Topological effects in two-dimensional quantum emitter systems

In this work, we show how novel topological effects appear when considering arrangements of increasing complexity of quantum emitters coupled to two-dimensional bosonic topological insulators. For a single emitter coupled to the Haldane model, we find a "fragile" quasibound state that makes the emitter dynamics very sensitive to the model's parameters and gives rise to effective long-range interactions that break time-reversal symmetry. We then discuss one-dimensional arrangements of emitters, emitter line defects, and how the topology of the bath affects the effective polariton models that appear in the weak-coupling regime when the emitters are spectrally tuned to a band gap. In the Harper-Hofstadter model, we link the nonmonotonic character of the effective interactions to the Chern numbers of the surrounding energy bands, while in the Haldane model, we show that the effective models are either gapless or not depending on the topology of the bath. Last, we discuss how the presence of emitters forming an ordered array, an emitter superlattice, can produce polariton models with nontrivial Chern numbers, and also modify the topology of the photonic states in the bath.