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arXiv:1403.4695 · Communications in Mathematical Physics

Thomas–Fermi Approximation for Coexisting Two Component Bose–Einstein Condensates and Nonexistence of Vortices for Small Rotation

Amandine Aftalion, Benedetta Noris, Christos Sourdis

Published Jan 14, 2015• 21 citations
arXivHTMLPDF
DOI
10.1007/s00220-014-2281-9

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We study the spatial distribution of particles in two-component Bose–Einstein condensates containing vortices. We show that the form in which the species are arranged inside the condensate may be easily understood using simple approximations. We obtain expressions for the location of particular points which are useful for describing the density of particles in two limiting situations, using either the Thomas–Fermi approximation or a low-dilution approximation. A discussion about the shape of vortex cores is also included.
We investigate a harmonically trapped two-component Bose-Einstein condensate within the miscible regime, close to its boundaries, for different ratios of effective intra- and interspecies interactions. We derive analytically a universal equation for the density around the different boundaries in one, two, and three dimensions, for both the coexisting and spatially separated regimes. We also present a general procedure to solve the Thomas-Fermi approximation in all three spatial dimensionalities, reducing the complexity of the Thomas-Fermi problem for the spatially separated case in one and three dimensions to a single numerical inversion. Finally, we analytically determine the frontier between the two different regimes of the system.