 Bose-Einstein condensation

Bose-Einstein condensation is macroscopic occupation of a single-particle mode in an appropriate many-boson limit. In an ideal equilibrium gas, the excited modes can hold only a finite density at a given temperature when their occupation integral saturates as the chemical potential reaches the ground energy. Extra particles then occupy the lowest mode macroscopically.

Whether a finite-temperature transition exists depends on dimension, dispersion and confinement; a uniform ideal gas in two dimensions does not have the same saturation condition as a three-dimensional one. For interacting systems, a macroscopic eigenvalue of the one-particle density matrix provides a more general definition than counting a chosen bare orbital.

Cold-atom measurements release or image a cooled cloud and look for a highly occupied low-momentum component with the predicted density/temperature dependence. Finite size, interactions and expansion must be modeled. Condensation is distinct from superfluidity, which is a response to flow and phase gradients.