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Abstract

This thesis reports on the preparation of a 2D Fermi gas in the BEC-BCS crossover and the observation of the BKT transition into a quasi long-range ordered superfluid phase. The pair momentum distribution of the gas is probed by means of a matter-wave focusing technique which relies on time-of-flight evolution in a weak harmonic potential. This distribution holds the coherence properties of the gas. The quasi long-range ordered phase manifests itself as a sharp low-momentum peak. The temperature where it forms is identified as the transition temperature. By tuning the temperature and the interaction strength, the phase diagram of the 2D Fermi gas in the BEC-BCS crossover is mapped out. The phase coherence is investigated in a self-interference experiment. Furthermore, algebraic decay of correlations is observed in the trap average of the first order corre- lation function, which is obtained from the Fourier transform of the pair momentum distribution. This is in qualitative agreement with predictions of homogeneous theory for the superfluid phase in a 2D gas. The presented results provide a foundation for future experimental and theoretical studies of strongly correlated 2D Fermi gases. They might thus help to elucidate complex systems such as the electron gas in high-Tc superconductors.