Excitation Spectrum of a Bose-Einstein Condensate

We report a measurement of the excitation spectrum $\omega \left(k\right)$ and the static structure factor $S\left(k\right)$ of a Bose-Einstein condensate. The excitation spectrum displays a linear phonon regime, as well as a parabolic single-particle regime. The linear regime provides an upper limit for the superfluid critical velocity, by the Landau criterion. The excitation spectrum agrees well with the Bogoliubov spectrum in the local density approximation, even close to the long-wavelength limit of the region of applicability. Feynman’s relation between $\omega \left(k\right)$ and $S\left(k\right)$ is verified, within an overall constant.