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arXiv:1804.06970 · Journal of the Physical Society of Japan

Onsager Vortex Formation in Two-component Bose–Einstein Condensates

Junsik Han, Makoto Tsubota

Published May 15, 2018• 9 citations
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Abstract

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.

DOI
10.7566/jpsj.87.063601

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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.
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.
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.
We study computationally dynamics of quantized vortices in two-dimensional superfluid Bose-Einstein condensates confined in highly oblate power-law traps. We have found that the formation of large-scale Onsager vortex clusters prevalent in steep-walled traps is suppressed in condensates confined by harmonic potentials. However, the shape of the trapping potential does not appear to adversely affect the evaporative heating efficiency of the vortex gas. Instead, the suppression of Onsager vortex formation in harmonic traps can be understood in terms of the energy of the vortex configurations. Furthermore, we find that the vortex-antivortex pair annihilation that underpins the vortex evaporative heating mechanism requires the interaction of at least three vortices. We conclude that experimental observation of Onsager vortices should be the most apparent in flat or inverted-bottom traps.
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.
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.