Figure 1

Evolution of a sinusoidally perturbed vortex-antivortex dipole. (a) The superflow around the vortices is denoted by the circulation vectors ${\kappa }_{\pm }$ and the oriented circles on top of the subfigure indicate the rotational motion of vortex line elements in the direction opposite to the circulating superflow. The pair translates in the $y$ direction shown by the arrow, due to the mutual induction field. (b) The amplitude of the instability grows. (c) Vortex reconnections occur at locations where vortices come in contact with each other. (d) The initial vortex pair has broken into a sequence of vortex loops. (e) Side view of frame (d). The projection of the vortex lines on the $z=-2d$ plane are shown on the bottom of each subfigure (a–d) which are plotted, respectively, for times $t/t_0=$0.02, 0.04, 0.05, and 0.06, where the unit of time $t_0=4m{d}^2/\hslash$. Parameters described in the text are $\epsilon =d/200$ and $k=5/d$.Reuse & Permissions

Figure 2

Crow instability of an elongated vortex dipole in a harmonically trapped Bose-Einstein condensate for $d=26{\xi }_0$. (a) Kelvin waves are being generated at the ends of the dipole. (b) Two vortex loops have been pinched off, one from each end of the dipole. (c) Five daughter vortex loops have been produced through reconnection events. (d) The five vortex loops have expanded in diameter appearing as ten vortex lines. The vorticity axis is now aligned along the $x$ axis. (e) A snapshot from a simulation using $d=5{\xi }_0$. The $x\times y\times z$ dimensions of each rectangular box are $10a_0\times 10a_0\times 60a_0$ and the times of the snapshots are marked in the frames.Reuse & Permissions

Figure 3

Vortex dipole creation and instability in a harmonically trapped Bose-Einstein condensate. (a) A laser beam shown in green translates in the $y$ direction. (b) Vortex dipole has formed in the wake of the laser spoon. (c) Decay of the dipole has begun. (d) Five daughter loops have been created. (e) Daughter vortex loops have been relinked in further reconnections. (f) A snapshot with two vortex rings. (g) Initial vortex dipole has disintegrated creating sound waves seen as ripples on the condensate surface. The $x\times y\times z$ dimensions of each rectangular box are $10a_0\times 10a_0\times 60a_0$ and the times of the snapshots are marked in the frames.Reuse & Permissions