Landau Damping And Frequency-shift Of Low Energy Collective Excitation Modes In A Spherical Bose-Einstein Condensate

Bose-Einstein Condensation(BEC)is a new matter state,which has many novel physical properties.Elementary excitation is a common phenomenon of disturbance in condensed and non-condensed parts in the BEC.The inter-particle interaction in the BEC can lead to damping and frequency shift of collective excitations.The study of damping and frequency shift is of great importance both in experimental work and theoretical work.Based on the mean-field theory of Hartree-Fock-Bogoliubov(HFB),the Landau damping and frequency shift of low-energy collective excitation in spherical BEC are studied in this paper.Our theoretical calculations is Based on the analytical method of Thomas-Fermi approximation(TFA).We get the damping and frequency-shift formula by introducing the relaxation of elementary excitation and the orthometric relation among the relaxations in the frequency correction formula of collective mode in HFB mean-field theory.In our analytic calculations,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.In this paper,we invested a completely and carefully calculation of the low energy collective excitation modes in the spherical BEC,which includes three breathing modes(n,l,m)(28)(n,0,0)n(28)1,2,3;ten surface modes(n,l,m)(28)(0,l,0),l(28)1,2,,10;and four modes(n,l,m)(28)(1,l,0),l(28)1,2,3,4.We calculated the three-mode coupling matrix elements and damping strength which contribute to the damping and frequency shift.The temperature dependence of damping and frequency shift is studied.Under the same conditions of atomic species,particle number and trapping frequencies,our theoretical results are indirectly compared with the experimental results of damping and frequency shift of collective excitation in axisymmetric BEC.In the preliminary work of this paper,the same method was used to calculate the damping and frequency shift of a monopole mode in an elongated-rubidium BEC,and of a scissors mode and a quadrupole mode in disc-shaped rubidium BEC,The calculation results are in agreement well with the experimental results.In this paper we calculated the damping and frequency shift of the low energy collective excitation modes in the spherical BEC.The theoretical results are expected to be better predictive experiments,with a view to further reference value in the further research.