"Ultracold atoms in optical lattices are a novel method of approaching many-body systems of strongly correlated particles, a scenario usually encountered in the context of interacting electrons in condensed matter systems. Many of these complex many-body states are notoriously hard to study, as strong interactions and correlations make a general theoretical description impossible. Ultracold atoms in lattices serve as model systems with a well-known Hamiltonian on the microscopic level, allowing for a careful analysis of those types of interacting systems for which a suitable Hamiltonian can be implemented. Our project aims to expand the range of phenomena accessible for implementation with ultracold atoms, by combining a setup of ultracold ytterbium atoms with state-dependent lattice potentials. The electronic structure of ytterbium gives rise to an extremely long-lived excited state and a high degree of decoupling of the nuclear spin from the electronic states. These two properties are central for several new approaches to implement new classes of quantum systems. Our experiment is focused on three specific systems, which are so far not reachable by using the current state of the art implementations with Alkali atoms: (1) to realize a Kondo model, relevant for example for heavy-fermion materials, which exhibit complex phase diagrams which are not yet fully understood (2) realizing a many body system with particles of half-integer spin larger than ½, exhibiting enlarged SU(N) symmetry, with complex spin-correlated quantum phases which are as yet inaccessible, often even by theoretical methods, and (3) to enable the creation of strong artificial gauge fields in optical lattices while avoiding the heating effects expected in Alkali atom implementations. Artificial gauge fields are important for quantum simulation, as they can provide effective magnetic fields for neutral atoms, which is necessary to investigate any phenomenon analog to electrons in magnetic fields."
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