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arXiv:1510.00139 · Physical Review A

Short-range intervortex interaction and interacting dynamics of half-quantized vortices in two-component Bose-Einstein condensates

Kenichi Kasamatsu, Minoru Eto, Muneto Nitta

Published Jan 19, 2016• 48 citations
arXivHTMLPDF

Abstract

We study the interaction and dynamics of two half-quantized vortices in two-component Bose-Einstein condensates. Using the Pad\'e approximation for the vortex core profile, we calculate the intervortex potential, whose asymptotic form for a large distance has been derived by Eto et al. [Phys. Rev. A 83, 063603 (2011)]. Through numerical simulations of the two-dimensional Gross-Pitaevskii equations, we reveal different kinds of dynamical trajectories of the vortices depending on the combinations of signs of circulations and the intercomponent density coupling. Under the adiabatic limit, we derive the equations of motion for the vortex coordinates, in which the motion is caused by the balance between Magnus force and the intervortex forces. The initial velocity of the vortex motion can be explained quantitatively by this point vortex approximation, but understanding the long-time behavior of the dynamics needs more consideration beyond our model.

DOI
10.1103/physreva.93.013615

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We study the interaction and dynamics of two half-quantized vortices in two-component Bose-Einstein condensates. Using the Pad'e approximation for the vortex core profile, we calculate the intervortex potential, whose asymptotic form for a large distance has been derived by Eto et al. [Phys. Rev. A 83, 063603 (2011)]. Through numerical simulations of the two-dimensional Gross-Pitaevskii equations, we reveal different kinds of dynamical trajectories of the vortices depending on the combinations of signs of circulations and the intercomponent density coupling. Under the adiabatic limit, we derive the equations of motion for the vortex coordinates, in which the motion is caused by the balance between Magnus force and the intervortex forces. The initial velocity of the vortex motion can be explained quantitatively by this point vortex approximation, but understanding the long-time behavior of the dynamics needs more consideration beyond our model.
We study the asymptotic interaction between two half-quantized vortices in two-component Bose-Einstein condensates. When two vortices in different components are placed at distance 2R2R2R, the leading order of the force between them is found to be $(\mathrm{ln}R/\ensuremath{\xi}\ensuremath{-}1/2)/{R}^{3}$, in contrast to 1/R1/R1/R between vortices placed in the same component. We derive it analytically using the Abrikosov ansatz and the profile functions of the vortices, confirmed numerically with the Gross-Pitaevskii model. We also find that the short-range cutoff of the intervortex potential linearly depends on the healing length.
We investigate the interaction and dynamics of vortices belonging to different components of a binary uniform quantum liquid. Using the coupled extended Gross-Pitaevskii equations with logarithmic beyond-mean-field corrections, we derive the asymptotic interaction potential between well-separated vortices. The interaction potential retains the asymptotic form s−2s^{-2}s−2 as a function of the intervortex distance s, but its coefficient depends on the background density through the quantum fluctuation. As a result, the interaction between vortices changes from attractive to repulsive at a critical density. Real-time simulations demonstrate a corresponding reversal of orbital motion of a vortex pair from clockwise to counterclockwise, consistent with their Magnus response.
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.
The dynamics of quantized vortices in two-dimensional two-component miscible Bose-Einstein condensates trapped by a box potential has been numerically studied using the Gross-Pitaevskii model. We have discovered a phenomenon where the vortices of the two components spatially separate from each other, which we call the phase separation of the distribution of vortices. This phase separation occurs when the intercomponent coupling is strong. Onsager vortices, on the other hand, are formed in both components when the intercomponent coupling is weak. We distinguish between Onsager vortices and phase-separated vortices by two types of effective distances between vortices. The dependence of the transition between the Onsager vortices and phase-separated vortices on the intercomponent interaction is also studied.
The dynamics and interaction of quantized vortices in Bose-Einstein condensates (BECs) are investigated by using the two-dimensional Gross-Pitaevskii equation (GPE) with/without an angular momentum rotation term. If all vortices have the same winding number, they would rotate around the trap center but never collide. In contrast, if the winding numbers are different, their interaction highly depends on the initial distance between vortex centers. The analytical results are presented to describe the dynamics of the vortex centers when β=0. While if β≠0, there is no analytical result but some conclusive numerical findings are provided for the further understanding of vortex interaction in BECs. Finally, the dynamic laws describing the relation of vortex interaction in nonrotating and rotating BECs are presented.
The dynamics of a phase-separated two-component Bose-Einstein condensate are investigated, in which a bubble of one component moves through the other component. Numerical simulations of the Gross-Pitaevskii equation reveal a variety of dynamics associated with the creation of quantized vortices. In two dimensions, a circular bubble deforms into an ellipse and splits into fragments with vortices, which undergo the Magnus effect. The B\'enard--von K\'arm\'an vortex street is also generated. In three dimensions, a spherical bubble deforms into toruses with vortex rings. When two rings are formed, they exhibit leapfrogging dynamics.