Non-Markovian spontaneous emission in a tunable cavity formed by atomic mirrors

Abstract: We analyze the non-Markovian spontaneous emission dynamics of a two-level test atom placed in a cavity formed by two atomic arrays in a waveguide quantum electrodynamics (QED) setup. We demonstrate a crossover from single-mode to multimode strong coupling cavity QED as the cavity length $ \sim d$ becomes comparable to the coherence length associated with collective spontaneous emission $\sim v/(N\gamma)$. The resulting non-Markovian dynamics of the test atom and the emergent spectral density of the field are analyzed as a function of various tunable atomic array parameters: number of atoms, length of the atomic cavity, and resonance frequency of the atoms forming the atomic mirrors. Our results show limitations to cooperatively enhanced light-matter coupling in the presence of time-delayed feedback. We further illustrate that the non-Markovian system dynamics can be efficiently approximated in terms of a few modes of the emergent spectral density of the field.