Topological spin models in Rydberg lattices

TL;DR

This paper demonstrates how resonant dipole-dipole interactions in Rydberg atom lattices can create artificial magnetic fields, leading to topologically non-trivial band structures characterized by non-zero Chern numbers.

Contribution

It introduces a method to engineer complex hopping amplitudes in Rydberg lattices, resulting in artificial magnetic fields and topological effects in the band structure.

Findings

Artificial magnetic fields are realized in Rydberg lattices.

The lowest band can have Chern numbers of 1 or 2.

Topological phases depend on lattice parameters and detuning.

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 $C=2$.