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arXiv:cond-mat/0111108 · Physical Review A

Vortex-vortex interaction in two-component Bose-Einstein condensates

Patrik Öhberg, Luis Santos

Published Jul 30, 2002• 10 citations
arXivHTMLPDF

Abstract

The vortex-vortex interaction in two-component Bose-Einstein condensates is shown to present characteristic effects not possible in single-component condensates. In particular, vortices in different components undergo separate, but concentric, orbits for both the same and opposite circulation. In addition, contrary to the well-known behavior in single-component condensates, vortices with the same circulation created in the less dense component merge in the presence of dissipation, allowing for the creation of metastable vortices with more than one quantum of circulation.

DOI
10.1103/physreva.66.013616

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The vortex-vortex interaction in two-component Bose-Einstein condensates is shown to present characteristic effects not possible in single-component condensates. In particular, vortices in different components undergo separate, but concentric, orbits for both the same and opposite circulation. In addition, contrary to the well-known behavior in single-component condensates, vortices with the same circulation created in the less dense component merge in the presence of dissipation, allowing for the creation of metastable vortices with more than one quantum of circulation.
The vortex structure in a space-homogeneous Bose-Einstein condensate of two particle species with different masses has been studied. It is shown that the vortex structure in the two-component condensate is described by three dimensionless parameters, which define the system. That is different from the usual one-component condensate, where the vortex is described by a parameter-less dimensionless equation with a fixed structure. A few types of vortices with different qualitative structure are explored. In particular, it is shown, that the vortex structure strongly depends on the sign of “interaction” constant of the components. There can exist the super-density vortices, when the “interaction” constant is positive. These vortices have the near-axis density greater than the equilibrium density of a homogeneous space Bose-Einstein condensate. We show that there can exist the vortices with opposite direction of the condensate rotation near the axis and far off the axis.
Abstract In contrast to one-component Bose-Einstein condensate case, the vortices in two-component condensate can have various complicated structures. The vortices in a space-homogeneous Bose-Einstein condensate have been studied in this paper. It is shown that the vortex structure is described by three dimensionless parameters. This is totally different from the usual one-component condensate case,where an isolated vortex is described by a parameterless dimensionless equation. The two-component vortex structure strongly depends on the sign of “interaction” constant of the components. A few types of vortices with different qualitative structure are explored. We show that the “super-density vortices” can exist, when the “interaction” constant is positive. The “super-density vortices” have the near-axis density greater than the equilibrium density of a homogeneous space Bose-Einstein condensate. We also show that the vortices with opposite direction of the condensate component rotation near the axis and far off the axis can exist.
We numerically study the dynamics of quantized vortices in two-dimensional two-component Bose-Einstein condensates (BECs) trapped by a box potential. For one-component BECs in a box potential, it is known that quantized vortices form Onsager vortices, which are clusters of same-sign vortices. We confirm that the vortices of the two components spatially separate from each other-even for miscible two-component BECs-suppressing the formation of Onsager vortices. This phenomenon is caused by the repulsive interaction between vortices belonging to different components, hence, suggesting a new possibility for vortex phase separation.
Static and dynamic properties of vortices in a two-component Bose-Einstein condensate with Rashba spin-orbit coupling are investigated. The mass current around a vortex core in the plane-wave phase is found to be deformed by the spin-orbit coupling, and this makes the dynamics of the vortex pairs quite different from those in a scalar Bose-Einstein condensate. The velocity of a vortex-antivortex pair is much smaller than that without spin-orbit coupling, and there exist stationary states. Two vortices with the same circulation move away from each other or unite to form a stationary state.
Counter-rotating vortices in miscible two-component Bose-Einstein condensates, in which superflows counter-rotate between the two components around the overlapped vortex cores, are studied theoretically in a pancake-shaped potential. In a linear stability analysis with the Bogoliubov--de Gennes model, we show that counter-rotating vortices are dynamically unstable against splitting into multiple vortices. The instability shows characteristic behaviors as a result of counter-superflow instability, which causes relaxation of relative flows between the two components in binary condensates. The characteristic behaviors are completely different from those of multiquantum vortices in single-component Bose-Einstein condensates; the number of vortices generated by the instability can become larger than the initial winding number of the counter-rotating vortex. We also investigate the nonlinear dynamics of the instability by numerically solving the Gross-Pitaevskii equations. The nonlinear dynamics drastically changes when the winding number of counter-rotating vortices becomes larger, which lead to nucleation of vortex pairs outside of the vortex core. The instability eventually develops into turbulence after the relaxation of the relative rotation between the two components.
This study aims to research on dynamics of two quantized vortices in miscible two-component Bose--Einstein condensates, trapped by a circular box potential by using the Gross--Pitaevskii equation. We consider a situation in which two vortices belong to different components and they are initially close. Their dynamics are significantly different from those of a vortex pair in a single-component condensate. When two vortices are initially co-located, they are split by dynamical instability or remain co-located depending on their intercomponent interaction. If the two split vortices have the same sign of circulation, they rotate around each other. Then, the angular velocity can be given as a function of the distance between two vortices, which is understood through the equations of motion and their interaction. If the circulations of two close vortices have different signs, however, they move in the same direction initially, then overlap during the dynamics. This subsequent overlap can be categorized into two types based on the initial distance between them. The mechanism of this overlapping can be understood from the interaction between the vortex and its image vortex, which makes the two vortices close to each other even if the intrinsic interaction between them is repulsive.