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Physica Scripta

Oblique collisions and catching-up phenomena of vortex dipoles in a uniform Bose–Einstein condensate

Guoquan Yang, Suying Zhang, Wei Han

Published Mar 21, 2019• 5 citations
Publisher

Abstract

Abstract We investigate the collisional dynamics of two vortex dipoles in a uniform two-dimensional Bose–Einstein condensate. It is found that the dynamics are deeply related to the moving directions and sizes of the initial vortex dipoles. For the oblique collisions of two vortex dipoles with the same size, we find that the vortices in the two initial vortex dipoles recombine into two new vortex dipoles which scatter in the opposite directions. For the catching-up processes of two vortex dipoles with different size, we find that the faster vortex dipole speeds up and passes through the slower vortex dipole. If the size of the vortex dipoles are small, we also observe vortex annihilation and vortex resurrection. The corresponding parameter ranges of different collisional dynamics are discussed.

DOI
10.1088/1402-4896/ab1220

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Abstract We investigate the collisional dynamics of two vortex dipoles in a uniform two-dimensional Bose–Einstein condensate. It is found that the dynamics are deeply related to the moving directions and sizes of the initial vortex dipoles. For the oblique collisions of two vortex dipoles with the same size, we find that the vortices in the two initial vortex dipoles recombine into two new vortex dipoles which scatter in the opposite directions. For the catching-up processes of two vortex dipoles with different size, we find that the faster vortex dipole speeds up and passes through the slower vortex dipole. If the size of the vortex dipoles are small, we also observe vortex annihilation and vortex resurrection. The corresponding parameter ranges of different collisional dynamics are discussed.
Abstract Understanding how two vortex dipoles interact with each other microscopically is helpful for understanding the dynamics of quantum turbulence in a two-dimensional Bose–Einstein condensate (BEC). We investigate the collision of two vortex dipoles propagating in opposite directions along parallel lines by numerically solving the two-dimensional Gross–Pitaevskii equation. By varying the impact parameter, we identify three general dynamical modes of the vortex dipoles in a homogeneous BEC, which are the vortex recombination mode, the encircling mode and the flyby mode. The existence of these three modes has been corroborated by numerical computations of the ordinary differential equations describing the vortex interactions. Furthermore, we show the corresponding parameter ranges for these modes.
Dynamics of vortex clusters is essential for understanding diverse superfluid phenomena. In this paper, we examine the dynamics of vortex quadrupoles in a trapped two-dimensional (2D) Bose-Einstein condensate. We find that the movement of these vortex-clusters fall into three distinct regimes which are fully described by the radial positions of the vortices in a 2D isotropic harmonic trap, or by the major radius (minor radius) of the elliptical equipotential lines decided by the vortex positions in a 2D anisotropic harmonic trap. In the "recombination" and "exchange" regimes the quadrupole structure maintains, while the vortices annihilate each other permanently in the "annihilation" regime. We find that the mechanism of the charge flipping in the "exchange" regime and the disappearance of the quadrupole structure in the "annihilation" regime are both through an intermediate state where two vortex dipoles connected through a soliton ring. We give the parameter ranges for these three regimes in coordinate space for a specific initial configuration and phase diagram of the vortex positions with respect to the Thomas-Fermi radius of the condensate. We show that the results are also applicable to systems with quantum fluctuations for the short-time evolution.
The static and dynamic properties of vortices in dipolar Bose-Einstein condensates (dBECs) can be considerably modified relative to their nondipolar counterparts by the anisotropic and long-ranged nature of the dipole-dipole interaction. Working in a uniform dBEC, we analyze the structure of single vortices and the dynamics of vortex pairs, investigating the deviations from the nondipolar paradigm. For a straight vortex line, we find that the induced dipolar interaction potential is axially anisotropic when the dipole moments have a nonzero projection orthogonal to the vortex line. This results in a corresponding elongation of the vortex core along this projection as well as an anisotropic superfluid phase and enhanced compressibility in the vicinity of the vortex core. Consequently, the trajectories of like-signed vortex pairs are described by a family of elliptical and oval-like curves rather than the familiar circular orbits. Similarly for opposite-signed vortex pairs their translation speeds along the binormal are found to be dipole-interaction dependent. We expect that these findings will shed light on the underlying mechanisms of many-vortex phenomena in dBECs such as quantum turbulence, vortex reconnections, and vortex lattices.
We study the dynamics of vortices in ideal and weakly interacting Bose-Einstein condensates using a Ritz minimization method to solve the two-dimensional Gross-Pitaevskii equation. For different initial vortex configurations we calculate the trajectories of the vortices. We find conditions under which a vortex-antivortex pair annihilates and is created again. For the case of three vortices we show that at certain times two additional vortices may be created, which move through the condensate and annihilate each other again. For a noninteracting condensate this process is periodic, whereas for small interactions the essential features persist, but the periodicity is lost. The results are compared to exact numerical solutions of the Gross-Pitaevskii equation confirming our analytical findings.
The static and dynamic properties of vortices in dipolar Bose-Einstein condensates (dBECs) can be considerably modified relative to their nondipolar counterparts by the anisotropic and long-ranged nature of the dipole-dipole interaction. Working in a uniform dBEC, we analyze the structure of single vortices and the dynamics of vortex pairs, investigating the deviations from the nondipolar paradigm. For a straight vortex line, we find that the induced dipolar interaction potential is axially anisotropic when the dipole moments have a nonzero projection orthogonal to the vortex line. This results in a corresponding elongation of the vortex core along this projection as well as an anisotropic superfluid phase and enhanced compressibility in the vicinity of the vortex core. Consequently, the trajectories of like-signed vortex pairs are described by a family of elliptical and oval-like curves rather than the familiar circular orbits. Similarly for opposite-signed vortex pairs their translation speeds along the binormal are found to be dipole-interaction dependent. We expect that these findings will shed light on the underlying mechanisms of many-vortex phenomena in dBECs such as quantum turbulence, vortex reconnections, and vortex lattices. Published by the American Physical Society 2024