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arXiv:cond-mat/9708080 · Physical Review Letters

Theoretical Study of the Damping of Collective Excitations in a Bose-Einstein Condensate

W. Vincent Liu

Published Nov 24, 1997• 98 citations
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Abstract

We study the damping of low-lying collective excitations of condensates in a weakly interacting Bose gas model within the framework of an imaginary time path integral. A general expression of the damping rate has been obtained for both the very low temperature regime and the higher temperature regime. For the latter, the result is new and applicable to recent experiments. Theoretical predictions for the damping rate are compared with the experimental values.

DOI
10.1103/physrevlett.79.4056

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We study the damping of low-lying collective excitations of condensates in a weakly interacting Bose gas model within the framework of an imaginary time path integral. A general expression of the damping rate has been obtained for both the very low temperature regime and the higher temperature regime. For the latter, the result is new and applicable to recent experiments. Theoretical predictions for the damping rate are compared with the experimental values.
We present the theory for low energy collective excitations of a trapped Bose-Einstein condensate which includes the dynamics of thermal quasiparticles. A linearized hydrodynamic description yields the equations expressed in terms of the small density fluctuation δn and velocity potential fluctuation δΦ , which is the generalization of the one given by Morii et al. to the non-uniform case. A expression of the damping rate of low energy collective excitations has been obtained for the higher temperature regime.
We calculate the frequencies and damping rates of the low-lying collective modes of a Bose-Einstein condensed gas at nonzero temperature. We use a complex nonlinear Schr\"odinger equation to determine the dynamics of the condensate atoms, and couple it to a Boltzmann equation for the noncondensate atoms. In this manner we take into account both collisions between noncondensate-noncondensate and condensate-noncondensate atoms. We solve the linear response of these equations, using a time-dependent Gaussian trial function for the condensate wave function and a truncated power expansion for the deviation function of the thermal cloud. As a result, our calculation turns out to be characterized by two dimensionless parameters proportional to the noncondensate-noncondensate and condensate-noncondensate mean collision times. We find in general quite good agreement with experiment, both for the frequencies and damping of the collective modes.
We present the theory of damping of low-energy excitations of a trapped Bose-Einstein condensate at finite temperatures, where the damping is provided by the interaction of these excitations with the thermal excitations. We emphasize the key role of stochastization in the behavior of the thermal excitations for damping in nonspherical traps. The damping rates of the lowest excitations, following from our theory, are in fair agreement with the data of recent JILA and MIT experiments. The damping of quasiclassical excitations is determined by the condensate boundary region, and the result for the damping rate is drastically different from that in a spatially homogeneous gas.
We investigate the Landau damping of the collective mode in a quasi-one-dimensional repulsive Bose—Einstein condensate by using the self-consistent time-dependent Hartree—Fock—Bogoliubov approximation. We put forward a new method to calculate the Landau damping rate of the collective mode in the condensate and discuss the dependence of the Landau damping on temperature, on transverse trapping frequency, on atom number in the condensate, and on length of the system. Different from the usual calculation method for the three dimension system, our new calculation method is an interactive one by considering the practical relaxation of the elementary excitation. With little approximation, our theoretical calculation results agree with the experimental ones. Comparing with the usual calculation method, our theory is helpful to deduce the inter-particle interactions in damping phenomenon.