1. Topological Euler Class as a Dynamical Observable in Optical Lattices
- Author
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Unal, F. Nur, Bouhon, Adrien, Slager, Robert-Jan, Unal, F. Nur, Bouhon, Adrien, and Slager, Robert-Jan
- 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 nontrivial 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 Chem insulators.
- Published
- 2020
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