Constructing classical field for a Bose-Einstein condensate in arbitrary trapping potential; quadrupole oscillations at nonzero temperatures

We optimize the classical field approximation of the version described in 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)]. Similarly to experiment, the system response to external perturbations strongly depends on the initial temperature and on 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.

💡 Research Summary

In this paper the authors develop and apply an optimized classical‑field (c‑field) approximation to study quadrupole collective excitations of a trapped Bose‑Einstein condensate (BEC) at finite temperature, reproducing the key observations of the JILA experiment (Jin et al., Phys. Rev. Lett. 78, 764 (1997)). The classical‑field method follows the formulation of Ref.