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These lecture notes contain an introduction to the physics of quantum mixtures of ultracold atoms trapped in multiple internal states. I will discuss the case of fermionic isotopes of alkaline-earth atoms, which feature an intrinsic SU(N) interaction symmetry and convenient methods for the optical manipulation of their nuclear spin. Some research directions will be presented, with focus on experiments performed in Florence with nuclear-spin mixtures of 173Yb atoms in optical lattices.
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