Non-equilibrium strongly interacting quantum many-body systems

Abstract

This thesis dissertation concerns the quantum dynamics of strongly interacting many-body systems under several non-equilibrium scenarios. Mimicking many real life settings, and specially some current major experiments, during most of this work we will deal with symmetrical interactions among the components, which will generate collective dynamics with high degree of correlation. The focus all throughout this work has been on the posssibility of accurately control the quantum properties of the system, even at the microscopic level, by cleverly choosing macroscopic manipulation protocols. Our main results can be summarized as follows. First, we thoroughly investigate the irreversible defect formation when the Dicke model, a paradigmatic light-matter system, is made to cross its quantum phase transition (QPT). Furthermore, we have been able to explain this dynamical QPT for totally connected lattices, which had remained unresolved by well-known theories like the Kibble-Zurek mechanism. This was done by means of a broad encompassing critical function theory. Also, by going beyond semi-adiabatic evolutions, we have discovered that the dynamical QPT of the Dicke model has an intermediate regime where non-equilibrium process provide a huge enhancing of quantum properties, far beyond the capabilities of equilibrium, quasi-equilibrium, or sudden quench schemes. Finally, we provided theoretical evidence and insights for the possibilities of quantum magnetism interactions in current high precision alkaline earth atom lattice clocks