Local probing and thermometry of a degenerate Fermi gas

Ultracold atomic gases are ideal systems to study many-body quantum physics. The development of increasingly sophisticated experimental probes now starts to give direct, \emph{in-situ} access to thermodynamic quantities of these systems. We have set up a new apparatus that allows local probing of a degenerate Fermi gas with an optical resolution of $700$ nm using a microscope objective. In this talk we will present results obtained by studying \emph{in-situ} atom number fluctuations of an optically trapped gas of degenerate $^6$Li atoms. In particular, we will discuss the experimental realization of an universal scheme for thermometry recently proposed by Q. Zhou and T.-L. Ho [arXiv:0908.3015v2].