Landau Damping And Frequency-shift Of A Scissors Mode In A Disc-shaped Rubidium Bose-einstein Condensate

Elementary excitation is a important subject in study of Bose-Einstein Condensation, there are a lot of experimental and theoretic work. The damping and frequency-shift, which are two accompanying experimental phenomena, are the main characters of elementary excitation in the experiments. The phenomena are widely experimental observed in trapped Bose-Einstein condensate. There are a lot of theoretic work on the damping and frequency-shift of the collective excitation in Bose-Einstein condensate, base on the mean-field theory or two fluid hydrodynamics theory, base on analytic work and numerical simulation work. Some experimental phenomena are explained theoreticaly.In this paper, we study Landau damping and frequency-shift of a scissors mode in a disc-shaped rubidium Bose-Einstein condensate. We adopt the Hartree-Fock-Bogoliubov mean-field theory approximation. We adopt the analytic method.In the framework of the mean-field theory, we get the damping rate and frequency-shift formula by introducing the practical relaxation of elementary excitation and the orthometric relation among the relaxations in the frequency correction formula of collective mode in mean-field theory. The analytic work can only be carried out by using the Thomas-Fermi approximation, The first approximation of Gaussian distribution function is employed for the ground-state wavefunction to suitably eliminate the divergence of the three-mode coupling matrix elements in Thomas-Fermi approximation. By using the parameters identical with the parameters in the experiment of JILA group, the damping rate and frequency-shift of the scissors mode have been analytically calculated. And the theoretical results are in agreement with the experimental ones performed by JILA group. In addition, the reasonableness that considering the relaxations of elementary excitations and the orthogonality relation among them and Beliaev mechanism to contribution of damping rate has been discussed with the additional calculations. Equally by using these method as well as the parameters identical with experimental ones, in our preliminary work the damping rates and frequency-shifts of a monopole mode in an elongated rubidium condensate and a quadrupole mode in a disk-shaped rubidium condensate have been calculated and the results are also in agreement with the experimental ones of MIT F.Chevy group and JILA D.S.Jin group respectively. Thus our developed method should be helpful to further understand the damping and frequency-shift mechanism of elementary excitations in the hyperfluid condensate.In the chapter 1, the basic concepts of Bose-Einstein condensation, laser cooling and trapping, and research trends are introduced. In the chapter 2, the mean-fieldtheory for Landau damping and frequency-shift, some experimental and theoretic work on collective mode in Bose-Einstein condensate are introduced. In the chapter 3,the research results of Landau damping and frequency-shift of a scissors mode in a disc-shaped rubidium Bose-Einstein Condensate are given. The reasonableness that considering the relaxations of elementary excitations and the orthogonality relation among them is discused. In the chapter 4, the summary and outlook are given.