The theory of open quantum systems provides a systematic approach to quantum relaxation, decoherence and transport dynamics. The central goal is the derivation of effective equations of motion for a reduced set of dynamical variables from the underlying microscopic theory.
The possible structures of dynamical equations for an open quantum system are not known in full generality. A well-known result of paramount importance has been obtained for Markovian dynamics. This provides a reference structure known as Lindblad equation, whose different terms and operators are often naturally amenable to a direct physical interpretation. Moreover, analytical approaches are usually feasible, as well as numerical studies can always be performed via Monte Carlo simulations.
Such a general and physically transparent characterization is not generally available for the non-Markovian case. However, systems exhibiting non-Markovian dynamics, such as memory effects and non-exponential decay behaviors, are also of great interest both for practical applications and from a conceptual standpoint. In this spirit major efforts have been devoted to derive possibly general classes of master equations accounting for non-Markovian effects.
Relying on a fruitful synergy between the research groups in open system dynamics and quantum information theory and their members' expertise, we plan to address the issue of non-Markovian dynamics in quantum systems, also extending the results already obtained on the subject (S Maniscalco, S Olivares, M G A Paris, Phys Rev A 75, 062119 (2007); B Vacchini, Non-Markovian dynamics for bipartite systems, arXiv:0805.0561).
The main aim is twofold: (1) development of new classes of master equations for non-Markovian systems by considering quantum generalizations of non-Markovian classical processes, in analogy with what has been done for the Markovian case, leading to the so-called quantum dynamical semigroups; (2) analytical and numerical study of their properties, with focus on physical quantities of interest for quantum information processing, such as entanglement and decoherence.
Closer to applications, we will perform analytical and numerical analysis of models obtained from the above studies, as well as from already existing non-Markovian ones known to be relevant for the description of noisy continuous variables quantum channels. As a relevant example we plan to investigate is the dynamics of one and two-mode quantum channels in photonic band gaps, which, for a suitable choice of spectral density, can be described by a master equation exhibiting time dependent coefficients. For the computational power required by simulations in point (2), our research will involve costs due to the acquisition of new hardware.
A series of seminars on the subject and a one-day workshop are also planned within our project.
All members of the research project were born after 1-1-1968.