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arXiv:cond-mat/0203060 · Journal of Experimental and Theoretical Physics Letters

Phase separation and vortex states in binary mixture of Bose-Einstein condensates in trapping potentials with displaced centers

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

Published Mar 1, 2002• 12 citations
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Abstract

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.

DOI
10.1134/1.1478520

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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.
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.
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 the stability of vortices in a binary system of Bose-Einstein condensat es, with their wave functions modeled by a set of coupled, time-dependent Gross-Pitaevskii equations. Beginning with an effective two-dimensional system, we identify miscible and immiscible regimes characterized by the inter- and intra-atomic interactions and the initial configuration of the system. We then consider a binary system of Bose-Einstein condensates placed in a rotating harmonic trap and study the single united vortex state in this system. We derive an approximate form for the energy of a single united vortex in the binary system and the critical angular velocity for the global stability of a vortex at the center of the trap. We also compute the metastability onset angular velocity for the local stability of a vortex at the center of the trap. Numerical solutions to the Gross-Pitaevskii equations support these expressions. These rotational results inform us of a novel bimodal formation within the miscible regime of the binary condensate system. We thus demonstrate the nontrivial aspects of vortex stability in interacting binary Bose-Einstein condensates as a result of their nonlinear interactions.
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.
We study the creation of vortex states in a trapped Bose-Einstein condensate by a rotating force. For a harmonic trapping potential the rotating force induces only a circular motion of the whole condensate around the trap center which does not depend on the interatomic interaction. For the creation of a pure vortex state it is necessary to confine the atoms in an anharmonic trapping potential. The efficiency of the creation can be greatly enhanced by a sinusoidal variation of the force's angular velocity. We present analytical and numerical calculations for the case of a quartic trapping potential. The physical mechanism behind the requirement of an anharmonic trapping potential for the creation of pure vortex states is explained.