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

Abstract

The dynamics of Bose-Einstein condensate (BEC) is studied at nonzero temperatures using our variational time-dependent-HFB formalism. We have shown that this approach is an efficient tool to study the expansion and collective excitations of the condensate, the thermal cloud and the anomalous correlation function at nonzero temperatures. We have found that the condensate and the anomalous density have the same breathing oscillations. We have investigated, on the other hand, the behavior of a single quantized vortex in a harmonically trapped BEC at nonzero temperatures. Generalized expressions for vortex excitations, vortex core size and Kelvin modes have been derived. An important and somehow surprising result is that the numerical solution of our equations predicts that the vortex core is partially filled by the thermal atoms at nonzero temperatures. We have shown that the effect of thermal fluctuations is important and it may lead to enhancing the size of the vortex core. The behavior of the singly anomalous vortex has also been studied at nonzero temperatures.

Dipolar Bose gas with three-body interactions at finite temperature

“…One possibility to fix this problem might be the inclusion of the dynamics of the noncondensed and the anomalous components. A suitable formalism to explore such a dynamics is the timedependent HFB theory [53][54][55][56][57].…”

“…To go consistently beyond the Popov theory, one should renormalize the coupling constant taking into account many-body corrections for scattering between the condensed atoms on one hand and the condensed and thermal atoms on the other. Following the procedure outlined in Refs [51][52][53][54][55] we obtain…”

Collective modes of a one-dimensional trapped Bose gas in the presence of the anomalous density

“…(4) can reproduce the mean-field result based on the HFB approximation. Working in the Bogoliubov quasiparticles space [37] one hasâ k = u kbk − v kb † −k , whereb † k andb k are operators of elementary excitations and u k , v k are the standard Bogoliubov functions. In the quasiparticle vacuum state,ñ andm may be written asñ…”

“…In order to study analytically the collective oscillations, we write the condensate wavefunction and the anomalous density of the set (1) in the form [21,30,37]:…”

“…The aim of the present work is to investigate the collective modes of both the condensate and the anomalous components in a quasi-1D trapped Bose gas at finite temperature utilizing our TDHFB theory [21,23,29,30,[34][35][36][37][38]. The TDHFB is a self-consistent approach describing the dynamics of ultracold Bose gases.…”