Topological photonics in planar atomic lattices
Résumé
We consider the band structure and topological properties of planar arrays of cold (immobile) two-level atoms interacting via the electromagnetic field. A band gap can be opened in the spectrum of a honeycomb lattice of atoms by either applying an external magnetic field, making the two atoms of the unit cell of the honeycomb lattice viewed as a triangular lattice with a two-atom unit cell, different from each other, or by deforming the lattice in a particular way. For certain combinations of parameters, the band gap is characterized by a nontrivial topological invariant, which results in the appearance of topologically protected edge modes for a lattice of finite size. These modes are robust to disorder in atomic positions as far as the gap remains open. Interestingly, disorder itself can induce a topologically nontrivial state termed a “topological Anderson insulator” in a lattice that otherwise would be topologically trivial. The considered atomic system provides a playground for studying the interplay between disorder and topology in photonics.