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

Elementary excitation in Bose-Einstein Condensate is a good subject forstudying the physics of many-body system. The damping and frequency-shift, whichare the main characters of elementary excitation, are the basic phenomena ofBose-Einstein condensate and widely observed in the experiments. Although there area lot of theoretic work on the Landau damping of the collective excitation inBose-Einstein condensate, the physical mechanism of the damping, especially thephysical mechanism of frequency-shift are not yet studied and understood adequately.In this paper, we study Landau damping and frequency-shift of a quadrupolemode in a disc-shaped rubidium Bose-Einstein condensate by using theHartree-Fock-Bogoliubov mean-field theory. In the calculation, we adopt the analyticmethod of beyond Thomas Fermi approximate, the first approximation of Gaussiandistribution function is employed for the ground-state wavefunction to suitablyeliminate the divergence of the analytic three-mode coupling matrix elements. Thethree-mode coupling matrix describing the interaction between particles and collectiveexcitation mode are evaluated by using the solution of Gross-Pitaeviskii equation forground state and Bogoliubov-de-Gennes equation for elementary excitation, and thedamping strength of the transitions satisfying the selection rules are calculated. Weadopt the damp and frequency formula, which are get by introducing the practicalrelaxation of elementary excitation and the orthometric relation among the relaxationsin the frequency correction formula, and take the approximation that the damping rateis proportional to the frequency, to calculate the damping rate in an interactive wayand calculate the frequency on the basis of the calculation result of the damping rate.And we discuss the temperature dependence of the damping rate and frequency-shift.All of our theoretic calculation results are agree with the experimental ones of D. S.Jin group of Joint Institute for Laboratory Astrophysics.In the chapter1, the concepts, history and research of Bose-Einsteincondensation and our work are introduced. In the chapter2, the basic theory ofLandau damping and frequency-shift in Bose-Einstein condensate and somecorresponding typical study are introduced. In the chapter3, the research results ofLandau damping and frequency-shift of quadrupole mode in a disc-shaped rubidiumBose-Einstein Condensate are introduced. In the chapter4, the summary and outlookare introduced.