Pseudogap Effects in Rotating Fermi Gases from BCS to BEC

In this talk we focus on pseudogap effects present in a rotating, ultracold Fermi gas as the system is tuned from a BCS regime to a BEC regime. Such pseudogap effects are expected to be present away from the BCS regime [1]. Importantly, no theory of rotating Fermi gases has yet incorporated these non-condensed pair effects. Our work is based on reformulating the Gor'kov equations, with the inclusion of a pseudogap, into a Landau level basis [2]. With this reformulation we can calculate quantities including the local density of states in the presence of vortices, and the upper critical rotation frequency. In a related way we present linear response calculations in the presence of a pseudogap which include the shear viscosity and moment of inertia. We show that finite size effects give rise to a non-classical moment of inertia even in the normal state. Testable predictions resulting from this theory, as well as connections with high temperature superconductors, will also be discussed.\\[4pt] [1] Stajic \textit{et al.} Phys. Rev. A \textbf{69} 063610 (2004).\\[0pt] [2] Scherpelz \textit{et al.} arXiv: 1112.1112.