Landau damping and frequency-shift of a quadrupole mode in a disc-shaped rubidium Bose—Einstein condensate

Abstract

The damping and frequency-shift in Landau mechanism of a quadrupole mode in a disc-shaped rubidium Bose—Einstein condensate are investigated by using the Hartree—Fock—Bogoliubov approximation. The practical relaxations of the elementary excitations and the orthometric relation among them are taken into account to obtain advisable calculation formula for damping as well as frequency-shift. The first approximation of Gaussian distribution function is employed for the ground-state wavefunction to suitably eliminate the divergence of the analytic three-mode coupling matrix elements. According to these methods, both Landau damping rate and frequency-shift of the quadrupole mode are analytically calculated. In addition, all the theoretical results agree with the experimental ones.