Bose-Einstein condensation of a finite number of particles trapped in one or three dimensions.

Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139~Received 16 January 1996!Bose-Einstein condensation~BEC! of an ideal gas is investigated for a finite number of particles. In threedimensions, we find a transition temperature which is lower than in the thermodynamic limit. Lowering thedimension increases the transition temperature and is therefore favorable for BEC. This is in contrast to thestandard result obtained in the thermodynamic limit which states that BEC is not possible in, e.g., a one-dimensional ~1D! harmonic potential. As a result, 1D atom traps, such as radially tightly confining magnetictraps or optical dipole traps, are promising for studying BEC. @S1050-2947~96!06807-2#PACS number~s!: 03.75.Fi, 05.30.Jp, 64.60.2i, 32.80.Pj