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arXiv:2105.02452 · Physical Review A

Annihilation and recurrence of vortex-antivortex pairs in two-component Bose-Einstein condensates

Junsik Han, Makoto Tsubota

Published May 17, 2021• 2 citations
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Abstract

The annihilation of vortex-antivortex pairs is a key event in two-dimensional Bose-Einstein condensates (BECs). It is known that dissipation or a catalyst vortex is required for the annihilation of the pairs in one-component BECs. We numerically confirmed in two-component BECs that the pairs can be annihilated even without any dissipation or catalyst vortices when the intercomponent interaction is strong. In addition, the pair is recreated alternately in two components under certain conditions, which we call the recurrence.

DOI
10.1103/physreva.103.053313

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The annihilation of vortex-antivortex pairs is a key event in two-dimensional Bose-Einstein condensates (BECs). It is known that dissipation or a catalyst vortex is required for the annihilation of the pairs in one-component BECs. We numerically confirmed in two-component BECs that the pairs can be annihilated even without any dissipation or catalyst vortices when the intercomponent interaction is strong. In addition, the pair is recreated alternately in two components under certain conditions, which we call the recurrence.
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Understanding the elementary mechanism for the dissipation of vortex energy in quantum liquids is one central issue in quantum hydrodynamics, such as quantum turbulence in systems ranging from neutron stars to atomic condensates. In a two-dimensional (2D) Bose-Einstein condensate (BEC) at zero temperature, in addition to the vortex drift-out process from the boundary, a vortex-antivortex pair can annihilate in bulk, but controversy remains on the number of vortices involved in the annihilation process. We find that a dynamic crossover exists from four-body to three-body vortex annihilation processes with time evolution in decaying 2D quantum turbulence of a boundary-less uniform quasi-2D BEC. Such a dynamical crossover depends on the initial vortex pair density and occurs when the sound waves generated in the vortex annihilation process surpass a threshold energy. As the confinement along the third direction is relaxed in a quasi-2D BEC, the threshold sound wave energy decreases due to the three-dimensional (3D) vortex line curve and reconnection, shifting the dynamical crossover to the early time. Our work reveals an elementary mechanism for the dissipation of vortex energy that may help understand exotic matter and dynamics in quantum liquids.
We numerically simulate the free decay of two-dimensional quantum turbulence in a large, homogeneous Bose-Einstein condensate. The large number of vortices, the uniformity of the density profile, and the absence of boundaries (where vortices can drift out of the condensate) isolate the annihilation of vortex-antivortex pairs as the only mechanism which reduces the number of vortices, Nv, during the turbulence decay. The results clearly reveal that vortex annihilation is a four-vortex process, confirming the decay law Nv ∼ t−1/3 where t is time, which was inferred from experiments with relatively few vortices in small harmonically trapped condensates.