Exact approach for spatiotemporal dynamics of spontaneous emissions in waveguide quantum electrodynamic systems

We propose an exact analytical approach to study the single-photon spontaneous emissions in waveguide quantum electrodynamic (QED) systems. Using the ab initio evolution technique, our approach provides a universal framework to investigate the full spatiotemporal dynamics of the atomic response, the cavity response, and the emitted photonic wave functions. The validity of the analytical approach is numerically confirmed. Our rigorous approach can be extensively applied to more complicated waveguide QED architectures. Moreover, such an approach can readily incorporate the effects of dissipations and has the potential to tremendously facilitate the design of spontaneous emission-driven quantum nanophotonic devices in the dissipative regime.