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Journal of Statistical Physics

Bose Condensates in Interaction with Excitations: A Two-Component Space-Dependent Model Close to Equilibrium

Leif Arkeryd, Anne Nouri

Published Mar 25, 2015• 13 citations
Publisher
DOI
10.1007/s10955-015-1229-6

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The paper considers a model for Bose gases in the so-called 'high-temperature range' below the temperature Tc, where Bose-Einstein condensation sets in.The model is of non-linear two-component type, consisting of a kinetic equation with periodic boundary conditions for the distribution function of a gas of excitations interacting with a Bose condensate, which is described by a Gross-Pitaevskii equation. Results on well-posedness and long time behaviour are proved in a H1-setting close to equilibrium.
Abstract In contrast to one-component Bose-Einstein condensate case, the vortices in two-component condensate can have various complicated structures. The vortices in a space-homogeneous Bose-Einstein condensate have been studied in this paper. It is shown that the vortex structure is described by three dimensionless parameters. This is totally different from the usual one-component condensate case,where an isolated vortex is described by a parameterless dimensionless equation. The two-component vortex structure strongly depends on the sign of “interaction” constant of the components. A few types of vortices with different qualitative structure are explored. We show that the “super-density vortices” can exist, when the “interaction” constant is positive. The “super-density vortices” have the near-axis density greater than the equilibrium density of a homogeneous space Bose-Einstein condensate. We also show that the vortices with opposite direction of the condensate component rotation near the axis and far off the axis can exist.
We investigate a model of a two-component Bose-Einstein condensate residing on an optical lattice. Within a Bogolioubov-approach at the mean-field level, we derive exact analytical expressions for the excitation spectrum of the two-component condensate when taking into account hopping and interactions between arbitrary sites. Our results thus constitute a basis for works that seek to clarify the effects of higher-order interactions in the system. We investigate the excitation spectrum and the two branches of superfluid velocity in more detail for two limiting cases of particular relevance. Moreover, we relate the hopping and interaction parameters in the effective Bose-Hubbard model to microscopic parameters in the system, such as the laserlight wavelength and atomic masses of the components in the condensate. These results are then used to calculate analytically and numerically the drag coefficient between the components of the condensate. We find that the drag is most effective close to the symmetric case of equal masses between the components, regardless of the strength of the intercomponent interaction and the lattice well depth.