  We address memory effects in the dynamics of a two-level open quantum system
interacting with a classical fluctuating field via dipole interaction. In
particular, we study the backflow of information for a field with a Lorentzian
spectrum, and reveal the existence of two working regimes, where memory effects
are governed either by the energy gap of the two-level system, or by the
interaction energy. Our results shows that non-Markovianity increases with
time, at variance with the results obtained for dephasing and despite the
dissipative nature of the interaction, thus suggesting that the corresponding
memory effects might be observed in practical scenarios.
