Hermitian and Non-Hermitian Topology from Photon-Mediated Interactions

Light can mediate effective dipole-dipole interactions between atoms or quantum emitters coupled to a common environment. Exploiting them to tailor a desired effective Hamiltonian can have major applications and advance the search for many-body phases. Quantum technologies are mature enough to engineer large photonic lattices with sophisticated structures coupled to quantum emitters. In this context, a fundamental problem is to find general criteria to tailor a photonic environment that mediates a desired effective Hamiltonian of the atoms. Among these criteria, topological properties are of utmost importance since an effective atomic Hamiltonian endowed with a non-trivial topology can be p…