Coherence length of an elongated condensate.

We measure the spatial correlation function of Bose-Einstein condensates in the cross-over region between phase-coherent and strongly phase-fluctuating condensates. We observe the continuous path from a Gaussian-like shape to an exponential-like shape characteristic of one-dimensional phase-fluctuations. The width of the spatial correlation function as a function of the temperature shows that the condensate coherence length undergoes no sharp transition between these two regimes. [ABSTRACT FROM AUTHOR]