Abstract
This article is written as a Lecture given in the 2006 Varenna Summer School on Ultracold Fermi Gases. Here we present a review of BCS--Bose Einstein condensation (BEC) crossover theory with emphasis on finite temperature effects. We discuss the role of temperature $T$ as it enters a theoretical formalism which is based on the standard BCS-Leggett ground state. We also discuss the role of temperature in the context of experiments ranging from thermometric issues to signatures of superfluidity. Particularly important to this discussion is the novel normal state associated with the crossover regime, intermediate between BCS and BEC. The experimental evidence for this unusual normal state (associated with pre-formed pairs) and its counterpart below $T_c$ (associated with non-condensed pairs) is presented in the context of different experiments. We end with a discussion of finite temperature effects in spin polarized superfluids, where $T$ is found to play a crucial role in both theory and experiment.
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