BEC and the New World of Coherent Matter Waves

This paper is based on three tutorial lectures given at the CRM Summer School in Banff, Alberta, June 27-July 10, 1999 on "Theoretical Physics at the End of the Twentieth Century". They will be published by Springer-Verlag. Lecture I gives a quick overview of recent studies of BEC in trapped atomic gases and reviews some properties of a trapped non-interacting Bose gas. Lecture II mainly discusses the collective modes of a pure condensate, based on the T=0 GP equation of motion. The Stringari quantum hydrodynamic theory is introduced. Lecture III discusses the coupled dynamics of the condensate and non-condensate at finite temperatures. A recent derivation of the two-fluid hydrodynamic equations is sketched. This theory predicts a new relaxational mode associated with the fact that the condensate and non-condensate may not be in diffusive equilibrium.