Quantification and Control of non-Markovian Evolution in Finite Quantum Systems via Feedback

We consider the unitary time evolution of continuous quantum mechanical systems confined to a cavity in contact with a finite bath of variable size. Measures for Markovianity for such finite system-bath configurations are developed in terms of Hilbert-Schmidt distances of time evolving wave packets. The relevant time scales are identified, which characterize pseudo-Markovian transient behavior, boundary scattering induced non-Markovian oscillations at intermediate times, and non-Markovian rephasing events at long time scales. It is shown how these time scales can be controlled by tunable parameters such as the bath size and the strength of the system-bath coupling.