Bose-Einstein condensates of sodium atoms have been prepared in optical and
magnetic traps in which the energy-level spacing in one or two dimensions
exceeds the interaction energy between atoms, realizing condensates of lowe
r dimensionality. The crossover into two-dimensional and one-dimensional co
ndensates was observed by a change in aspect ratio and by the release energ
y converging to a nonzero value when the number of trapped atoms was reduce
d.