Ultracold Atoms as Weakly Correlated Systems

In this chapter, we first describe the imaging techniques for ultracold atomic gases, and the first generation of experiments in which quantum degenerate behavior of Bose and Fermi gases has been explored. Following the historical path, this implies to first focus on Bose gases, as the first evidences of quantum degenerate behavior in Fermi gases occurred about 5 years later, mainly due to the difficulties in cooling Fermi gases discussed in the previous chapter. From a theoretical standpoint, the mean-field approach on which the Gross-Pitaevskii equation relies is sufficient for the interpretation of these experiments. We then proceed to study the response of a Bose-Einstein condensate to external forces and torques. Always in a mean-field approach, this allows to describe some features of quantum transport common to superfluidity in \({ }^4\) He, including the presence of localized solutions with nontrivial topology in form of quantized vortices. Finally, by reducing the effective dimensionality of the Bose-Einstein condensate, we consider a simpler example of topological solutions in the form of solitons.