Cooperative scattering measurement of coherence in a spatially modulated Bose gas

Correlations of a Bose gas released from an optical lattice are measured using superradiant scattering. Conditions are chosen so that, after initial incident light pumping at the Bragg angle for diffraction, superradiant scattering into the Bragg diffracted mode is preponderant due to matter-wave amplification and mode competition. A temporal analysis of the superradiant scattering gain reveals periodical oscillations and damping due to the initial lack of coherence between lattice sites. Such damping is used for characterizing first-order spatial correlations in our system with a precision of one lattice period.