We find that in very elongated 3D trapped Bose gases, even at temperatures far below the BEC transition temperature Tc, the equilibrium state will be a 3D condensate with fluctuating phase (quasicondensate). At sufficiently low temperatures the phase fluctuations are suppressed and the quasicondensate turns into a true condensate. The presence of the phase fluctuations allows for extending thermometry of Bose-condensed gases well below those established in current experiments.

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Journal Phys. Rev. Lett.
Petrov, D. S, Shlyapnikov, G. V, & Walraven, J. T. M. (2001). Phase-fluctuating 3D Bose-Einstein condensates in elongated traps. Phys.Rev.Lett., 87(50404, Article number: 50404), 1–4.