Many-body physics with Ytterbium Fermi gases in optical lattices: from one-dimensional systems to orbital magnetism

Ultracold atoms provide a powerful platform to address fundamental problems in manybody quantum physics. Owing to their rich electronic structure, ultracold two-electron atoms o er new exciting possibilities, enlarging the range of physical phenomena that it is possible to investigate with these atomic systems. This thesis reports on the experimental investigation of ultracold fermionic Ytterbium atoms in optical lattices. These alkaline-earth-like atoms are characterized by purely nuclear spin, completely decoupled from the electronic degrees of freedom. Consequently their low-energy scattering properties are independent of the nuclear spin orientation, giving rise to a SU(N) symmetry class, where N is the number of nuclear spin components. These features allowed us to demonstrate the rst experimental realization of onedimensional quantum gases of ultracold fermions interacting within the SU(N) symmetry class, where N can be adjusted from 2 to 6. The ndings of this work are interpretable in the framework of the Tomonaga-Luttinger liquid model, which is the paradigmatic description for one-dimensional interacting quantum systems. By tuning the number of spin components, we observed that the static and dynamic properties of the system deviate from those of ideal fermions and, for N > 2, from those of a spin-1=2 Luttinger liquid. In particular, we validated for the rst time the prediction that, in the large-N limit, one-dimensional Fermi gas exhibits properties of a bosonic spinless liquid. All the experimental results have been enabled by the construction of a versatile setup that makes possible the manipulation of atomic clouds of fermionic 173Yb in optical lattices as well as the optical detection and accurate control of the number of nuclear spin components by means of optical pumping processes. Moreover, atomic Ytterbium provides the possibility to engineer coherent Raman couplings between di erent nuclear spin states. By studying and implementing such Raman processes, we paved the way to the investigation of spin-orbit physics and arti cial gauge elds with multi-component fermions. In addition to their nuclear spin, two-electron fermions o er experimental access to long-lived electronically-excited states. Coherent control of Ytterbium clock transition 1S0 ! 3P0 in three-dimensional optical lattices has led to the rst observation of fast, coherent spin-exchange oscillations between two 173Yb atoms in di erent electronic orbitals. These experiments show that two-electrons atoms in optical lattices can be used as novel quantum simulators of unique many-body phenomena such as SU(N) orbital magnetism.