Constructing a classical field for a Bose-Einstein condensate in an arbitrary trapping potential: Quadrupole oscillations at nonzero temperatures

Abstract

We optimize the classical field approximation of the version described by M. Brewczyk, M. Gajda, and K. Rz\k{a}\ifmmode \dot{z}\else \.{z}\fi{}ewski [J. Phys. B 40, R1 (2007)] for the oscillations of a Bose gas trapped in a harmonic potential at nonzero temperatures, as experimentally investigated by Jin et al. [Phys. Rev. Lett. 78, 764 (1997)]. Similar to experiment, the system response to external perturbations strongly depends on the initial temperature and the symmetry of perturbation. While for lower temperatures the thermal cloud follows the condensed part, for higher temperatures the thermal atoms oscillate rather with their natural frequency, whereas the condensate exhibits a frequency shift toward the thermal cloud frequency ($m=0$ mode) or in the opposite direction ($m=2$ mode). In the latter case, for temperatures approaching critical, we find that the condensate begins to oscillate with the frequency of the thermal atoms, as in the $m=0$ mode. A broad range of frequencies of the perturbing potential is considered.