A Variational Sum-Rule Approach to Collective Excitations of a Trapped Bose-Einstein condensate

T. Kimura, Hiroki Saito, Masahito Ueda

Yongli Ma, S. T. Chui

T. Kimura, Hiroki Saito, Masahito Ueda

It is found that combining an excitation-energy sum rule with Fetter's trial wave function gives almost exact low-lying collective-mode frequencies of a trapped Bose-Einstein condensate at zero temperature.

T. Kimura

The breathing mode collective-excitation frequency of a Bose-Einstein condensate is studied in a highly asymmetric (two- or one-dimensional) trap by using a sum-rule method and a time-dependent variational method. The collective-excitation frequency of the breathing mode in the Thomas-Fermi limit for a purely two- or one-dimensional trap is reproduced by a general result for a three-dimensional trap. In the case of a two- or one-dimensional trap, we obtain the lowest-order correction for the excitation frequency due to the finiteness of the trap frequency in the tightly trapped direction or the finiteness of the number of atoms.

正人 大矢

Hirofumi Morise, Miki Wadati

The phase separation and collective excitations of two-component Bose-Einstein condensates in traps are studied. Using the variational method, we show that the separated state is favorable in the case where the interspecies interaction is strongly repulsive and the number of atoms is large enough. This phase separation condition is explained in terms of the softening of a dipole mode collective excitation. Other low-lying excitation modes and their softenings which lead to the instability of the mixed state are also studied by use of the sum-rule approach.