NON-MARKOVIAN QUANTUM EVOLUTIONS IN STRUCTURED ENVIRONMENTS
The field of quantum information has usually treated dissipation and decoherence as unwanted effects to be minimized for the successful completion of quantum information tasks. Recently the possibility to actually control and even exploit them has been demonstrated, for instance in reservoir computing. General treatments of decoherence effects rely in over-simplified models of an infinite reservoir in an ever-lasting unmodifiable thermal state and with time scales so fast that any memory it could have about the slower dynamics of the decohering system of interest would be immediately washed out. All these (Born-Markov) approximations lead to master equations without memory. In recent years however there has been a revival of interest in descriptions beyond this crude approximation, specifically in order to include memory effects in the dissipative system evolution. In the last 5 years those so-called non-Markovian effects have opened up a whole field of research where more realistic dissipation models are required, not only to give a more accurate description of ever-improving quantum experiments, but also in order to understand whether more complex evolutions can yield any advantage over simplified models.
The intent of our project is to provide specific microscopic models of environments, namely finite bosonic networks, to explore memory effects beyond approximations. We will tackle the problem of correlated environments by trying to bridge the gap between two typical descriptions, common and separate baths, by investigating a finite coupled harmonic chain where real physical distances translate into diminishing correlations. We will investigate complex bosonic networks as heat baths, trying to locally probe their properties. In this way, a possible link between topology/connectivity and the dissipation characteristics will be pursued. A microscopic treatment will allow us to analyze thermodynamical aspects related to correlated environments, trying to generalize the second law of thermodynamics to the case of out-of-equilibrium heat baths with quantum correlations.
Dealing with finite coupled models for heat baths is challenging but rewarding, as it allows to track the creation and distribution of information both between system and environment as well as among bath units. The study of the detailed dynamics of systems in complex networks environments will permit the study of quantum Darwinism, the redundant distribution of classical information on the system in the environment, or to check (and engineer) whether clusters of entangled units exist when synchronization conditions are met. Finally, quantum speed limits can be studied under different heat bath settings. It was recently reported that quantum speed limits can actually be improved by the presence of memory effects. We aim to go beyond these analysis in simple non-Markovian master equations, focusing in finite heat bath setting, a largely unexplored subject to establish which are the optimal decoherence conditions to improve quantum speed limits.