Realization of an atomic quantum Hall system in four dimensions

Abstract

Modern condensed matter physics relies on the concept of topology to classify matter, from quantum Hall systems to topological insulators. Engineered systems, benefiting from synthetic dimensions, can potentially give access to novel topological states predicted in dimensions $D>3$. We report the realization of an atomic quantum Hall system evolving in four dimensions (4D), with two spatial dimensions and two synthetic ones encoded in the large spin of dysprosium atoms. The non-trivial topology is evidenced by measuring a quantized electromagnetic non-linear response and observing anisotropic hyperedge modes. We also excite non-planar cyclotron motion, contrasting with its circular equivalents in $D\le 3$. Our work opens to the investigation of strongly-correlated topological liquids in 4D generalizing fractional quantum Hall states.

14 pages, 13 figures. This is the author's version of the work. It is posted here by permission of the AAAS for personal use, not for redistribution. The definitive version was published in Science 384 doi: 10.1126/science.adf8459

References in corpus (33)

• Non-Abelian Anyons and Topological Quantum Computation
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Topological Field Theory of Time-Reversal Invariant Insulators
• Discovery of a Weyl Fermion Semimetal and Topological Fermi Arcs
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Colloquium: Topological Band Theory
• Synthetic magnetic fields for ultracold neutral atoms
• Experimental observation of Weyl points
• Observation of chiral edge states with neutral fermions in synthetic Hall ribbons
• Visualizing edge states with an atomic Bose gas in the quantum Hall regime
• Synthetic gauge fields in synthetic dimensions
• A Four Dimensional Generalization of the Quantum Hall Effect
• Photonic topological pumping through the edges of a dynamical four-dimensional quantum Hall system
• Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump
• Topological quantum matter in synthetic dimensions
• Synthetic dimensions in integrated photonics: From optical isolation to 4D quantum Hall physics
• Mapping topological order in coordinate space
• Four-Dimensional Quantum Hall Effect in a Two-Dimensional Quasicrystal
• Four-Dimensional Quantum Hall Effect with Ultracold Atoms
• Quantum Hall Effect in Higher Dimensions
• Circuit Implementation of a Four-Dimensional Topological Insulator
• Observation of a non-Abelian Yang Monopole: From New Chern Numbers to a Topological Transition
• Probing chiral edge dynamics and bulk topology of a synthetic Hall system
• Effective field theory description of the higher dimensional quantum Hall liquid
• The 6D quantum Hall effect and 3D topological pumps
• Measurement of Chern numbers through center-of-mass responses
• The effective action for edge states in higher dimensional quantum Hall systems
• Experimental Observation of Tensor Monopoles with a Superconducting Qudit
• A Five Dimensional Generalization of the Topological Weyl Semimetal
• Electromagnetic response of quantum Hall systems in dimensions five and six and beyond
• Local Topological Markers in Odd Dimensions
• Superfluid Vortices in Four Spatial Dimensions
• Simulating two-dimensional dynamics within a large-size atomic spin

Cited by in corpus (15)

• A comprehensive review on developments of synthetic dimensions
• Quantum mixtures of ultracold gases of neutral atoms
• Synthetic multi-dimensional Aharonov-Bohm cages in Fock state lattices
• Observation of chiral edge transport in a rapidly-rotating quantum gas
• Colloquium: Synthetic quantum matter in non-standard geometries
• Topological Insulators with Hybrid-order Boundary States
• Second Euler number in four dimensional synthetic matter
• Topological Chiral Edge States in a Synthetic Dimension of Atomic Trap States
• Curved vortex surfaces in four-dimensional superfluids: II. Equal-frequency double rotations
• Curved vortex surfaces in four-dimensional superfluids: I. Unequal-frequency double rotations
• Synthetic-lattice Bloch wave dynamics in a single-mode microwave resonator
• Liouville Fock state lattices and potential simulators
• Ultracold atomic lattice systems for simulating topological phases: A review
• Encoding a topological gauge theory on a ring-shaped Raman-coupled Bose gas
• Determination of the ground state polarizability of ${}^{162}$Dy near 530 nm