Understanding the far-from-equilibrium quantum dynamics of strongly correlated systems is a highly demanding and challenging task as already described above for areas A and B. The identification of basic or, even more interesting, universal processes and their associated time scales is an intriguing task when the system cannot be described by weakly interacting excitations. Moreover, the interactions among the constituents of quantum many-body system in nature vary from short-range (ultracold atom-atom collisions) to extremely long-range (Coulomb interaction among charges) and from isotropic to a distinct anisotropic (e.g. dipole-dipole interaction) behaviour. This leads to an enormous diversity with respect to not only the structural properties but in particular the resulting highly correlated non-equilibrium dynamics. It is thus of utmost importance to focus on systems and experimental scenarios that display in a representative manner as much as possible of the complexity and beauty of the strongly correlated non-equilibrium physics but nevertheless represent simple and fundamental paradigms, which allow for meaningful confrontations between theory and experiments. It is absolutely crucial for comparisons between experiment and theory to identify the relevant observables, which allow us to understand and conclude upon the fundamental principles and mechanisms at work. Unfortunately, solid state materials often do not satisfy these requirements because of uncontrolled disorder and impurities or limited system control and precision connected with the general difficulty to prepare small clean subsystems with moderate coupling to the environment. The preparation of laboratory model systems with paradigmatic character is a major challenge for experimentalists in condensed matter physics.
A particularly promising class of model systems, permitting to simulate many-body physics with unparalleled control, is realized by atomic or molecular quantum degenerate gases. Since the first observation of Bose-Einstein condensation in the mid nineties, the formation of quantum gases has become a well-mastered technique to access the realms of quantum many body physics at ultralow temperatures. In area C we set out to explore the non-equilibrium dynamics of strongly correlated systems by means of quantum gases of ultracold atoms. This includes both experiment and theory. Ultracold atoms are ideal candidates for this task, since they offer near-perfect isolation from the environment, slow timescales and an enormous degree of control on both their external (centre of mass) as well as internal (electronic) degrees of freedom. The excellent isolation was a necessary precondition for the achievement of Bose-Einstein condensation of atomic gases, which are so dilute that the timescales of non-equilibrium processes are easily accessible and offer a plethora of possibilities to probe the underlying structural and dynamical properties. Indeed the enormous progress of the field in the past one to two decades has brought about a level of control unparalleled by any other many-body quantum system. The interaction strength can be tuned employing magnetic, optical or confinement-induced Feshbach resonances, while magnetic trapping and optical lattices created with off-resonant lasers enable us to realize a diversity of traps and specifically periodic potentials. As a consequence, it is possible to prepare and explore systems of different dimensionality and, on a more detailed level, to change the band structure and adjust the corresponding tunnelling properties.
In effect, these developments have enabled us to bridge the gap between atomic and solid state physics in a systematic and persistent manner. Milestones in this context have been the experimental realization of model systems for strong correlations such as the Hubbard model which displays the superfluid to Mott-insulator phase transition with varying strengths of the underlying optical lattice and/or interactions. Another striking example is the BEC-BCS crossover that can be quantitatively investigated with high precision in quantum gas experiments using fermionic atoms prepared in two different magnetic sublevels. The purity inherent to cold atomic systems makes it possible to prepare a well-controlled initial state, evolve it under the action of a precisely defined microscopic Hamiltonian, and monitor the effects of the characteristic relaxation processes. Hence, fundamental issues in non-equilibrium dynamics can now be addressed for the first time in parallel by theory and experiment.
While in the early stage of quantum gas research the scope of many-body scenarios, possibly accessible with quantum gas models still seemed limited, recent developments impressively show that the fundamental building blocks of strongly correlated electronic matter can be included into the rapidly growing toolbox of quantum gas physicists. One example is the recent demonstration of optical lattices using the orbital degrees of freedom in excited bands. Orbital degrees of freedom play a prominent role in the physics of transition metal compounds, which still provide long standing riddles like high-Tc superconductivity of Kondo physics. As another remarkable example, it was shown recently how the action of the Lorentz-force upon electric charges can be simulated with neutral atoms by means of artificial gauge fields, thus opening the platform of quantum gas systems for studies of quantum Hall physics.