Many-Body Quantum Systems under Dissipation and Drive

A lot of research on cold atomic gases has centered so far on the many-body physics of closed systems in thermodynamic equilibrium. Recent experimental developments move systems into the focus, which instead call for a proper treatment as open systems, in which adding to the coherent effects also dissipative ones occur. Going one step beyond, harnessing the manipulation tools available for cold atomic systems offers unique possibilities to extend the customary idea of Hamiltonian engineering for closed atomic systems to a more general scenario of tailoring Hamiltonian and driven-dissipative dynamics on equal footing. Under these circumstances, dissipation does not appear as a perturbation, but potentially as the dominant resource of dynamics. This situation raises new theoretical challenges, which shall be addressed in this project. While the systems encompassed here are well- described microscopically by many-body master equations, efficient theoretical tools for performing the necessary transition form micro- to macrophysics for such open systems with a continuum of spatial degrees of freedom are still missing. One goal will thus be to merge the realms of quantum optics and many-body physics based on a Keldysh functional integral approach for markovian dissipative actions. Within such framework, a large variety of novel questions can be raised and answered. This concerns natural occurrences of dissipation, where an exemplary fundamental issue concerns the fate of a Fermi liquid in the presence of a complex scattering length, where elastic and inelastic couplings compete with each other. But it also embraces scenarios with tailored dissipation, which can be used to drive systems into specifically targeted many-body states with quantum mechanical properties such as phase coherence or entanglement far away form thermodynamic equilibrium, where no immediate condensed matter counterpart exists. Challenges here are to understand fundamental properties of a strong competition of coherent and dissipative dynamics, and to identify hallmark signatures for the intrinsic nonequilibrium nature of these systems. In these searches, contact to related fields such as nonlinear dynamics and nonequilibrium statistical mechanics will be made. Complementary to these theoretical investigations, we will propose realistic experimental implementations of the proposed scenarios. To this end, we will explore the engineering opportunities in a broad spectrum of physical platforms, such as cold atoms, but also arrays of microcavities, and trapped ion chains. In this combined approach, we hope to substantially contribute to shaping the fledging field of many-body quantum physics beyond thermodynamic equilibrium.

Recent experimental developments in systems as diverse as light-driven semiconductor systems, ultracold atoms and trapped ions move systems into the focus, which qualify as driven open quantum systems. One characteristic feature is the appearance of reversible quantum dynamics and irreversible, driven dissipative dynamics on an equal footing. At the same time, these systems exhibit a continuum of spatial degrees of freedom. In this way, they contribute to a novel, emerging interdisciplinary interface connecting two grand disciplines of modern theoretical physics quantum optics and many-body physics. Crucially, those systems are instances of quantum systems beyond the realm of thermodynamic equilibrium, due to the microscopic drive exerted by, e.g. external laser fields.In this project, we have focused on identifying universal macroscopic phenomena, which unambiguously witness the microscopic drive conditions. As reserach highlights, we (i) proposed to cool in a targeted and robust way into so-called topologically ordered states of matter with possible applications for topologically protected quantum information processing, (ii) identified structural differences in the dynamical critical behavior appearing close to phase transitions between equilibrium and driven systems, (iii) demonstrated that the long distance correlations in driven systems in reduced dimensionality behaves strikingly, but universally, different from their equilibrium counterparts and (iv) pioneered the understanding of the real time evolution of open quantum systems.To achieve these results, we have developed and put into practice a unified formalism based on the concept of Keldysh field theory, which allows us to systematically perform the transition from micro- to macrophysics in such driven open quantum systems. This approach provides a basis, and paves the way for future investigations in this rapidly growing field. Finally, we have connected our theoretical results to diverse experimental platforms, including the ones mentioned above. Some of our theoretical ideas have already been explored experimentally, while others are subject of ongoing and future research.