SU(N) orbital magnetism and synthetic dimensions with two-electron fermions

I will report on recent experiments performed at LENS with ultracold 173Yb Fermi gases. These two-electron atoms offer a range of new opportunities for quantum simulation with ultracold gases, since they grant the access to two stable degrees of freedom--nuclear spin and electronic state--that can be manipulated independently and coherently. By controlling the electronic state via an ultranarrow clock transition, we have obtained the first demonstration of fast, coherent spin-exchange oscillations between fermionic atoms trapped in two different long-lived electronic orbitals [1]. This result paves the way to the observation of exotic quantum magnetism and of paradigmatic condensed-matter effects in a fermionic system exhibiting SU(N)-invariant interactions. Finally, I will present the results of a very recent experiment, where we have used Raman transitions between different 173Yb nuclear spin states to synthesize an effective lattice dynamics in a finite-sized ``extra dimension.'' By using this innovative approach, we have realized synthetic magnetic fields for effectively-charged fermions and we have demonstrated the emergence of chiral edge states propagating along the edges of the system, thus providing a direct evidence of a prominent feature of quantum Hall physics in condensed-matter systems [2]. \\[4pt] [1] G. Cappellini et al., Direct observation of coherent inter-orbital spin-exchange dynamics, Phys. Rev. Lett. 113, 120402 (2014).\\[0pt] [2] M. Mancini et al., Observation of chiral edge states with neutral fermions in a synthetic Hall ribbon, preprint arXiv:1502.02495 (2015).