Non‐Markovian Dynamics with Λ$\Lambda$‐Type Atomic Systems in a Single‐End Photonic Waveguide

Abstract In this work, the non‐Markovian dynamical evolution of a ‐type atom interacting with a semi‐infinite 1D photonic waveguide via two atomic transitions is investigated. The waveguide terminates at a perfect mirror, which reflects the light and introduces boundary effects. Exact analytical expressions are derived and it is shown that, under suitable conditions, the instantaneous and retarded decay rates reach equilibrium, leading to the formation of an atom‐photon bound state that suppresses dissipation. Consequently, the atom retains a long‐lived population in the asymptotic time limit. Furthermore, the output field intensity is analyzed and it is demonstrated that blocking one of the coupling channels forces the atomic system to emit photons of a single frequency. Finally, the model is extened to a two‐atom system and the disentanglement dynamics of the two spatially separated atoms are examined. These findings elucidate the dynamic process of spontaneous emission involving multi‐frequency photons from multi‐level atoms and provide insights into the complex interference between different decay pathways.