Strongly Interacting Many-Body Systems in Cold Atomic Gases

The remarkable progress in control over cold atomic gases has led to a point where people are no longer satisfied with merely studying these systems, but rather put them to use to understand complex quantum many-body systems. The basis of this development is a deep understanding of the interaction between atoms, and how to exploit those in order to engineer interesting and novel quantum-systems. The aim of this particular thesis is to contribute to this third quantum revolution [1] and hence help to understand the inner workings of complex many-body systems. We present a method to control the shape and character of the interaction between cold atoms based on dressing the atomic ground-state with a Rydberg-state. The latter induces a van der Waals interaction between all the atoms in the ensemble, and allows for control via the coupling light-field. We find that with increasing atom densities the ensemble shows a direct transition into a collective regime that preempts the onset of three-body interactions associated with a break-down of the first Born-approximation. The reason for this intriguing behavior is the strong interaction between Rydberg atoms that gives rise to the blockade-mechanism, and prevents the simultaneous excitation to the Rydberg-state for spatially close atoms. The non-trivial behavior of the interaction-potential within the collective regime yields a novel tool for shaping the interaction between ground-state atoms beyond s-wave scattering. We study this collective regime and the resulting interactionpotential between the atoms within a variational/mean-field approach, and discuss its effects on a trapped Bose-Einstein condensate. Artificial atoms show remarkable properties, that are often superior to real atoms. In particular, since they are built out of many constituents, such systems often exhibit an enhanced coupling to the light-field as well as strong optical non-linearities even for small light-fields. On the other hand, noise in quantum-mechanical systems can not only destroy coherence, but rather can be used in order to robustly drive a system into an interesting state. We study the effect of a controlled dephasing onto an artificial atom in the context of an ensemble of atoms coherently coupled to a Rydberg state and demonstrate that such an enhanced artificial atom allows for the deterministic absorption of a single photon from an arbitrary incoming probe field. Such behavior yields a unique tool in light-matter interaction, and opens the path to realise quantum-networks or to fabricate novel quantum-devices. Here, we discuss the applicability of this single-photon absorber as a single-photon