Spin physics in dipolar quantum gases of erbium atoms

Over the last two decades, quantum gases have proven to be ideal systems to study novel few- and many-body quantum phenomena in ultracold physics. Recently, a new class of atomic species has been brought to quantum degeneracy, namely the magnetic lanthanide. Such strongly magnetic species open fascinating possibilities to investigate the long-range and anisotropic dipole-dipole interactions and their impact on manybody quantum phases and spin physics. The work presented in this thesis has been conducted in a fully operational quantum gas experiment in Innsbruck (AT), realizing degenerate Bose and Fermi gas of erbium. The ground state of Er has a total angular momentum J=6 (F=19/2) giving rise to 13 (20) different spin states for bosons (fermions). This thesis describes different schemes to create spin mixture starting from spin-polarized ultracold atoms loaded into a deep lattice. At our typical magnetic field strength, the Zeeman splitting for the bosonic isotopes between adjacent spin states is equal; hence a deterministic preparation of one particular spin state is not possible with standard methods such as radio-frequency (RF) coupling. On the contrary, the quadratic Zeeman shift, in the fermionic case, enables us to obtain a deterministic spin preparation with RF pulse or RF sweep. Several unexplored phases are predicted to occur with a spin mixture of highly magnetic atoms in a deep lattice. We start to characterize our system with a measurement of the on-site interaction between two different spin states loaded into an optical lattice. Additionally, as a step towards the predicted phases, we present a method to obtain a deterministic spin preparation and a single spin state control, which exploits the tensorial AC-Stark Shift and can be implemented for both fermionic and bosonic isotopes. For this aim, I developed an External Cavity Diode Laser (ECDL) source, emitting close to a narrow transition at 631 nm, together with an optical setup that allows different schemes for spin manipulation. This study provides new elements to increase the knowledge of our system and opens the door to investigate quantum magnetism and the stability of ordered magnetic phases in a well-controlled manner