Suppressed Solitonic Cascade in Spin-Imbalanced Superfluid Fermi Gas

Cold atoms experiments offer invaluable information on superfluid dynamics, including decay cascades of topological defects. While the cascade properties are well established for Bose systems, our understanding of their behavior in Fermi counterparts is very limited, in particular in spin-imbalanced systems, where superfluid (paired) and normal (unpaired) particles naturally coexist giving rise to complex spatial structure of the atomic cloud. Here we show, based on a newly developed microscopic approach, that the decay cascades of topological defects are dramatically modified by the spin polarization. We demonstrate that decay cascades end up at different stages: “dark soliton,” “vortex ring,” or “vortex line,” depending on the polarization. We reveal that it is caused by sucking of unpaired particles into the soliton’s internal structure. As a consequence vortex reconnections are hindered and we anticipate that quantum turbulence phenomenon can be significantly affected, indicating new physics induced by polarization effects.

Figure 1

(a) Time evolution of the ultracold atomic cloud after the phase imprint measured by the MIT experiment [30]. In the right column, a reconstructed spatial structure of a topological defect from the tomographic images is displayed. The figure has been reprinted with permission from Ref. [30]. Copyright 2016 American Physical Society. (b) Selected frames from numerical simulation by TDASLDA showing consecutive stages of the solitonic cascade. Blue surfaces indicate topology of the order parameter $\mathrm{\Delta }(\mathit{r})$. By arrows we demonstrate that the numerical simulation provides the same time evolution of the system as seen in the experiment. For a full movie see the Supplemental Material [20]. (c) Internal structures of the stages containing quantized vortices. The three frames contain, respectively, $\mathrm{\Phi }$ soliton, deformed vortex ring, and vortex line. Arrows indicate the gas circulation in the vicinity of the topological defects.

Figure 2

(a) Selected stages of the solitonic cascade in a spin-imbalanced cloud of atoms. Number of atoms is $N_{\uparrow }=304$ and $N_{\downarrow }=202$, which corresponds to the total polarization $P=20\%$. Blue contours show profile of the order parameter and define the volume where the condensate of Copper pairs resides. Regions containing topological defects are highlighted in red. Two contours around the condensate indicate places where density of spin-down (internal contour) and spin-up (external contour) decreases by 90% with respect to the value at the center of the cloud. Between them highly polarized gas in a normal state exists. See the Supplemental Material [20] for a full movie. (b) Final states of the cascade as a function of the cloud polarization $P$. Red contour indicates the topology of nodal plane of the order parameter. Slice of the cloud presents local polarization of the medium $p(\mathit{r})=\mathbf{(}{n}_{\uparrow }(\mathit{r})-n_{\downarrow }(\mathit{r})\mathbf{)}/\mathbf{(}{n}_{\uparrow }(\mathit{r})+n_{\downarrow }(\mathit{r})\mathbf{)}$ in the vicinity of the topological defect. Two black contours indicate shell of the normal component, as defined above. Its thickness becomes wider as we increase the spin imbalance of the cloud.

Figure 3

(a) Sketch of the imprinting potential for vortex reconnection studies. (b) Consecutive stages of the time evolution of a pair of vortex lines for unpolarized $P=0\%$ (top row) and polarized $P=20\%$ (bottom row) cases. Meaning of surfaces is the same as in Fig. 2.