Interferometry of non-Abelian band singularities and Euler class topology

Abstract

In systems with a real Bloch Hamiltonian band nodes can be characterised by a non-Abelian frame-rotation charge. The ability of these band nodes to annihilate pairwise is path dependent, since by braiding nodes in adjacent gaps the sign of their charges can be changed. Here, we theoretically construct and numerically confirm two concrete methods to experimentally probe these non-Abelian braiding processes and charges in ultracold atomic systems. We consider a coherent superposition of two bands that can be created by moving atoms through the band singularities at some angle in momentum space. Analyzing the dependency of excitations on the frame charges, we demonstrate an interferometry scheme passing through two band nodes, which reveals the relative frame charges and allows for measuring the multi-gap topological invariant. The second method relies on a single wavepacket probing two nodes sequentially, where the frame charges can be determined from the band populations. Our results present a feasible avenue for measuring non-Abelian charges of band nodes and the direct experimental verification of braiding procedures, which can be applied in a variety of settings including the recently discovered anomalous non-Abelian phases arising under periodic driving.

7+11 pages, 3+7 figures. Updated version, with new calculations in Supplemental Material

References in corpus (43)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Topological Insulators
• Topological insulators and superconductors
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Classification of topological quantum matter with symmetries
• Topological Crystalline Insulators
• Periodic table for topological insulators and superconductors
• Topological quantum chemistry
• Topological characterization of periodically-driven quantum systems
• Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice
• Topological Bands for Ultracold Atoms
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Exploring phase coherence in a 2D lattice of Bose-Einstein condensates
• The space group classification of topological band insulators
• Topological classification of crystalline insulators through band structure combinatorics
• Selective scattering between Floquet-Bloch and Volkov states in a topological insulator
• Fragile Topology and Wannier Obstructions
• Failure of Nielsen-Ninomiya theorem and fragile topology in two-dimensional systems with space-time inversion symmetry: application to twisted bilayer graphene at magic angle
• Periodic Table for Floquet Topological Insulators
• Realization of an anomalous Floquet topological system with ultracold atoms
• An Aharonov-Bohm interferometer for determining Bloch band topology
• Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time reversal symmetry
• Non-Abelian band topology in noninteracting metals
• Tenfold Way for Quadratic Lindbladians
• Measuring topology by dynamics: Chern number from linking number
• Non-Abelian reciprocal braiding of Weyl points and its manifestation in $\text{ZrTe}$
• Topological Euler class as a dynamical observable in optical lattices
• Experimental observation of non-Abelian topological charges and bulk-edge correspondence
• Observation of non-Abelian topological semimetals and their phase transitions
• Measuring Topological Number of a Chern-Insulator from Quench Dynamics
• Dual gauge field theory of quantum liquid crystals in two dimensions
• Geometric approach to fragile topology beyond symmetry indicators
• Phonons as a platform for non-Abelian braiding and its manifestation in layered silicates
• Hopf characterization of two-dimensional Floquet topological insulators
• Floquet multi-gap topology: Non-Abelian braiding and anomalous Dirac string phase
• Multi-gap topology and non-Abelian braiding of phonons from first principles
• How to Directly Measure Floquet Topological Invariants in Optical Lattices
• Observation of topological Euler insulators with a trapped-ion quantum simulator
• Manipulation and braiding of Weyl nodes using symmetry-constrained phase transitions
• Observation of topological Bloch-state defects and their merging transition
• Direct Geometric Probe of Singularities in Band Structure
• Beyond the Berry Phase: Extrinsic Geometry of Quantum States
• Berry's phase and the anomalous velocity of Bloch wavepackets

Cited by in corpus (9)

• Floquet multi-gap topology: Non-Abelian braiding and anomalous Dirac string phase
• Anomalous geometric transport signatures of topological Euler class
• Floquet non-Abelian topological charges and edge states
• Anomalous multi-gap topological phases in periodically driven quantum rotors
• Anomalous Topological Bloch Oscillations under Non-Abelian Gauge Fields
• Non-Abelian interference of topological edge states
• Three-dimensional spinless Euler insulators with rotational symmetry
• Gapped spinful phases obtained via Gutzwiller projections of Euler states
• Experimental Proposal on Non-Abelian Aharonov-Bohm Caging Effect with a Single Trapped Ion