  The coherence properties of phase fluctuating Bose-Einstein condensates are
studied both theoretically and experimentally. We derive a general expression
for the N-particle correlation function of a condensed Bose gas in a highly
elongated trapping potential. The second order correlation function is analyzed
in detail and an interferometric method to directly measure it is discussed and
experimentally implemented. Using a Bragg diffraction interferometer, we
measure intensity correlations in the interference pattern generated by two
spatially displaced copies of a parent condensate. Our experiment demonstrates
how to characterize the second order correlation function of a highly elongated
condensate and to measure its phase coherence length.
