We investigate the damping mechanism of two transverse quadrupole oscillations in the single-vortex state of Bose-Einstein condensates using the linear response theory. It is demonstrated theoretically that the Kelvin modes as a propagation wave along a vortex line can be excited via Beliaev damping processes for only the counter-rotating quadrupole mode. We calculate the spectral weight of the density-response function within the Bogoliubov-Popov theory in a cylindrical system taking into account both Beliaev and Landau processes. Furthermore, we extend these considerations to the full 3D cigar-shaped system, which enables us to discuss the effects of the longitudinal confinement on the damping processes. These results are compared with the recent experiment on 87Rb by Bretin et al. [Phys. Rev. Lett. 90, 100403 (2003)].
|Number of pages||7|
|Publication status||Published - Feb 1 2004|
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics
- Condensed Matter Physics
- Industrial and Manufacturing Engineering