An ab initio calculation of nuclear physics from Quantum Chromo-dynamics (QCD), the fundamental SU(3) gauge theory of the strong interaction, remains an outstanding challenge.
We will discuss the emergence of key elements of nuclear physics using an SO(3) lattice gauge theory as a toy model for QCD. We will show that this model is accessible to state-of-the-art quantum simulation experiments with ultra-cold atoms in an optical lattice. First, we will demonstrate that our model shares characteristic many-body features with QCD, such as the spontaneous breakdown of chiral symmetry, its restoration at finite baryon density, as well as the existence of few-body bound states. Then, we will show that, in the one-dimensional case, the dynamics in the gauge-invariant sector can be encoded as a spin-3/2 Heisenberg model, i.e., as quantum magnetism, which has a natural realization with bosonic mixtures in optical lattices, and thus sheds light on the connection between non-Abelian gauge theories and quantum magnetism.

with: M. Dalmonte, P. Zoller, D. Banerjee, M. Boegli, P. Stebler, U.-J. Wiese