Topological Euler class as a dynamical observable in optical lattices

Abstract

The last years have witnessed rapid progress in the topological characterization of out-of-equilibrium systems. We report on robust signatures of a new type of topology -- the Euler class -- in such a dynamical setting. The enigmatic invariant $(\xi )$ falls outside conventional symmetry-eigenvalue indicated phases and, in simplest incarnation, is described by triples of bands that comprise a gapless pair, featuring $2\xi$ stable band nodes, and a gapped band. These nodes host non-Abelian charges and can be further undone by converting their charge upon intricate braiding mechanisms, revealing that Euler class is a fragile topology. We theoretically demonstrate that quenching with non-trivial Euler Hamiltonian results in stable monopole-antimonopole pairs, which in turn induce a linking of momentum-time trajectories under the first Hopf map, making the invariant experimentally observable. Detailing explicit tomography protocols in a variety of cold-atom setups, our results provide a basis for exploring new topologies and their interplay with crystalline symmetries in optical lattices beyond paradigmatic Chern insulators.

6+7 pages, 3+3 figures; new version features improved exposition and new appendix describing simplified models

References in corpus (8)

• Topological Crystalline Insulators
• Topological characterization of periodically-driven quantum systems
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• The space group classification of topological band insulators
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• Optical Flux Lattices for Ultracold Atomic Gases
• Non-equilibrium Fractional Hall Response After a Topological Quench
• Observation of the Hopf Links and Hopf Fibration in a 2D topological Raman Lattice

Cited by in corpus (1)

• Geometric approach to fragile topology beyond symmetry indicators