NON-MARKOVIANITY AND INITIAL CORRELATIONS IN THE DYNAMICS OF OPEN QUANTUM SYSTEMS

In the present thesis we investigate two basic issues in the dynamics of open quantum systems, namely, the concept of non-Markovianity and the effects of initial system-environment correlations in the subsequent reduced dynamics. In recent research, a great effort has been put into the study and understanding of non-Markovian features within the dynamics of open quantum systems. At the same time, quantum non-Markovianity has been defined and quantified in terms of quantum dynamical maps, using either a divisibility property or the behavior of the trace distance between pairs of reduced states evolved from different initial states. We investigate these approaches by means of several examples, focusing in particular on their relation with the very definition of non-Markov process used in classical probability theory. Indeed, the notion of non-Markovian behavior in the dynamics of the state of a physical system and the notion of non-Markov process are quite different and it will appear how the former represents sufficient, but not necessary condition with respect to the latter. In particular, we explicitly show that the above-mentioned divisibility property in the classical case is not, in general, equivalent to the Chapman-Kolmogorov equation, proper to Markov stochastic processes. Furthermore, by taking into account a bipartite open system, we emphasize how the presence of non-Markovian effects strongly depends on where the border between open system and environment is set. A second relevant topic investigated in this thesis concerns the dynamics of open quantum system in the presence of initial system-environment correlations. By means of the approach based on trace distance, we go beyond the usual assumption that the open system and the environment are initially uncorrelated. The trace-distance analysis provides a characterization of open-system dynamics relying on measurements on the open system only, without the need for any extra information about the total system or system-environment interaction. After an introduction to the general theoretical scheme, we report an all-optical experimental realization, in which the total system under investigation consists of a couple of entangled photons generated by spontaneous parametric down conversion and initial correlations are introduced in a general fashion by means of a spatial light modulator. Finally, we take into account the Jaynes-Cummings model, showing how trace distance establishes general connections between correlation properties of initial total states and dynamical quantities that characterize the evolution of the open system.