On the Thomas-Fermi approximation in the bulk of trapped Bose-Einstein condensed gases

TL;DR

This paper examines the limitations of the Thomas-Fermi approximation in trapped Bose-Einstein condensates, emphasizing the need for corrections to accurately predict low-lying mode frequencies and exploring related spin fluctuation phenomena.

Contribution

It provides a quantitative analysis of the failure of the Thomas-Fermi approximation in the bulk of condensates and discusses similar effects in spin fluctuations within optical traps.

Findings

Corrections are necessary for accurate mode frequency predictions.

The Thomas-Fermi approximation fails not only at the surface but also in the bulk.

Spin fluctuations exhibit similar correction effects in optical traps.

Abstract

Corrections to the Thomas-Fermi-type solution of the Gross-Pitaevskii equation are inevitable in order to get correctly the frequencies of the low lying modes out of the Bogolyubov equations. These corrections are important in the bulk, too, thus the failure of the Thomas-Fermi approximation is not confined to the surface. We discuss this effect quantitatively and consider similar phenomena of spin fluctuations in Bose-Einstein condensed gases in an optical trap.