  Even at zero temperature, there exist phase fluctuations associated with an
array of Bose-Einstein condensates confined in a one-dimensional optical
lattice. We demonstrate a method to measure the phase fluctuations based on the
Fourier spectrum of the atomic density for a condensate released from the
optical lattice. The phase variance is extracted from the relative intensities
of different peaks in the Fourier spectrum. This method works even for high
lattice strength where interference peaks disappear in the atomic density
distribution.
