Non-abelian anyons from degenerate Landau levels of ultracold atoms in artificial gauge potentials

Abstract

We show that non-abelian potentials acting on ultracold gases with two hyperfine levels can give rise to ground states with non-abelian excitations. We consider a realistic gauge potential for which the Landau levels can be exactly determined: the non-abelian part of the vector potential makes the Landau levels non-degenerate. In the presence of strong repulsive interactions, deformed Laughlin ground states occur in general. However, at the degeneracy points of the Landau levels, non-abelian quantum Hall states appear: these ground states, including deformed Moore-Read states (characterized by Ising anyons as quasi-holes), are studied for both fermionic and bosonic gases.

Published version

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• Exact diagonalization of cubic lattice models in commensurate Abelian magnetic fluxes and translational invariant non-Abelian potentials
• Quasimomentum distribution and expansion of an anyonic gas
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• Three-dimensional non-Abelian generalizations of the Hofstadter model: spin-orbit-coupled butterfly trios
• Universal properties of boundary and interface charges in multichannel one-dimensional continuum models
• An exactly solvable model for anyons with non-Abelian flux
• Topological quantum electrodynamics in synthetic non-Abelian gauge fields