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Phase separation and vortex states in binary mixture of Bose-Einstein condensates

S. T. Chui, Valentin Nikolaevich Ryzhov, Elena E. Tareyeva

Published Jan 1, 2000• 21 citations
OpenAlex

Abstract

The phase separation and vortex states in two-component Bose-Einstein condensate consisting of |F = 1,mf = −1> and |2,1> internal spin states of 87Rb atoms are considered in the framework of Thomas-Fermi approximation. It is shown that in nonrotating system the atoms in the state |1, −1> form a shell about the atoms in the state |2,1>. The critical angular velocity for each state is calculated. These velocities depend drastically on the relative concentrations of the components, the critical angular velocity of the outer component being less than the angular velocity of the inner one. It is shown that the atoms in the |1, −1> state can form a rotating ring about the resting core of the atoms in the state |2,1>. PACS:03.75.Fi; 05.30.Jp; 32.80.Pj. The realization of Bose-Einstein Condensation (BEC) in dilute atomic gases offers new opportunities for studying quantum degenerate fluids [1]. These condensates, which contain thousands of atoms confined to microscale clouds, have similarities to superfluidity and laser,

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The phase separation and vortex states in two-component Bose-Einstein condensate consisting of |F = 1,mf = −1> and |2,1> internal spin states of 87Rb atoms are considered in the framework of Thomas-Fermi approximation. It is shown that in nonrotating system the atoms in the state |1, −1> form a shell about the atoms in the state |2,1>. The critical angular velocity for each state is calculated. These velocities depend drastically on the relative concentrations of the components, the critical angular velocity of the outer component being less than the angular velocity of the inner one. It is shown that the atoms in the |1, −1> state can form a rotating ring about the resting core of the atoms in the state |2,1>. PACS:03.75.Fi; 05.30.Jp; 32.80.Pj. The realization of Bose-Einstein Condensation (BEC) in dilute atomic gases offers new opportunities for studying quantum degenerate fluids [1]. These condensates, which contain thousands of atoms confined to microscale clouds, have similarities to superfluidity and laser,
The phase separation and vortex states in a two-component Bose-Einstein condensate consisting of | F = 1, m f = 1〉 and |2, 1〉 internal spin states of 87 Rb atoms are considered in the framework of the Thomas-Fermi approximation. It is shown that in the nonrotating system, the atoms in the state |1, −1〉 form a shell around the atoms in the state |2, 1〉. The critical angular velocity for each state is calculated. These velocities depend drastically on the relative concentrations of the components, the critical angular velocity of the outer component being less than the angular velocity of the inner one. It is shown that the atoms in the |1, −1〉 state can form a rotating ring around the resting core of the atoms in the |2, 1〉 state.
Equilibrium vortex formation in rotating binary Bose gases with a rotating frequency higher than the harmonic trapping frequency is investigated theoretically. We consider the system being evaporatively cooled to form condensates and a combined numerical scheme is applied to ensure the binary system being in an authentic equilibrium state. To keep the system stable against the large centrifugal force of ultrafast rotation, a quartic trapping potential is added to the existing harmonic part. Using the Thomas-Fermi approximation, a critical rotating frequency ${\ensuremath{\Omega}}_{c}$ is derived, which characterizes the structure with or without a central density hole. Vortex structures are studied in detail with rotation frequency both above and below ${\ensuremath{\Omega}}_{c}$ and with respect to the miscible, symmetrically separated, and asymmetrically separated phases in their nonrotating ground-state counterparts.
A system of two simultaneously trapped condensates consisting of 87 Rb atoms in two different hyperfine states is investigated theoretically in the case where the minima of the trapping potentials are displaced with respect to each other. It is shown that the small shift of the minima of the trapping potentials leads to a considerable displacement of the centers of mass of the condensates, in agreement with the experiment. It is also shown that the critical angular velocities of the vortex states of the system drastically depend on the shift and the relative number of particles in the condensates, and there is a possibility to exchange the vortex states between condensates by shifting the centers of the trapping potentials.
Characteristic features in phases of Bose-Einstein condensations (BEC) for systems of two-components in gas phases of Alkali-metal atoms trapped by harmonic potentials are discussed on the basis of numerical calculations by the use of Gross-Pitaevskii equation. Condensations with and without vortices are considered in order to make clear spatial distributions. The shape of spatial distribution is essentially dependent on the ratio of interaction strengths between intra-components and inter-components. We emphasize the possibility of coexistence of vortex-free state (where the angular momentum ℓ is 0.) for the one component in BEC and vortex state (ℓ z =1) for another component whose shape is the donut-like spatial distribution. Furthermore, fluctuations of these states are discussed. In partiucular, we concentrate our attention to the appearance of the core modes with ℓ z =0 symmetry for the component with a vortex. In connection with the behavior of the core modes, the contribution of the component without a vortex to the stability of the above vortex is discussed on the basis of numerical calculation.
The vortex density of a rotating superfluid, divided by its particle mass, dictates the superfluid's angular velocity through the Feynman relation. To find how the Feynman relation applies to superfluid mixtures, we investigate a rotating two-component Bose–Einstein condensate, composed of bosons with different masses. We find that in the case of sufficiently strong interspecies attraction, the vortex lattices of the two condensates lock and rotate at the drive frequency, while the superfluids themselves rotate at two different velocities, whose ratio equals the ratio between the particle masses of the two species. In this paper, we characterize the vortex-locked state, establish its regime of stability, and find that it survives within a disk smaller than a critical radius, beyond which vortices become unbound and the two Bose-gas rings rotate together at the frequency of the external drive.
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.