Spatio-temporal correlations in many-body quantum systems

A long-standing source of debate is the fact that we understand the world from quantum principles, yet we see a classical world in o ur everyday life scales. This led first Einstein, Podolsky and Rosen and then Bell to formulate more precisely the idea that quantum mechanics would be incomplete. However, the violation of classical principles, through the experimental demonstration of what was called entanglement by Schrödinger, drove a profound change of viewpoint about physics, with the research in quantum information that nowadays is driving a technological revolution with applications in all areas of research. However, a big foundational question still stands: how far in the macroscopic regime can we witness quantum effects ? Is there any fundamental mechanism that leads to the emergence of classical physics at certain scales? In a modern perspective, this has also implications f or the afore-mentioned technological revolution, for example in understanding its limitations. In this project we aim at understand ing from a quantitative point of view, how quantum resources (entanglement) can be traded with classical thermodynamic resources such as energy and time. A concrete path to s tudy this question is to analyse many-body quantum systems (thus almost reaching the realm of chemistry) and their usage in the fundamental task of measuring time. This points to one of the main current technological applications of the manipulation of quantum systems, namely atomic clocks. However, perhaps surprisingly, such devices dont make use of entanglement or other genuinely quantum resources yet. This hints, on the one hand, at looking for improv ed versions of quantum clocks that do make use of entanglement, and, on the other hand, at some fundamental mechanism that at least prevents entanglement to be useful for such a practical, yet fundamental task. The final goal is also to distill what are the basic resources necessary t o set the most precise time standard. From a more speculative perspective, this could even help reformulating our intuitive understanding of time itself.