Quantum Zeno effect and non-Markovianity in a three-level system

We study the coexistence of the quantum Zeno-type effect and non-Markovianity for a system decayingin a structured bosonic environment and subject to a control field. The interaction with the environmentinduces decay from the excited to the ground level, which, in turn, is coherently coupled to anothermeta-stable state. The control of the strength of the coherent coupling between the stable levelsallows the engineering of both the dissipation and of the memory effects, without modifying neitherthe system-reservoir interaction, nor environmental properties. We use this framework in two differentparameter regimes corresponding to fast (bad cavity limit) and slow dissipation (good cavity limit) in theoriginal and un-controlled qubit system. Our results show a non-monotonic behavior of memory effectswhen increasing the effectiveness of the Zeno-like freezing. Moreover, we identify a new source ofmemory effects which allows the persistence of non-Markovianity for long times while the excited statehas already been depleted.