Bragg spectroscopy of the multi-branch Bogoliubov spectrum of elongated Bose-Einstein condensates

This paper presents Bragg spectroscopy of the multi-branch Bogoliubov spectrum of elongated Bose-Einstein condensates. The condensate consists of N=10/sup 5/ atoms of /sup 87/Rb which was excited at wavenumber k by using two Bragg beams. Results are analyzed by numerically solving the Gross-Pitaevskii (GP) equation for the order parameter of the condensate. This study shows that the response of the condensate to a Bragg pulse is indeed significantly affected by the radial degrees of freedom. By using Bragg pulses longer than in previous measurements, this multi-branch spectrum is resolved, finding good agreement with the predictions of Gross-Pitaevskii theory.