Static properties of trapped bose gases at finite temperature: Thomas-Fermi limit

Abstract

We rely on a variational approach to derive a set of equations governing a trapped self-interacting Bose gas at finite temperature. In this work, we analyze the static situation both at zero and finite temperature in the Thomas-Fermi limit. We derive simple analytic expressions for the condensate properties at finite temperature. The noncondensate and anomalous density profiles are also analyzed in terms of the condensate fraction. The results are quite encouraging owing to the simplicity of the formalism.

Finite temperature correction to the Thomas–Fermi approximation for a Bose–Einstein condensate: comparison between theory and experiment

“…In our case, the Gaussian shape of the noncondensate cloud is preserved due to the uniform character of the condensate repulsive mean field adopted. In a recent paper [15], the authors indicate that such a modified thermal cloud profile tends to be more uniform to large and dense clouds.…”

“…To our knowledge, no other work deals with the quantity R 5 /N 0 × N 0 /N, which is a relevant quantity within the Thomas-Fermi (TF) approximation, and neither do they produce analytical analysis for the problem. In fact, most of the existing work deals with numerical corrections to these individual quantities [11] or rely on analytical approaches still based on the T = 0 regime, neglecting the thermal atoms [15].…”

Collective modes and generation of a new vortex in a trapped Bose gas at finite temperature

“…, which shows clearly that neglecting m Δ does not necessarily mean neglecting n Δ and therefore omitting the anomalous pressure does not mean neglecting the thermal pressure [63]. Such feature we shall adopt in what follow.…”

Non-Thomas–Fermi behaviour of a finite-temperature Bose–Einstein condensate in the presence of a thermal cloud

“…The density profiles that we have just determined as functions of the temperature are seen to keep the same overall structures, which are not altered for high atom numbers until the TF regime is reached. This is to be contrasted with [15], where in particularñ(r) andm(r) do not present any particular structure near the origin. We believe that the absence of this structure is an artefact of the finite-temperature TF approximation used there.…”

“…Moreover, in a recent work [15], it was found that for high atom numbers, the non-condensate density and the anomalous density have no special structure near the centre of the trap which seems compatible with the experiment [10] (at least for the thermal cloud) but which contradicts the results of [8]. We must recall however that the generalized Hartree-Fock-Bogoliubov (GHFB) numerical calculations performed in the latter reference consider only small atom numbers; hence, there is a necessity to perform the same calculations for high atom numbers in order to see to what extent the predictions of the GHFB approximation remain true.…”