Dynamics and Interaction of Vortex Lines in an Elongated Bose-Einstein Condensate

We study the real-time dynamics of vortices in a large elongated Bose-Einstein condensate (BEC) of sodium atoms using a stroboscopic technique. Vortices are produced via the Kibble-Zurek mechanism in a quench across the BEC transition and they slowly precess keeping their orientation perpendicular to the long axis of the trap as expected for solitonic vortices in a highly anisotropic condensate. Good agreement with theoretical predictions is found for the precession period as a function of the orbit amplitude and the number of condensed atoms. In configurations with two or more vortices, we see signatures of vortex-vortex interaction in the shape and visibility of the orbits. In addition, when more than two vortices are present, their decay is faster than the thermal decay observed for one or two vortices. The possible role of vortex reconnection processes is discussed.

Figure 1

(a)–(c) Sequences of 20 images of the density distribution of the atoms extracted from three BECs; frames are taken every $\mathrm{\Delta }t=84\mathrm{ms}$, each after a 13 ms expansion. (a) Static vortex. (b),(c) Vortices precessing with different amplitudes. Each vortex is randomly oriented in the $xy$ plane and, after expansion, it forms a planar density depletion [23] which is visible as a stripe. (d)–(i) Sequences with two and three vortices, with $\mathrm{\Delta }t=28\mathrm{ms}$; here frames are not to scale and vertically squeezed to enhance visibility. (j)–(m) Destructive absorption images of the whole BEC taken along the axial direction $z$ after 120 ms of expansion, showing (j) a single vortex filament crossing the condensate from side to side and (k)–(m) two vortices with different relative orientation and shape. All images show the residuals after subtracting the fitting TF profile.

Figure 2

(a),(b) Vortex axial position after expansion for the condensates in Figs. 1 and 1. (c),(d) Instantaneous period normalized to the trapping period $T_z=77\mathrm{ms}$ (points) obtained by fitting the above oscillations; the solid line is the theoretical prediction (1) for the measured atom number $N(t)$ and its 20% uncertainty (grey region); the dashed line is the prediction for a dark or grey soliton. (e) BEC atom number, with (green) and without (grey) the extraction sequence. (f) Period $T$ extracted from the vortex position in the first frames in units of $T_z$ as a function of $r_{\mathrm{o}}^2$; the solid line represents the predicted $(1-r_{\mathrm{o}}^2)$ behavior, with no free parameters. (g) Probability density of the measured period $T_0$ vs the theoretical one $T_{\text{th}}$ in the same conditions. Red (blue) bars refer to 30 (27) cases with a single vortex (two vortices), all of them with the same $N$ within a 20% uncertainty.

Figure 3

Average vortex number $⟨N_V⟩$ remaining in a condensate at time $t$ starting from configurations with $N_V=1$ (circles), 2 (triangles), and 3 (diamonds) at $t=0$. Solid lines are exponential fits.

Figure 4

Vortex axial position in BECs. (a) Two vortices with no apparent interaction. (b) Two crossing vortices change their visibility and experience a phase shift in their trajectory. (c) Two vortices becoming hardly visible after crossing. (d) Two vortices oscillating with unperturbed trajectories while a third one disappears. (a)–(d) correspond to the data in Figs. 1, respectively. Solid and empty symbols are used to distinguish high and low density contrast, respectively.