Topological spin models in Rydberg lattices

Martin Kiffner; Edward O'Brien; Dieter Jaksch

doi:10.1007/s00340-016-6596-4

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arXiv · 1609.02736

Topological spin models in Rydberg lattices

Martin Kiffner·Edward O'Brien·Dieter Jaksch

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Abstract

We show that resonant dipole-dipole interactions between Rydberg atoms in a triangular lattice can give rise to artificial magnetic fields for spin excitations. We consider the coherent dipole-dipole coupling between $np$ and $ns$ Rydberg states and derive an effective spin-1/2 Hamiltonian for the $np$ excitations. By breaking time-reversal symmetry via external fields we engineer complex hopping amplitudes for transitions between two rectangular sub-lattices. The phase of these hopping amplitudes depends on the direction of the hop. This gives rise to a staggered, artificial magnetic field which induces non-trivial topological effects. We calculate the single-particle band structure and investigate its Chern numbers as a function of the lattice parameters and the detuning between the two sub-lattices. We identify extended parameter regimes where the Chern number of the lowest band is $C=1$ or $C=2$.

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Martin Kiffner, Edward O'Brien, Dieter Jaksch. 2017-01-16. Topological spin models in Rydberg lattices. https://doi.org/10.1007/s00340-016-6596-4

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