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Ultracold atoms in optical lattices have proven to provide an extremely clean and controlled setting to explore strongly interacting quantum many-body phases of matter. Imaging of atoms in such lattice structures has reached the level of single-atom sensitive detection combined with the highest resolution down to the level of individual lattice sites. This has opened up fundamentally new opportunities for the characterization and the control of quantum many-body systems including quantum magnetism. These lecture notes cover selected parts of the course given at the Varenna Summer School on “Quantum Matter at Ultralow Temperatures”.
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