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arXiv:cond-mat/0201563 · Physical Review A

Structure of vortices in two-component Bose-Einstein condensates

Dora M. Jezek, P. Capuzzi, Horacio M. Cataldo

Published Jul 10, 2001• 45 citations
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Abstract

We develop a three-dimensional analysis of the phase separation of two-species Bose-Einstein condensates in the presence of vorticity within the Thomas-Fermi approximation. We find different segregation features according to whether the more repulsive component is in a vortex or in a vortex-free state. An application of this study is aimed at describing systems formed by two almost immiscible species of rubidium-87 that are commonly used in Bose-Einstein condensation experiments. In particular, in this work we calculate the density profiles of condensates for the same conditions as the states prepared in the experiments performed at JILA [Matthews et al., Phys. Rev. Lett. 83, 2498 (1999)].

DOI
10.1103/physreva.64.023605

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We develop a three-dimensional analysis of the phase separation of two-species Bose-Einstein condensates in the presence of vorticity within the Thomas-Fermi approximation. We find different segregation features according to whether the more repulsive component is in a vortex or in a vortex-free state. An application of this study is aimed at describing systems formed by two almost immiscible species of rubidium-87 that are commonly used in Bose-Einstein condensation experiments. In particular, in this work we calculate the density profiles of condensates for the same conditions as the states prepared in the experiments performed at JILA [Matthews et al., Phys. Rev. Lett. 83, 2498 (1999)].
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 study the stability and dynamics of vortices in two-species condensates as prepared in the recent JILA experiment [Matthews et al., Phys. Rev. Lett. 83, 2498 (1999)]. We find that of the two possible configurations, in which one species has vorticity m = 1 and the other one has m = 0, only one is linearly stable, which agrees with the experimental results. However, it is found that in the unstable case the vortex is not destroyed by the instability, but may be transferred from one species to the other or display complex spatiotemporal dynamics.
The vortex configurations in the Bose-Einstein condensate of a mixture of two different spin states $|{F=1,m}_{f}=\ensuremath{-}1〉$ and ∣2,1〉|2,1〉∣2,1〉 of 87Rb{}^{87}\mathrm{Rb}87Rb atoms corresponding to the recent experiments by Matthews et al. [Phys. Rev. Lett. 83, 2498 (1999)] are considered in the framework of the Thomas-Fermi approximation as functions of N2/N1,{N}_{2}{/N}_{1},N2​/N1​, where N1{N}_{1}N1​ is the number of atoms in the state $|1,\ensuremath{-}1〉$ and N2{N}_{2}N2​ in the state ∣2,1〉.|2,1〉.∣2,1〉. Ranges of this ratio are determined within which the various configurations of the binary condensate are stable.
We study the stability and dynamics of vortices in two-species condensates using a two-mode model. The recent experimental results obtained at JILA [M. R. Matthews et al., Phys. Rev. Lett. 83, 2498 (1999)] and recent numerical simulations based on the Gross-Pitaevskii equations are explained using this simple model. We also make an exhaustive analysis of the stability properties of the system when the relative populations of the two species and/or their relative scattering lengths are changed and prove that stabilization of otherwise unstable configurations can be attained by controlling the relative population of both species.
We investigate vortex states of immiscible two-component Bose-Einstein condensates under rotation through numerical simulations of the coupled Gross-Pitaevskii equations. For strong intercomponent repulsion, the two components undergo phase separation to form several density domains of the same component. In the presence of the rotation, the nucleated vortices are aligned between the domains to make up winding chains of singly quantized vortices, a vortex sheet, instead of periodic vortex lattices. The vortices of one component are located at the region of the density domains of the other component, which results in the serpentine domain structure. The sheet configuration is stable as long as the imbalance of the intracomponent parameter is small. We employ a planar sheet model to estimate the distance between neighboring sheets, determined by the competition between the surface tension of the domain wall and the kinetic energy of the superflow via quantized vortices. By comparing the several length scales in this system, the phase diagram of the vortex state is obtained.
We examine the dynamics associated with the miscibility-immiscibility transition of trapped two-species Bose-Einstein condensates (TBECs) of dilute atomic gases in the presence of vortices. In particular, we consider TBECs of Rb hyperfine states and Rb-Cs mixture. In the case of a singly charged vortex in only one of the condensates, there is enhancement when the vortex is present in the species which occupies the edges at phase separation. But suppression occurs when the vortex is in the species which occupies the core region. To examine the role of the vortex, we quench the interspecies interactions to drive the TBECs from miscible to immiscible phase, and use the time-dependent Gross-Pitaevskii equation to probe the phenomenon of phase separation. We also examine the effects of higher charged vortex to phase separation.