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Bose-Einstein condensation is unique among phase transitions betweendifferent states of matter in the sense that it occurs even in the absence ofinteractions between particles. In Einstein's textbook picture of an ideal gas,purely statistical arguments set an upper bound on the number of particlesoccupying the excited states of the system, and condensation is driven by thissaturation of the quantum vapour. Dilute ultracold atomic gases are celebratedas a realisation of Bose-Einstein condensation in close to its purelystatistical form. Here we scrutinise this point of view using an ultracold gasof potassium (39K) atoms, in which the strength of interactions can be tunedvia a Feshbach scattering resonance. We first show that under typicalexperi-mental conditions a partially condensed atomic gas strongly deviatesfrom the textbook concept of a saturated vapour. We then use measurements at arange of interaction strengths and temperatures to extrapolate to thenon-interacting limit, and prove that in this limit the behaviour of a Bose gasis consistent with the saturation picture. Finally, we provide evidence for theuniversality of our observations through additional measurements with adifferent atomic species, 87Rb. Our results suggest a new way of characterisingcondensation phenomena in different physical systems.

Can a Bose gas be saturated?