Topological spin models in rydberg lattices

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.