0 Cold Trapped Atoms : A Mesoscopic System ∗

The Bose-Einstein condensates recently created in trapped atomic gases are mesoscopic systems, in two senses: (a) Their size fall between macroscopic and microscopic systems; (b) They have a quantum phase that can be manipulated in experiments. We review the theoretical and experimental facts about trapped atomic gases, and give examples that emphasize their mesoscopic characters. One is the dynamics of collapse of a condensate with attractive interactions. The other is the creation of a 1D kink soliton that can be used as a mode-locked atom laser. 1 Mesoscopic systems A mesoscopic system has two distinctive characteristics: • It contains many more particles than a microscopic system, but is small enough for us to manipulate in the laboratory. • It possesses a quantum phase that we can control. The term “mesoscopic” has been associated with “quantum dots,” in which the passage of electrons can be controlled singly. Now we have new ∗Expanded version of an invited talk given at the third joint meeting of Chinese physicists worldwide, Chinese University of Hong Kong, August, 2000.