  We report on the direct observation of spin-exchanging interactions in a
two-orbital SU(N)-symmetric quantum gas of ytterbium in an optical lattice. The
two orbital states are represented by two different (meta-)stable electronic
configurations of fermionic Yb-173. A strong spin-exchange between particles in
the two separate orbitals is mediated by the contact interaction between atoms,
which we characterize by clock shift spectroscopy in a 3D optical lattice. We
find the system to be SU(N)-symmetric within our measurement precision and
characterize all relevant scattering channels for atom pairs in combinations of
the ground and the excited state. Elastic scattering between the orbitals is
dominated by the antisymmetric channel, which leads to the strong spin-exchange
coupling. The exchange process is directly observed, by characterizing the
dynamic equilibration of spin imbalances between two large ensembles in the two
orbital states, as well as indirectly in atom pairs via interaction shift
spectroscopy in a 3D lattice. The realization of a stable SU(N)-symmetric
two-orbital Hubbard Hamiltonian opens the route towards experimental quantum
simulation of condensed-matter models based on orbital interactions, such as
the Kondo lattice model.
