= Dilute-gas Bose-Einstein condensation
In a dilute gas, <Bose-Einstein condensation> makes a single <one-particle state> hold a substantial fraction of the <bosons>. This is a population effect: cooling reduces the number that the excited <energy eigenstates> can accommodate at <thermal equilibrium>. The surplus accumulates in a <Bose-Einstein condensate>. For an <ideal gas> the occupied mode is the trap <ground state>; interactions can deform that mode, as described by the <Gross–Pitaevskii equation>. Dilute does not mean classical: a small <number density> can still give overlapping <thermal de Broglie wavelengths> at sufficiently low <temperature>.
The appeal is that changing the trap changes a calculable <Quantum Hamiltonian>, while <absorption imaging> makes its population distribution visible. The <Bose condensation in a three-dimensional harmonic trap> below turns <density of states> into a prediction for a <critical temperature> and <condensate fraction>. These are separate questions from measuring <matter-wave coherence> or <superfluidity>.
<Eric A. Cornell> and <Carl E. Wieman>'s joint lecture emphasizes the competition between useful <elastic collisions>, which restore <thermal equilibrium> during <evaporative cooling (atomic physics)>, and collisions that remove or heat the trapped sample. A long trap lifetime alone is insufficient: reequilibration must keep up with evaporation.<Nobel Lecture: Bose-Einstein condensation in a dilute gas, the first 70 years and some recent experiments by Eric A. Cornell and Carl Wieman>[pp. 878–879 and 890, collisional requirements]{ref}
\Image[/bose-condensation-apparatus-stages.png]
{title=Functional stages of the 1995 dilute-gas condensation experiments}
{description=Original schematic of preparation, trapping, <evaporative cooling (atomic physics)>, release and <absorption imaging>. The two trapping routes differ; the boxes represent functions rather than physical component locations.}
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