Excitation Spectrum of a Bose-Einstein Condensate

TLDR

The study aims to measure the excitation spectrum ω(k) and static structure factor S(k) of a Bose–Einstein condensate. The authors perform spectroscopic measurements of ω(k) and S(k) on a trapped condensate. The measured spectrum displays a linear phonon regime and a parabolic single‑particle regime, agrees with the Bogoliubov prediction in the local density approximation, satisfies Feynman’s relation, and the linear regime sets an upper bound on the superfluid critical velocity via the Landau criterion.

Abstract

We report a measurement of the excitation spectrum omega(k) and the static structure factor S(k) 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(k) and S(k) is verified, within an overall constant.