An ab initio calculation of nuclear physics from Quantum Chro-modynamics (QCD), the fundamental SU(3) gauge theory of thestrong interaction, remains an outstanding challenge. Here, wediscuss the emergence of key elements of nuclear physics usingan SO(3) lattice gauge theory as a toy model for QCD. We showthat this model is accessible to state-of-the-art quantum simula-tion experiments with ultracold atoms in an optical lattice. First,we demonstrate that our model shares characteristic many-bodyfeatures with QCD, such as the spontaneous breakdown of chiralsymmetry, its restoration at finite baryon density, as well as theexistence of few-body bound states. Then we show that in the one-dimensional case, the dynamics in the gauge invariant sector canbe encoded as a spin S =32Heisenberg model, i.e., as quantummagnetism, which has a natural realization with bosonic mixturesin optical lattices, and thus sheds light on the connection betweennon-Abelian gauge theories and quantum magnetism.
