Seminaire Poincare 1 (2003) 11 { 20 Seminaire Poincare Looking Back at Super uid Helium

Abstract. A few years after the discovery of Bose Einstein condensation in several gases, it is interesting to look back at some properties of super uid helium. After a short historical review, I comment shortly on boiling and evaporation, then on the role of rotons and vortices in the existence of a critical velocity in super uid helium. I nally discuss the existence of a condensate in a liquid with strong interactions, and the pressure variation of its super uid transition temperature. The discovery of super uidity In January 1938, J.F. Allen and A.D. Misener [1] published the experimental evidence that the hydrodynamics of liquid helium was not classical below 2.2 K. In the same issue of Nature, Kapitza introduced the word \super uid " to qualify this anomalous behavior [2]. Soon after this discov-ery, F. London suggested that super uid helium forms a macroscopic liquid matter wave, as a consequence of \Bose-Einstein condensation " (BEC). 65 years later, it is generally accepted that London was right, but it happened to be very dicult to prove. On the contrary, when BEC was discovered in cold alkali vapors (in 1995), the experimental evidence was immediately very clear. The super uidity of these cold gases was soon demonstrated as well. It is thus interesting to look back at some properties of super uid helium now. As we shall see, not everything is completel