Mode Hybridization and Radiative Properties of an Artificial Atom coupled to a Josephson Junction Array

We study the radiative properties of an artificial atom coupled to a Josephson junction array (JJA). Using a normal mode analysis of the system, we classify two regimes of weak and strong hybridization between the atomic and JJA modes based on their effective coupling strengths. In the weak hybridization regime we find a distinct spatially localized atomic mode both when the atomic frequency lies within and outside of the photonic band. However, for strong atom-JJA hybridization there is no such localized mode within the band. In this regime concepts such as spontaneous emission and Lamb shift are not well-defined as this situation represents a case of non-perturbative 1+1D quantum electrodynamics. We present a theoretical framework that replaces perturbative descriptions of radiative corrections, bridging the perturbative and the non-perturbative limits.