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Topological Euler Class as a Dynamical Observable in Optical Lattices.

F Nur Ünal1, Adrien Bouhon2,3, Robert-Jan Slager1

  • 1TCM Group, Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom.

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|August 16, 2020
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Summary
This summary is machine-generated.

Researchers discovered a new topology, the Euler class, in dynamic systems. This fragile topology features stable band nodes and is experimentally observable through monopole-antimonopole pairs in cold-atom setups.

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Area of Science:

  • Topological physics
  • Quantum dynamics
  • Condensed matter theory

Background:

  • Recent advancements in characterizing topological properties of non-equilibrium systems.
  • Conventional topological phases are often defined by symmetry and eigenvalues.
  • The need for new topological invariants beyond existing classifications.

Purpose of the Study:

  • To report robust signatures of a novel topological invariant, the Euler class, in dynamical systems.
  • To investigate the properties and experimental observability of this new topology.
  • To explore the interplay between Euler topology and crystalline symmetries.

Main Methods:

  • Theoretical demonstration of the Euler class using band structures with stable band nodes.
  • Analysis of non-Abelian charges and braiding mechanisms associated with band nodes.
  • Utilizing the Hopf map to link momentum-time trajectories and induce observable phenomena.
  • Proposing explicit tomography protocols for cold-atom experimental setups.

Main Results:

  • Identification of the Euler class as a distinct topological invariant (ξ) outside conventional classifications.
  • Observation of 2ξ stable band nodes in gapless band triples, alongside a gapped band.
  • Demonstration of stable monopole-antimonopole pairs generated by quenching with a nontrivial Euler Hamiltonian.
  • Experimental observability of the Euler class through linked momentum-time trajectories.

Conclusions:

  • The Euler class represents a fragile topology with unique properties, including non-Abelian charges.
  • Dynamical systems provide a viable platform for realizing and observing the Euler topology.
  • This work opens avenues for exploring novel topological phases and their interactions with crystalline symmetries in quantum systems.