Several Aspects Of Bose-Einstein Condensation In Trapped Atomic Gases

This is a theoretical investigation of Bose-Einstein condensation of dilute atomic gases in traps. Researches have been focused on the critical temperature and thermodynamic properties. The effects of space dimensionality, trapping potential, finite particle number, and interaction are studied; and some generalized analytical results are derived. In Chapter 2, we investigate the effects of trapping potential and spatial dimensionality. A system of noninteracting particles trapped in a generic power-law potential in any-dimensional space is studied. The density of states of such a system is derived. This expression is quite general, and embodies all information of the space dimensionality, external potential especially its shape, and kinetic characteristics of particles. Thus the effects of external potential, space dimensionality and kinetic characteristics of particles are obtained straightforwardly because of the special role played by the density of states in statistical mechanics. Tuning the critical temperature and adiabatic cooling are possible by changing the shape of the trapping potential, or changing the space dimensionality. When only the strength of external potential is changed, the atomic gases do not come closer to condensation. It is favorable for BEC to take place in sharper trapping potentials. Concerning the possibility of condensation and the continuity of heat capacity at the critical temperature, simple criteria are obtained and explicitly describe the different roles played by the trapping potential, the space dimensionality, and the kinetic characteristics of particles. We find that effects of an external potential may be expressed as effects of a different space dimensionality. Starting from a same formula of the critical temperature, we derive the maximum thickness and maximum radius of a Bose-Einstein condensate, respectively, in two-and one-dimensional space. It is interesting to find that all of the maximum extensions in the reduced space dimensionalities are proportional to 1/m^1/2. This is sensible since the matter wavelength is also proportional to 1/m^1/2. With a longer wavelength, the atom has a worse...