Topologically protected edge states, localization, and tunable interactions in a Rydberg composite

We examine topological phases and symmetry-protected electronic edge states in the context of a Rydberg composite: a Rydberg atom interfaced with a structured arrangement of ground-state atoms. We show that the spectrum of such a composite possesses a mapping, reminiscent of the mapping between partner Hamiltonians in supersymmetric quantum mechanics, to that of a tight-binding Hamiltonian. The Rydberg electron moves in a combined potential including the long-ranged Coulomb interaction with the Rydberg core and the zero-range interactions with each neutral atom; the effective hopping amplitudes between sites are determined by this combination. As a result, the system is capable of exhibiting non-trivial topology depending on the arrangement of the atoms and the Rydberg state. We first confirm the existence of topologically-protected edge states in a Rydberg composite by constructing a Su-Schrieffer-Heeger dimer model. Following that, we show that more complicated systems with trimer unit cells can be studied in a Rydberg composite.