Guiding-center dynamics of vortex dipoles in Bose-Einstein condensates

A quantized vortex dipole is the simplest vortex molecule, comprising two countercirculating vortex lines in a superfluid. Although vortex dipoles are endemic in two-dimensional superfluids, the precise details of their dynamics have remained largely unexplored. We present here several striking observations of vortex dipoles in dilute-gas Bose-Einstein condensates, and develop a vortex-particle model that generates vortex line trajectories that are in good agreement with the experimental data. Interestingly, these diverse trajectories exhibit essentially identical quasiperiodic behavior, in which the vortex lines undergo stable epicyclic orbits.

Figure 1

Symmetric vortex configuration. (a) Experimental images of the atomic density (optical depth), 1% extraction. (b) Polar plot of the experimental data (triangles) and the theoretical prediction from Eq. (2) (solid line). The colored circles correspond to the calculated vortex coordinates at the same times as the experimental data. Downward (upward) triangles indicate configurations in which a surface fit to the images in (a) succeeded (failed) to distinguish the vortices. Only the inner region of the condensate is shown.

Figure 2

Asymmetric vortex configurations. [(a)–(c)] Experimental images of the atomic density overlaid with calculated vortex positions from the model, Eq. (2) (colored rings). The images in (c) originally appeared in Ref. [11]. [(d)–(f)] Trajectories for the data in panels (a)–(c), using the notation of Fig. 1. [(g)–(i)] Trajectories for the data in panels (d)–(f) in the indicated rotating frames. In (a) and (b) the extracted fraction is 1%, whereas in (c) it is 5% and the image intensity is scaled by a factor of 2.