Towards quantum simulation of the Kondo-Lattice-Model

Ultracold quantum gases of alkaline-earth-like metals are a versatile tool to investigate interacting many-body physics by realizing clean and controllable experimental model systems. Their intriguing properties range from energetically low-lying clock transitions, which allow for high-resolution spectroscopy, over meta-stable states, which can be regarded as a second species with orbital degree of freedom, to SU(N) symmetry, allowing novel magnetic phases. These open up new possibilities for quantum simulators. Using them in combination with optical lattices dissipative Fermi-Hubbard models and the Kondo-lattice-model can be realized, two promising examples for probing strongly correlated systems. This thesis presents an experimental apparatus for producing ultracold samples of fermionic ¹⁷³Yb (N≤6). A new bicolor dipole trap was implemented with a final, average trap frequency of anti ω=36 Hz. Using optical, resonant pumping and an Optical-Stern-Gerlach scheme, the spin mixture can arbitrarily be changed from a six- to a one-component gas. Typically the degenerate Fermi gases consist of 87000 atoms at 17.5% T_F (N=6) and of 47000 atoms at 19.4% T_F (N=1). The lowest lying meta-stable state ³P₀ (578 nm) is coherently controlled using a clock-laser setup with a linewidth of FWHM=1 Hz by means of Rabi oscillations or rapid adiabatic passage. By conducting spectroscopic measurements in a 3D magic lattice (759 nm) we demonstrate inter band transitions and observe the ¹S₀<=>³P₀ excitation with a resolution of FWHM=50(2) Hz. Applying these techniques to a two-component spin mixture reveals a shift of the clock-transition caused by spin-exchange interaction between the orbital symmetric vertical stroke eg right angle ⁺ vertical stroke ↑↓ right angle ^- and the orbital antisymmetric vertical stroke eg right angle ^- vertical stroke ↑↓ right angle ⁺ state. Using the inelastic properties of the ³P₀ state a dissipative Fermi-Hubbard model is realized. The dynamics in this system can not be described by a simple two-body loss model. We identify two relevant time scales and observe a spin dependence of the g⁽²⁾ correlation function. The here presented apparatus and experimental results constitute an important step towards a profound understanding of strongly correlated many-body systems and for bridging the gap between quantum gases and condensed matter physics.