Synthetic non-Abelian topological charges in ultracold atomic gases

Abstract

Topological phases associated with non-Abelian charges can exhibit a distinguished bulk-edge correspondence compared with Abelian phases, although elucidating this relationship remains challenging in traditional solid-state systems. In this paper, we propose a theoretical framework for synthesizing non-Abelian quaternion charges in ultracold atomic gases. By designing artificial spin-orbit coupling patterns, the topological edge modes demonstrate a clear correspondence with the band topology determined by various quaternion charges. This paves the way for observing the interface modes whose existence is attributed to the nonconservation multiplication relation, which is fundamental to non-Abelian charges. This scheme can be readily implemented using current ultracold atom techniques, offering a promising approach to explore the intriguing non-Abelian characteristics of the system.

10 pages, 8 figures

References in corpus (34)

• Tunable gauge potential for neutral and spinless particles in driven lattices
• A Bose-Einstein Condensate in a Uniform Light-induced Vector Potential
• Non-Abelian gauge potentials for ultra-cold atoms with degenerate dark states
• Synthetic dimensions and spin-orbit coupling with an optical clock transition
• Spin-orbit coupled fermions in an optical lattice clock
• Spin Hall effects for cold atoms in a light induced gauge potential
• Quantum Gases in Optical Boxes
• Dicke-type phase transition in a spin-orbit coupled Bose-Einstein condensate
• Topological Euler class as a dynamical observable in optical lattices
• Orbital analogue of quantum anomalous Hall effect in $p$-band systems
• Experimental observation of non-Abelian topological charges and bulk-edge correspondence
• Observation of non-Abelian topological semimetals and their phase transitions
• Realization of a fractional quantum Hall state with ultracold atoms
• Geometric approach to fragile topology beyond symmetry indicators
• Realizing and Detecting the Haldane's Quantum Hall effect with Ultracold Atoms
• Localization and topological transitions in non-Hermitian quasiperiodic lattices
• Observation of Non-Abelian Thouless Pump
• Hamiltonian engineering of spin-orbit coupled fermions in a Wannier-Stark optical lattice clock
• Four-band non-Abelian topological insulator and its experimental realization
• Floquet multi-gap topology: Non-Abelian braiding and anomalous Dirac string phase
• Real-space detection and manipulation of topological edge modes with ultracold atoms
• Measurement of spin Chern numbers in quantum simulated topological insulators
• Compressibility and the Equation of State of an Optical Quantum Gas in a Box
• Observation of unitary p-wave interactions between fermions in an optical lattice
• Floquet Non-Abelian Topological Insulator and Multifold Bulk-Edge Correspondence
• Quantized Topological Anderson-Thouless Pump
• Experimental realization of spin-tensor momentum coupling in ultracold Fermi gases
• Extracting non-Abelian quantum metric tensor and its related Chern numbers
• Non-Abelian quantum geometric tensor in degenerate topological semimetals
• Link between \emph{Zitterbewegung} and topological phase transition
• Synthetic Topological Vacua of Yang-Mills Fields in Bose-Einstein Condensates
• Tunable boson-assisted finite-range interaction and engineering Majorana corner modes in optical lattices
• Effective Hamiltonian with tunable mixed pairing in driven optical lattices
• Artificial topological models based on a one-dimensional spin-dependent optical lattice

Cited by in corpus (5)

• Floquet non-Abelian topological charges and edge states
• Synthetic spin-orbit coupling for the multispin models in optical lattices
• Anomalous Topological Bloch Oscillations under Non-Abelian Gauge Fields
• Coupled-wire construction of non-Abelian higher-order topological phases
• Proposal for realizing and probing topological crystalline insulators in optical lattices