Topological bands in the continuum using Rydberg states

TL;DR

This paper proposes a continuum model using Rydberg atom clouds to realize topological bands with non-zero Chern numbers, demonstrating edge states tunable by atomic density, advancing topological physics in artificial matter.

Contribution

It introduces a novel continuum approach with Rydberg states to achieve topological bands, extending topological physics beyond lattice systems.

Findings

Topological band structure with Chern number C=2 identified in the continuum.

Edge states appear at interfaces controlled by atomic density.

System behavior is independent of atomic spatial arrangement.

Abstract

The quest to realize topological band structures in artificial matter is strongly focused on lattice systems, and only quantum Hall physics is known to appear naturally also in the continuum. In this letter, we present a proposal based on a two-dimensional cloud of atoms dressed to Rydberg states, where excitations propagate by dipolar exchange interaction, while the Rydberg blockade phenomenon naturally gives rise to a characteristic length scale, suppressing the hopping on short distances. Then, the system becomes independent of the atoms' spatial arrangement and can be described by a continuum model. We demonstrate the appearance of a topological band structure in the continuum characterized by a Chern number $C=2$ and show that edge states appear at interfaces tunable by the atomic density.