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

We measure the response of an elongated Bose-Einstein condensate to a two-photon Bragg pulse. If the duration of the pulse is long, the total momentum transferred to the condensate exhibits a nontrivial behavior which reflects the structure of the underlying Bogoliubov spectrum. It is thus possible to perform a spectroscopic analysis in which axial phonons with different number of radial nodes are resolved. The local density approximation is shown to fail in this regime, while the observed data agrees well with the results of simulations based on the numerical solution of the Gross-Pitaevskii equation.