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

TL;DR

This paper improves the classical field approximation to model Bose-Einstein condensate oscillations in arbitrary traps at nonzero temperatures, revealing temperature-dependent dynamics and mode frequency shifts consistent with experimental observations.

Contribution

The authors optimize the classical field method for arbitrary trapping potentials and analyze temperature-dependent oscillation modes in Bose gases, extending previous models.

Findings

Thermal cloud follows condensate at low temperatures.

At higher temperatures, thermal atoms oscillate at their natural frequency.

Condensate frequency shifts toward thermal cloud frequency near critical temperature.

Abstract

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.