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Abstract

In this thesis I report on the experimental study of fermionic systems in two complementary experimental settings, i.e. large ensembles of dipolar erbium atoms and few-particle systems of fermionic lithium trapped in optical tweezers.

Compared to alkali atoms, dipolar quantum gases offer new avenues to explore due to their long-range anisotropic interactions and a rich internal structure. Such richness comes at the cost of complexity and therefore requires precise investigations of the atomic properties as well as the development of new experimental methods. In the first part of this thesis we present measurements of the anisotropic light shift of erbium atoms and compare the results to semiempirical electronic-structure calculations. Measurements of scalar and tensor polarizabilies of the ground and one excited state show good agreement with calculated values. We furthermore present the first experimental realization of a two-component strongly-interacting Fermi gas with dipolar interactions. We identify several intra and interspin Feshbach resonances at low magnetic field and precisely map out the scattering length across one broad resonance.

The second part of this thesis is dedicated to the characterization of small fermionic systems with momentum correlation measurements. Starting with systems of two or three indistinguishable fermions, we detect and discuss second and third-order momentum correlations that arise from quantum statistics alone. We then extend the study of correlation functions to interacting systems and develop a scheme to constrain large parts of the density matrix. Based on these constraints we reconstruct physical density matrices via Bayesian inference. We finally use the reconstructed states to address the influence of exchange symmetry on particle-particle entanglement in systems of identical fermions. Using the simple notion of an Antisymmetric Negativity we are able to separate entanglement from antisymmetrization from entanglement induced by interaction.