Measurement of phase fluctuations of Bose-Einstein condensates in an optical lattice

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 depth where interference peaks disappear in the atomic density distribution.