The ability to vary the force constants of a trapping potential makes it possible to create very elongated or highly flattened clouds of atoms. This opens up the study of Bose–Einstein condensation in lower dimensions, since motion in one or more directions may then effectively be frozen out at sufficiently low temperatures. In a homogeneous system Bose–Einstein condensation cannot take place at non-zero temperature in one or two dimensions, but in traps the situation is different because the trapping potential changes the energy dependence of the density of states. This introduces a wealth of new phenomena associated with lower dimensions which have been explored both theoretically and experimentally. A general review may be found in the lecture notes Ref.

For a system in thermal equilibrium, the condition for motion in a particular direction to be frozen out is that the energy difference between the ground state and the lowest excited state for the motion must be much greater than the thermal energy kT. This energy difference is ħωi if interactions are unimportant for the motion in the i direction. If the interaction energy nU0 is large compared with ħωi and the trap is harmonic, the lowest excited state is a sound mode with wavelength comparable to the spatial extent of the cloud in the i direction.