Landau Damping And Frequency-shift Of A Monopole Mode In A Sperical Rubidium Bose-Einstein Condensate

Elementary excitation in Bose-Einstein condensate is a good subject forstudying the physics of many-body system. The inter-particle interaction results innot only the collective excitation but also the energy-level shifts of collectiveexcitations (called as frequency-shift) and the decay of their amplitudes (called asdamping). Although there exists a lot of theoretical studies on the Landau damping ofcollective excitations, the damping especially the frequency are not yet studied andunderstood adequately.The Landau damping and frequency-shift of monopole mode in a sphericalrubidium Bose-Einstein condensate are investigated by using the time-dependentHartree-Fock-Bogiliubov approximation. Wo adopt the analytical method of thebeyond Thomas-Fermi approximation, the first approximation of Gaussiandistribution function is employed for the ground-state wavefunction to suitablyeliminate the divergence of three mode coupling matrix elements. Three modecoupling matrix elements and the damping strength of all allowed transitions areevaluated by using the solution of Gross-Pitaevskii equation for groud-state andBogoliubov-de-Gennes equation for elementary excitions. We adopt the damp andfrequency-shift formula obtained by introducing the practical relaxation ofelementary excitions and the orthometric relation among the relaxations in thefrequency correction formula, and take the approximation that the damping rate isproportional to the frequency, to calculate the damping rate in an interactive way andcalculate the frequency on the basis of the calculation results of the damping rate.And we discuss the temperature dependence of the damping rate and frequency-shift.Without direct experiment data reported, at the condition of the same atom,same particle number, same trapping frequency, and similar collective modefrequency, we calculate the damping rate and frequency-shift and their temperaturedependence by using the previous method and indirectly compare our analyticresults with the experiment ones of the axisymmetric condensate, to discuss therationality of taking into account the practical relaxations of the elementaryexcitations and the orthometric relation among them in calculation formula fordamping and frequency-shift. We use the same experimental parameters and thesame calculation method of the present numerical simulation study to calculate thedamping rate, and our analytic results are found to be close to the numericalsimulation ones. It is illustrated that the employing the first approximation of Gaussian distribution function for the ground-state wavefunction is reasonable.In the chapter1, the concepts, history and research of Bose-Einsteincondensate and our work are introduced. In the chapter2, the basic theory forLandau damping and frequency-shift in Bose-Einstein condensate and some typicalstudy on Landau damping and frequency-shift are introduced. In the chapter3, theresearch results of Landau damping and frequency-shift of monopole mode in asperical rubidium Bose-Einstein Condensate are introduced. In the chapter4, thesummary and outlook are introduced.