Excited states of a dilute Bose-Einstein condensate in a harmonic trap

TL;DR

This paper analyzes the low-lying excited states of a dilute Bose-Einstein condensate in a harmonic trap, providing explicit constructions of modes and the dynamic structure function in the Thomas-Fermi limit.

Contribution

It offers a detailed analysis of the hydrodynamic modes and Bogoliubov amplitudes, including explicit mode constructions and structure function calculations in the condensate.

Findings

Low-lying modes have large occupation numbers at low temperature.

Total noncondensate number scales as R^6 with condensate radius.

Explicit construction of dipole modes in Bogoliubov approximation.

Abstract

The low-lying hydrodynamic normal modes of a dilute Bose-Einstein gas in an isotropic harmonic trap determine the corresponding Bogoliubov amplitudes. In the Thomas-Fermi limit, these modes have large low-temperature occupation numbers, and they permit an explicit construction of the dynamic structure function $S(q,\omega)$. The total noncondensate number $N'(0)$ at zero temperature increases like $R^6$, where $R$ is the condensate radius measured in units of the oscillator length. The lowest dipole modes are constructed explicitly in the Bogoliubov approximation.