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

TL;DR

This paper demonstrates Bragg spectroscopy as a method to probe the complex multi-branch Bogoliubov spectrum of elongated Bose-Einstein condensates, revealing detailed phonon structures beyond local density approximation predictions.

Contribution

It introduces a spectroscopic technique to resolve axial phonons with different radial nodes in elongated BECs, validated by numerical simulations.

Findings

Observation of nontrivial momentum transfer behavior with long Bragg pulses

Resolution of multiple phonon branches with different radial nodes

Failure of local density approximation in describing the spectrum

Abstract

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.