly in a bosonic Mott insulator with relativistic dispersion background