Topological states in a Rydberg composite

A Rydberg composite is an assembly of ground-state atoms interacting with a single Rydberg atom. Since the perturbing atoms lift the degeneracy of high angular momentum states of the Rydberg atom, by constraining the atomic positions to certain geometries we can tailor the resulting energy eigenspectrum and electronic wave functions to reveal topologically interesting effects. In particular, the exemplary Su-Schrieffer-Heeger model can be realized by arranging the atoms with staggered positions in a ring around the Rydberg atom. With the versatility of the Rydberg composite we expand on this scenario to study the effect of long-range hopping interactions, on-site and hopping disorder, and mixed-dimensional systems in order to develop new insights into topological physics.