Fluctuations and state preparation in quantum degenerate gases of sodium and lithium
Ultracold atoms enable the precise study of novel systems where the correlations between particles are strong. These systems can be simple to describe yet impossible to efficiently simulate on a classical computer; understanding their behavior addresses fundamental questions in condensed-matter physics. The first part of this thesis describes measurements of spin and density fluctuations in degenerate Fermi gases. We begin by presenting a proof-of-principle experiment that demonstrates how information about atomic fluctuations can be extracted from experimental images and used to measure the temperature of a noninteracting system. We then describe a new technique for measuring spin fluctuations that employs an effect analogous to optical speckle, using it to characterize the pair correlations in a strongly attractive Fermi gas. Finally, we use the methods we have developed to characterize the magnetic correlations of a Fermi gas with strong repulsive interactions on the upper branch of a Feshbach resonance, and show that, contrary to earlier experimental and theoretical predictions, this system does not undergo a ferromagnetic phase transition. The second part describes the development of an apparatus for performing experiments with sodium and lithium in optical lattices. We describe progress towards the implementation of synthetic magnetic fields in systems of lattice fermions, which would enable the study of new topological phases. This includes the development of general precursors such a Bose-Einstein condensate and a stable Mott insulator of bosons, as well as more specific studies of heating and dynamical instabilities in tilted and shaken lattices.
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