Spontaneous emission dynamics of an artificial atom in the presence of non-perturbative light-matter coupling

Engineered superconducting electrodynamical systems provide a versatile platform for realizing some of the strongest interactions between light and matter, providing a glimpse of how basic notions anchored on perturbative quantum electrodynamics (QED) are modified in the presence of stronger light-matter interactions. A case in point are recent studies of high-impedance Josephson junction array (JJA) resonators which have been successfully put to use to study simulation of quantum impurity models. QED in such a setting requires a theoretical approach that intrinsically builds on non-perturbative coupling while still retaining the notion of modes that can be defined within a finite but open volume. We present one such approach that builds on what is known as the singular function expansion in the theory of integral equations, extending it to the quantum field theory domain. We show that the current experiments are in a regime where the notion of spontaneous emission is dramatically modified and propose an experiment to study the cross-over from a perturbative to non-perturbative regime