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Abstract

This thesis presents correlation measurements in two different few-fermion systems of ultracold 6Li atoms. The measurements have been performed with a new spatially and spin-resolved imaging method with single-atom sensitivity, with which we can probe coherences of the initial system as correlations in the momenta. First, we study attractively interacting atoms in a single microtrap, which serves as a basis for understanding the expansion dynamics of strongly interacting Fermi gases. We observe correlation features in the relative coordinate for different interaction strengths. We explain several of these features theoretically by calculating the initial interacting state in the microtrap and projecting it on a molecular bound state and scattering waves. Next, we study a small number of repulsively interacting particles in the ground state of a double-well potential. This system constitutes the fundamental building block of the Hubbard model. We observe interference patterns in the coordinates of the individual particles and in their relative coordinates. From the amplitude and phase of these patterns, we extract off-diagonal density matrix elements of the state, which we use to directly show coherence and entanglement in our system.