Abstract
The aim of this lecture has been to study the link between the condensation of a gas of bosonic particles and its possible superfluidity. We started from the fact that Bose-Einstein condensation of a fluid, whether perfect or interacting, is characterized by a simple mathematical property: the existence of a macroscopic eigenvalue for the one-body density operator, which reflects long-range order. We therefore began by describing the method used in practice to access this quantity for gases of cold atoms.
We then turned to the phenomenon of superfluidity. The very definition of superfluidity and the determination of its accompanying parameters - superfluid density, superfluid velocity - are complex. The notion of superfluidity calls on a variety of physical phenomena that need to be clearly identified. We have done this by considering two situations that are emblematic of the study of superfluids; these are "thought experiments" in which the fluid is either at equilibrium or in a metastable state. As far as cold atoms are concerned, these thought experiments have been carried out recently, and we have briefly described their protocols and main results. Once we had identified these two situations, we described the two-fluid model initially proposed by Tisza, then further developed by Landau, to account for the superfluidity of liquid helium.
