Landau damping and frequency-shift of monopole mode in an elongated-rubidium Bose-Einstein condensate

Abstract

The Landau damping and frequency-shift of monopole mode in an elongated-rubidium Bose-Einstein condensate are investigated by using the time-dependent Hartree-Fock-Bogoliubov approximation. Improving the previous approach, We have taken into account the practical relaxations of elementary excitations and the orthogonal relation among them. With such an approach, we provide a new calculation formula for Landau damping rate and frequency-shift. In addition, our previous method of eliminating the divergence in three-mode coupling matrix elements is also improved by zeroing the kinetic energy at the condensate boundary instead of minimizing the ground-state energy. Based on these improvements, both the Landau damping rate and the frequency-shift of the monopole mode are analytically calculated and their temperature dependences are also discussed. And all the theoretical results are in agree meat with experimental data.

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

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] The damping and frequency-shift, which are the main characters of the elementary excitation, are the basic phenomena of BEC and widely observed in the experiments. [19][20][21][22][23][24][25][26] Although there are a lot of theoretic works on the Landau damping of the collective excitation in BEC, [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46] the problem is not yet studied and understood adequately. Although the damping is accompanied by the frequency-shift, only in Ref.…”

“…Although the damping is accompanied by the frequency-shift, only in Ref. [44] is the frequency-shift calculated in the study of Landau damping.…”

“…The dynamic of a collective mode is described respectively by the theory of two fluid hydrodynamics at high temperature and high density [27][28][29][30][31][32] and the mean-field theory at low temperature and low density. [33][34][35][36][37][38][39][40][41][42][43][44][45][46] In the framework of the mean-field theory, the Landau damping of a collective mode in BEC trapped in inhomogeneously harmonical potential is studied by Refs. [40]- [44].…”

“…[33][34][35][36][37][38][39][40][41][42][43][44][45][46] In the framework of the mean-field theory, the Landau damping of a collective mode in BEC trapped in inhomogeneously harmonical potential is studied by Refs. [40]- [44]. In Refs.…”

“…[45] and [46], the orthometric relation among the relaxations is also taken into account in Ref. [44]. The problem will be carefully discussed in Section 2.…”