Bragg spectroscopy of a cigar-shaped Bose condensate in optical lattices

We study the properties of excited states of an array of weakly coupled quasi-two-dimensional Bose condensates using hydrodynamic theory. We calculate the multibranch Bogoliubov-Bloch spectrum and its corresponding eigenfunctions. The spectrum of the axial excited states and its eigenfunctions strongly depends on the coupling among various discrete radial modes within a given symmetry. This mode coupling is due to the presence of a radial trapping potential. The multibranch nature of the Bogoliubov-Bloch spectrum and its dependence on the mode coupling can be realized by analysing the dynamic structure factor and momentum transferred to the system in Bragg spectroscopy experiments. We also study the dynamic structure factor and momentum transferred to the condensate due to the Bragg spectroscopy experiment