Flows with fractional quantum circulation in Bose-Einstein condensates induced by nontopological phase defects

It is a common view that rotational motion in a superfluid can exist only in the presence of topological defects, i.e., quantized vortices. However, in our numerical studies on the merging of two concentric Bose-Einstein condensates with axial symmetry in two-dimensional space, we observe the emergence of a spiral dark soliton when one condensate has a nonzero initial angular momentum. This spiral dark soliton enables the transfer of angular momentum between the condensates and allows the merged condensate to rotate even in the absence of quantized vortices. Our examination of the flow field around the soliton strikingly reveals that its sharp endpoint can induce flow like a vortex point but with a fraction of a quantized circulation. This interesting nontopological “phase defect” may generate broad interest since rotational motion is essential in many quantum transport processes.

Figure 1

(a) Schematic of the potential $\tilde{V}(\tilde{\mathbf{r}},\tilde{t})$ used in the GPE simulation. (b) The initial configurations of the Bose-Einstein condensates.

Figure 2

Case 1 representative snapshots showing the time evolution of the BEC density, phase, and angular momentum density ${\tilde{L}}_z$. The “+” and “$-$” signs indicate the locations of the positive and negative vortex points.

Figure 3

Case 2 representative snapshots showing the time evolution of the BEC density, phase, and angular momentum density ${\tilde{L}}_z$. The “+” and “$-$” signs indicate the locations of the positive and negative vortex points.

Figure 4

(a) The time evolution of the integrated angular momentum for case 2. (b) Schematic diagrams showing how the sharp endpoint of a dark soliton stripe can induce rotational motion in a condensate and how such motion bends the soliton stripe. (c) Schematics illustrating the mass and angular momentum transfer in case 2.

Figure 5

Variation of the calculated vortex charge number $Z$ in the condensate along the solid yellow lines that are shown in the inset.