Emergence of non-Markovianity in the emission process of an atom in a half-cavity

We study quantum non-Markovianity in the early stage of the emission process of a two-level atom coupled to a semi-infinite waveguide, where the waveguide termination behaves like a perfect mirror. Specifically, we restrict ourselves to analysis of the process for times shorter than twice the time delay t(d), where t(d) is the duration of a round trip along the atom-mirror path. We show the emergence of a threshold in the parameter space separating the Markovian and non-Markovian regions.