The ability to study ultracold atomic Fermi gases holds the promise of significant advances in testing fundamental theories of many-body quantum physics. Of particular interest are strongly interacting Fermi gases in the BCS to BEC crossover that exhibit a transition to a superfluid state at temperatures near 0.2TF , where TF is the Fermi temperature. This transition, as a fraction of TF, is extremely high compared to any known superfluid or superconductor. These gases are also in a universal regime where the physics is independent of the details of the atomic interactions and is therefore relevant to fields as diverse as condensed matter, nuclear physics and astrophysics. In this thesis, I present an experimental probe of atomic gases that uses momentum-resolved RF spectroscopy to realize an analog of angle-resolved photoemission spectroscopy (ARPES) in materials. This measurement reveals the energy and momentum of single-particle states in the strongly interacting Fermi gas. In condensed matter, ARPES has proved to be one of the most powerful experimental techniques for studying the electronic structure of strongly correlated electron materials. The ability to perform analogous measurements in ultracold Fermi gases constitutes a significant advance in our ability to directly connect ultracold atomic gases to strongly correlated electron systems. Taking advantage of this new measurement technique, I investigate a long-standing problem in the field of strongly interacting fermions, namely whether a pseudogap state consisting of incoherent fermion pairs exists at temperatures above the critical temperature for superfluidity. The photoemission data I present provide strong evidence for this state and have implications for fundamental theories of strongly interacting Fermi gases and strongly correlated electron materials. I also discuss the experimental confirmation of recently predicted universal relations for strongly interacting Fermi gases, as well as some of the first experiments involving atomic Fermi gases with p-wave pairing.
Experiments on ultra-cold atomic gases at nano-Kelvin temperatures are revolutionizing many areas of physics. Their exceptional adaptability and simplicity allows tests of many-body theory in areas long thought to be inaccessible, due to strong interactions. Ultra-cold Fermi gases are now providing new insight into the foundations of quantum theory. They are expected to exhibit a universal thermodynamic behaviour in the strongly interacting limit, independent of any microscopic details of the underlying interactions. Here, we present a systematic theoretical study of strong interacting fermions, using different field-theoretic methods and comparisons with quantum Monte Carlo simulations. Pioneering measurements have dramatically confirmed our theoretical predictions, giving the first known evidence for universal fermion thermodynamics.