Collective and single particle excitations of a trapped Bose gas

TL;DR

This paper compares different theoretical models to analyze the excitation spectrum of a trapped Bose gas, highlighting the importance of single-particle excitations and the effectiveness of semiclassical approximations.

Contribution

It demonstrates that Hartree-Fock theory accurately describes the excitation spectrum and explores the crossover between hydrodynamic and particle regimes in a trapped Bose gas.

Findings

Hartree-Fock provides excellent spectrum description

Semiclassical approximation yields accurate density of states

Surface mode frequency varies with angular momentum

Abstract

The density of states of a Bose-condensed gas confined in a harmonic trap is investigated. The predictions of Bogoliubov theory are compared with the ones of Hartree-Fock theory and of the hydrodynamic model. We show that the Hartree-Fock scheme provides an excellent description of the excitation spectrum in a wide range of energy, revealing a major role played by single-particle excitations in these confined systems. The crossover from the hydrodynamic regime, holding at low energies, to the independent particle regime is explicitly explored by studying the frequency of the surface mode as a function of their angular momentum. The applicability of the semiclassical approximation for the excited states is also discussed. We show that the semiclassical approach provides simple and accurate formulae for the density of states and the quantum depletion of the condensate.