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Damping of Collective Excitations in a Trapped Bose-Einstein Condensate at Finite Temperatures

正人 大矢

Published Dec 1, 2001• 0 citations
OpenAlex

Abstract

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.

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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.
Recent experimental observations of collective excitations of Bose condensed atomic vapours have stimulated interest in the microscopic description of the dynamics of a Bose-Einstein condensate confined in an external potential. We present a finite temperature field theory for collective excitations of trapped Bose-Einstein condensates and use a finite-temperature linear response formalism, which goes beyond the simple mean-field approximation of the Gross-Pitaevskii equation. The effect of the non-condensed thermal atoms we include using perturbation theory in a quasiparticle basis. This presents a simple scheme to understand the interaction between condensate and non-condensed atoms and enables us to include the effect the condensate has on collision dynamics. At first we limit our treatment to the case of a spatially homogeneous Bose gas. We include the effect of pair and triplet anomalous averages and thus obtain a gapless theory for the excitations of a weakly interacting system, which we can link to well known results for Landau and Beliaev damping rates. A gapless theory for trapped systems with a static thermal component follows straightforwardly. We then investigate finite temperature excitations of a condensate in a spherically symmetric harmonic trap. We avoid approximations to the density of states and thus emphasise finite size aspects of the problem. We show that excitations couple strongly to a restricted number of modes, giving rise to resonance structure in their frequency spectra. Where possible we derive energy shifts and lifetimes of excitations. For one particular mode, the breathing mode, the effects of the discreteness of the system are sufficiently pronounced that the simple picture of an energy shift and width fails. Experiments in spherical traps have recently become feasible and should be able to test our detailed quantitative predictions.
We utilize a two-gas model to simulate collective oscillations of a Bose-Einstein condensate at finite temperatures. The condensate is described using a generalized Gross-Pitaevskii equation, which is coupled to a thermal cloud modeled by a Monte Carlo algorithm. This allows us to include the collective dynamics of both the condensed and noncondensed components self-consistently. We simulate quadrupolar excitations, and measure the damping rate and frequency as a function of temperature. We also observe revivals in condensate oscillations at high temperatures, and in the thermal cloud at low temperature. Extensions of the model to include nonequilibrium effects and describe more complex phenomena are discussed.
Recently it was shown that the Landau-Khalatnikov two-fluid hydrodynamics describes the collision-dominated region of a trapped Bose condensate interacting with a thermal cloud. We use these equations to discuss the low frequency hydrodynamic collective modes in a trapped Bose gas at finite temperatures. We derive variational expressions based on these equations for both the frequency and damping of collective modes. A new feature is our use of frequency-dependent transport coefficients, which produce a natural cutoff by eliminating the collisionless low-density tail of the thermal cloud. Above the superfluid transition, our expression for the damping in trapped inhomogeneous gases is analogous to the result first obtained by Landau and Lifshitz for uniform classical fluids. We also use the moment method to discuss the crossover from the collisionless to the hydrodynamic region. Recent data for the monopole-quadrupole mode in the hydrodynamic region of a trapped gas of metastable 4He{}^{4}\mathrm{He}4He is discussed. We also present calculations for the damping of the analogous m=0m=0m=0 monopole-quadrupole condensate mode in the superfluid phase.
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.