Elementary excitations in trapped Bose gases beyond mean field approximation

TL;DR

This paper derives the first correction beyond mean field theory to the collective excitation frequencies of trapped Bose gases, showing it is the dominant correction under typical experimental conditions.

Contribution

It introduces a hydrodynamic approach combined with the Lee-Huang-Yang equation to quantify non-mean field effects on collective frequencies in Bose gases.

Findings

Non-mean field correction is approximately 1% of the frequency shift.

The correction surpasses finite size, non-linearity, and finite temperature effects.

Trap deformation effects are also analyzed.

Abstract

Using hydrodynamic theory of superfluids and the Lee-Huang-Yang equation of state for interacting Bose gases we derive the first correction to the collective frequencies of a trapped gas, due to effects beyond mean field approximation. The corresponding frequency shift, which is calculated at zero temperature and for large N, is compared with other corrections due to finite size, non-linearity and finite temperature. We show that for reasonable choices of the relevant parameters of the system, the non-mean field correction is the leading contribution and amounts to about 1%. The role of the deformation of the trap is also discussed.