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arXiv:cond-mat/9605081

Alkali Bose Condensate Mixtures

Tin-Lun Ho, Vivek B. Shenoy

Published May 13, 1996• 0 citations
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Abstract

We show that binary mixtures of Bose-condensates of alkali atoms have a great variety of ground state and vortex structures which can be accessed experimentally by varying the particle numbers of different alkalis. We have constructed a simple algorithm to determine the density profiles of these states, and have worked out their phase diagrams within Thomas-Fermi approximation. Many structures of the alkali binary contain a coexisting region, which is the analog of the long sought $^{3}$He-$^{4}$He interpenetrating superfluids in ultra-low temperature physics.

DOI
10.48550/arxiv.cond-mat/9605081

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We show that binary mixtures of Bose-condensates of alkali atoms have a great variety of ground state and vortex structures which can be accessed experimentally by varying the particle numbers of different alkalis. We have constructed a simple algorithm to determine the density profiles of these states, and have worked out their phase diagrams within Thomas-Fermi approximation. Many structures of the alkali binary contain a coexisting region, which is the analog of the long sought 3^{3}3He-4^{4}4He interpenetrating superfluids in ultra-low temperature physics.
We show that binary mixtures of Bose condensates of alkali atoms have a great variety of ground state and vortex structures which can be accessed experimentally by varying the particle numbers of different alkalis. We have constructed a simple algorithm to determine the density profiles of the mixtures within Thomas-Fermi approximation. Many structures of the alkali binary contain a coexisting region, which is the analog of the long sought 3He{}^{3}\mathrm{He}3He- 4He{}^{4}\mathrm{He}4He interpenetrating superfluids in ultralow temperature physics.
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.
Experimental realizations of a variety of atomic binary Bose-Fermi mixtures have brought opportunities for studying composite quantum systems with different spin statistics. The binary atomic mixtures can exhibit a structural transition from a mixture into phase separation as the boson-fermion interaction increases. By using a path-integral formalism to evaluate the grand partition function and the thermodynamic grand potential, we obtain the effective potential of binary Bose-Fermi mixtures. Thermodynamic quantities in a broad range of temperatures and interactions are also derived. The structural transition can be identified as a loop of the effective potential curve, and the volume fraction of phase separation can be determined by the lever rule. For $^{6}\mathrm{Li}\ensuremath{-}^{7}\mathrm{Li}$ and $^{6}\mathrm{Li}\ensuremath{-}^{41}\mathrm{K}$ mixtures, we present the phase diagrams of the mixtures in a box potential at zero and finite temperatures. Due to the flexible densities of atomic gases, the construction of phase separation is more complicated when compared to conventional liquid or solid mixtures where the individual densities are fixed. For harmonically trapped mixtures, we use the local density approximation to map out the finite-temperature density profiles and present typical trap structures, including the mixture, partially separated phases, and fully separated phases.
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,
We study a binary mixture of Bose–Einstein condensates, confined in a generic potential, in the Thomas–Fermi approximation. We search for the zero-temperature ground state of the system, both in the case of fixed numbers of particles and fixed chemical potentials. For generic potentials, we analyze the transition from mixed to separated ground-state configurations as the inter-species interaction increases. We derive a simple formula that enables one to determine the location of the domain walls. Finally, we find criteria for the energetic stability of separated configurations, depending on the number and the position of the domain walls separating the two species.
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)].