Four-Dimensional Quantum Hall Effect with Ultracold Atoms

Abstract

We propose a realistic scheme to detect the 4D quantum Hall effect using ultracold atoms. Based on contemporary technology, motion along a synthetic fourth dimension can be accomplished through controlled transitions between internal states of atoms arranged in a 3D optical lattice. From a semi-classical analysis, we identify the linear and non-linear quantized current responses of our 4D model, relating these to the topology of the Bloch bands. We then propose experimental protocols, based on current or center-of-mass-drift measurements, to extract the topological 2nd Chern number. Our proposal sets the stage for the exploration of novel topological phases in higher dimensions.

6 pages, 2 figures + appendix (10 pages)

References in corpus (20)

• Many-Body Physics with Ultracold Gases
• Non-Abelian Anyons and Topological Quantum Computation
• Topological Field Theory of Time-Reversal Invariant Insulators
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Observation of chiral edge states with neutral fermions in synthetic Hall ribbons
• Single-Spin Addressing in an Atomic Mott Insulator
• Visualizing edge states with an atomic Bose gas in the quantum Hall regime
• Observation of topological surface state quantum Hall effect in an intrinsic three-dimensional topological insulator
• Periodically-driven quantum matter: the case of resonant modulations
• Scattering Theory for Floquet-Bloch States
• Magnetic crystals and helical liquids in alkaline-earth fermionic gases
• Spin Gauge Fields: from Berry Phase to Topological Spin Transport and Hall Effects
• Semiclassical Diagonalization of Quantum Hamiltonian and Equations of Motion with Berry Phase Corrections
• Population dynamics in Floquet realisation of Harper-Hofstadter Hamiltonian
• Transverse collisional instabilities of a Bose-Einstein condensate in a driven one-dimensional lattice
• Metallic phase of the quantum Hall effect in four-dimensional space
• On the Hamiltonian nature of semiclassical equations of motion in the presence of an electromagnetic field and Berry curvature
• Topological meaning of Z${}_2$ numbers in time reversal invariant systems
• Adiabatic Control of Atomic Dressed States for Transport and Sensing
• Reply to Comment on "Berry phase correction to electron density of states in solids"

Cited by in corpus (162)

• Topological Photonics
• Topological Photonics
• Topological phases of non-Hermitian systems
• Topological Bands for Ultracold Atoms
• Topological Quantum Matter with Ultracold Gases in Optical Lattices
• Photonic topological pumping through the edges of a dynamical four-dimensional quantum Hall system
• Synthetic Dimension in Photonics
• Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump
• Topological quantum matter in synthetic dimensions
• Photonic Topological Insulator in Synthetic Dimensions
• Synthetic dimensions in integrated photonics: From optical isolation to 4D quantum Hall physics
• Dirac Electrons in a Dodecagonal Graphene Quasicrystal
• Topological quantum matter with cold atoms
• Synthetic dimensions and spin-orbit coupling with an optical clock transition
• Topological exceptional surfaces in non-Hermitian systems with parity-time and parity-particle-hole symmetries
• Thouless pumping and topology
• Matter-wave diffraction from a quasicrystalline optical lattice
• Circuit Implementation of a Four-Dimensional Topological Insulator
• Observation of a non-Abelian Yang Monopole: From New Chern Numbers to a Topological Transition
• Topologically Enhanced Harmonic Generation in a Nonlinear Transmission Line Metamaterial
• Synthetic Dimensions for Cold Atoms from Shaking a Harmonic Trap
• Topological one-way fiber of second Chern number
• Probing topology by "heating": Quantized circular dichroism in ultracold atoms
• 4D spinless topological insulator in a periodic electric circuit
• Giant Atoms in a Synthetic Frequency Dimension
• Competition and interplay between topology and quasi-periodic disorder in Thouless pumping of ultracold atoms
• Tutorial: synthetic frequency dimensions in dynamically modulated ring resonators
• The 6D quantum Hall effect and 3D topological pumps
• Topological circuits of inductors and capacitors
• Measurement of Chern numbers through center-of-mass responses
• Revealing tensor monopoles through quantum-metric measurements
• Laughlin-like states in bosonic and fermionic atomic synthetic ladders
• Semi-synthetic zigzag optical lattice for ultracold bosons
• A Five Dimensional Generalization of the Topological Weyl Semimetal
• Dynamically manipulating topological physics and edge modes in a single degenerate optical cavity
• Probing Weyl Physics with One-dimensional Sonic Crystals
• Synthetic Dimensions with Magnetic Fields and Local Interactions in Photonic Lattices
• Floquet Semimetal with Floquet-band Holonomy
• Electromagnetic response of quantum Hall systems in dimensions five and six and beyond
• Second Chern Number and Non-Abelian Berry Phase in Topological Superconducting Systems
• Field-Tunable One-Sided Higher-Order Topological Hinge States in Dirac Semimetals
• Exploring 2D synthetic quantum Hall physics with a quasi-periodically driven qubit
• Boundary states of 4D topological matter: Emergence and full 3D-imaging of nodal Seifert surfaces
• A comprehensive review on developments of synthetic dimensions
• Relating the topology of Dirac Hamiltonians to quantum geometry: When the quantum metric dictates Chern numbers and winding numbers
• Electric circuit simulations of $n$th-Chern insulators in $2n$-dimensional space and their non-Hermitian generalizations for arbitral $n$
• Piezoelectric actuation for integrated photonics
• Smart patterning for topological pumping of elastic surface waves
• Topological energy conversion through bulk or boundary of driven systems
• Tensor Berry connections and their topological invariants
• Three-dimensional Chiral Lattice Fermion in Floquet Systems
• Synthetic dimensions in the strong-coupling limit: supersolids and pair-superfluids
• Ground-state quantum geometry in superconductor-quantum dot chains
• Dynamical piezoelectric and magnetopiezoelectric effects in polar metals from Berry phases and orbital moments
• Coupled-wire constructions: a Luttinger liquid approach to topology
• Creating topological interfaces and detecting chiral edge modes in a 2D optical lattice
• Topological Gapless Matters in Three-dimensional Ultracold Atomic Gases
• Hyperbolic non-Abelian semimetal
• Local Topological Markers in Odd Dimensions
• Different lattice geometries with synthetic dimension
• Four-dimensional semimetals with tensor monopoles: From surface states to topological responses
• Theory of a 3+1D fractional chiral metal: interacting variant of the Weyl semimetal
• Pretopological fractional excitations in the two-leg flux ladder
• Topological Sliding Moiré Heterostructure
• Realization of an atomic quantum Hall system in four dimensions
• Exploring interacting topological insulator of extended Su-Schrieffer-Heeger model
• Antichiral states in twisted graphene multilayers
• Topologically nontrivial Andreev bound states
• Efficient algorithm to compute the second Chern number in four dimensional systems
• Axial anomaly in multi-Weyl and triple-point semimetals
• Dissipative analog of four-dimensional quantum Hall physics
• No-go theorem for topological insulators and sure-fire recipe for Chern insulators
• Measuring second Chern number from non-adiabatic effects
• Loading Ultracold Gases in Topological Floquet Bands: Current and Center-of-Mass Responses
• Bose-Hubbard physics in synthetic dimensions from interaction Trotterization
• Four-dimensional topological lattices through connectivity
• Devil's staircases in synthetic dimensions and gauge fields
• Light-induced fractional quantum Hall phases in graphene
• Exploring topological phase transition andWeyl physics in five dimensions with electric circuits
• Measuring Chern numbers in Hofstadter strips
• Exceptional Cones in 4D Parameter Space
• Estimate of the critical exponent of the Anderson transition in the three and four dimensional unitary universality classes
• Six-dimensional time-space crystalline structures
• The Hofstadter Butterfly in a Dynamic Cavity-Induced Synthetic Magnetic Field
• Different models of gravitating Dirac fermions in optical lattices
• Synthetic gauge field and chiral physics on two-leg superconducting circuits
• Light-matter interactions near photonic Weyl points
• Real space mean-field theory of a spin-1 Bose gas in synthetic dimensions
• Interplay of Band Geometry and Topology in Ideal Chern Insulators in Presence of External Electromagnetic Fields
• Non-Hermitian topology and criticality in photonic arrays with engineered losses
• Tunable Flux through a Synthetic Hall Tube of Neutral Fermions
• Entangled multi-component 4D quantum Hall states from photonic crystal defects
• T-duality simplifies bulk-boundary correspondence: some higher dimensional cases
• Topological Number of Edge States
• Dimension transcendence and anomalous charge transport in magnets with moving multiple-$Q$ spin textures
• Topological Dissipative Photonics and Topological Insulator Lasers in Synthetic Time-Frequency Dimensions
• Superfluid Vortices in Four Spatial Dimensions
• Revealing the boundary Weyl physics of the four-dimensional Hall effect via phason engineering in metamaterials
• Chiral Anomaly, Topological Field Theory, and Novel States of Matter
• Ergodic Edge Modes in the 4D Quantum Hall Effect
• Perfect transmission of 3D massive Kane fermions in HgCdTe Veselago lenses
• Non-Abelian quantum geometric tensor in degenerate topological semimetals
• Inducing a many-body topological state of matter through Coulomb-engineered local interactions
• Tensor monopoles and negative magnetoresistance effect in optical lattices
• Weyl singularities in polaritonic multi-terminal Josephson junctions
• Topological Electromagnetic Effects and Higher Second Chern Numbers in Four-Dimensional Gapped Phases
• Linking topological features of the Hofstadter model to optical diffraction figures
• Periodic driving induced helical Floquet channels with ultracold atoms in momentum space
• Gauge Invariance and Anomalies in Condensed Matter Physics
• Periodic Clifford symmetry algebras on flux lattices
• Simulating artificial one-dimensional physics with ultra-cold fermionic atoms: three exemplary themes
• Fractional Topological States in Quantum Spin Chains with Periodical Modulation
• Simulating quantum transport with ultracold atoms and interaction effects
• Fractional Quantum Hall Effect for Extended Objects: from Skyrmionic Membranes to Dyonic Strings
• Plateau transitions of spin pump and bulk-edge correspondence
• A semiclassical treatment of spinor topological effects in driven, inhomogeneous insulators under external electromagnetic fields
• Topological gap labeling with the third Chern numbers in three-dimensional quasicrystals
• On the uniqueness of ghost-free special gravity
• Exact diagonalization of cubic lattice models in commensurate Abelian magnetic fluxes and translational invariant non-Abelian potentials
• ADHM and the 4d Quantum Hall Effect
• Kinetic derivation of generalized phase space Chern-Simons theory
• Topological Insulators with Hybrid-order Boundary States
• $SO(5)$ Landau Model and 4D Quantum Hall Effect in The $SO(4)$ Monopole Background
• Four-dimensional Floquet topological insulator with an emergent second Chern number
• Simulating Higher-Order Topological Insulators in Density Wave Insulators
• Geometrical Rabi oscillations and Landau-Zener transitions in non-Abelian systems
• Spin-tensor Meissner currents of ultracold bosonic gas in an optical lattice
• Simulating two-dimensional dynamics within a large-size atomic spin
• Higher Derivative Theories for Interacting Massless Gravitons in Minkowski Spacetime
• Synthetic Hall tube of interacting fermions
• Second Euler number in four dimensional synthetic matter
• Topological optical Raman superlattices
• Topology in quasicrystals
• Creating high-dimensional topological physics using a single ring resonator
• Generalized Aubry-Andre-Harper Models in Optical Superlattices
• Curved vortex surfaces in four-dimensional superfluids: I. Unequal-frequency double rotations
• Unconventional Topological Insulators from Extended Topological Band Degeneracies
• Topological Chiral Edge States in a Synthetic Dimension of Atomic Trap States
• Tensor Theory for Higher Dimensional Chern Insulators with Large Chern Numbers
• Dynamical characterization of $Z_2$ Floquet topological phases via quantum quenches
• Curved vortex surfaces in four-dimensional superfluids: II. Equal-frequency double rotations
• Geometry induced quantum Hall effect and Hall viscosity
• Quantum Signatures of Topological Phase in Bosonic Quadratic System
• Phase space curvature in spin-orbit coupled ultracold atom systems
• Hopf Semimetals
• Three-dimensional $\mathbb{Z}$ topological insulators without reflection symmetry
• Evaluation of real-space second Chern number using the kernel polynomial method
• Topology and criticality in non-Hermitian multimodal optical resonators through engineered losses
• Decoding the drive-bath interplay: A guideline to enhance superconductivity
• Topology vs localization in synthetic dimensions
• Fractional Quantum Hall States on CP2 Space
• openMMF: a library for multimode driven quantum systems
• Higher-dimensional magnetic Skyrmions
• Emergent Weyl-like points in periodically modulated systems
• Real-space representation of the second Chern number
• Synthetic-lattice Bloch wave dynamics in a single-mode microwave resonator
• Numerical calculation of the $k$-space second Chern number in four dimensions
• Polarization-dependent topology in quantum emitter chains
• Gapless hinge states from adiabatic pumping of axion coupling
• Advances in Synthetic Gauge Fields for Light Through Dynamic Modulation
• From Bopp Shifts to Toroidal Shadows: K-Theoretic Gap Labels in Noncommutative Quantum Mechanics
• Synthetic Weyl points in generalized parameter space and their topological properties