Quantum simulation of mesoscopic systems with highly excited atoms and ions

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At ultracold temperatures (within a few billionths of a degree of Absolute Zero) and on very small scales (nanometres) quantum effects dominate the properties of physical systems. Even systems with relatively few components might be so complex that their properties can be calculated neither analytically nor numerically. Moreover, even experiments may yield little information about the systems. This becomes even more dramatic if many particle systems are considered, e.g. condensed matter systems such as electrons in a metal. In particular, if interactions between the particles are strong, the quantum properties are very difficult to determine and to characterize experimentally and theoretically.One approach to gain information about complex quantum systems which are not easily accessible is to mimic - or simulate - them. Here, the original system parameters are replaced by ones which can be more precisely monitored and manipulated. In recent years it has turned out that gases of ultracold atoms are particularly useful to perform this task. Electric, magnetic and optical fields are used to create potential landscapes in which the atomic motion takes place. For example, counter propagating laser beams give rise to a periodic potential which is equivalent to the scenario encountered by electrons in a crystalline solid. Moreover, the interaction between the atoms is tunable by applying small magnetic fields (using the so-called Feshbach resonances). Here, attraction, repulsion or even no interaction is achievable. Ultracold atoms thus can serve as a building block for a quantum simulator of condensed matter systems where the atoms assume the role of the electrons. One major achievement of such a simulator was the study of a phase transition in a gas of ultracold atoms in an optical lattice from a Mott-insulator to a superfluid. In the former case the atoms are tightly trapped in the individual lattice sites whereas in the latter case a non-classical state is formed which extends over the entire lattice.In the proposed work we theoretically investigate a quantum simulator which mimics mesoscopic systems on fast timescales. This interdisciplinary research project is of direct relevance to condensed matter physics, molecular physics and ultracold chemistry. It will deepen our understanding of physical processes that take place in molecules, clusters and small spin chains. The basic building-block of the quantum simulator comprises atoms or ions held in traps with a spacing of several micrometers - large enough for laser beams to intreract with (address) individual atoms. In this simulator, the ultracold atoms define an underlying lattice structure in which the electronic dynamics takes place. This is directly analogous to a crystalline solid or a molecule. However, unlike in a 'conventional' molecule individual nuclei can be manipulated.The aim of the project is to explore these systems, to characterize their properties and to illuminate their potential to simulate mesoscopic systems. This opens a doorway to direct monitoring of fundamental physical processes, such as charge transfer, which normally take place hidden from the observer's eye. A key feature of the proposal is a strong interaction with the experiments.