Cavity QED beyond linear response in topological systems

We explore the interaction between quantized electromagnetic fields and 1D atomic chains under the framework of cavity QED, by studying the cavity transmission. When the coupling between subsystems is small, the transmission can be used as a way to probe the properties of the fermonic system in a non-invasive way, while at large coupling rates, these properties are highly modified and hybrid excitations of the total system appear.
When considering systems with topological properties, such as topological insulators (TIs), the topological and trivial phase can be distinguished by the presence of in-gap edge states in the former case, topologically protected against local perturbations.
In this work, we propose a general method to compute the cavity transmission through the photonic Green’s function, which allows to go beyond the usual linear response regime, while studying the interplay between the photonic field and non-trivial topology, captured by the well-known SSH model for TIs in 1D. We find that the cavity transmission can be used to distinguish between both phases at different coupling rates.