Core filling and snaking instability of dark solitons in spin-imbalanced superfluid Fermi gases

We use the time-dependent Bogoliubov–de Gennes equations to study dark solitons in three-dimensional spin-imbalanced superfluid Fermi gases. We explore how the shape and dynamics of dark solitons are altered by the presence of excess unpaired spins which fill their low-density core. The unpaired particles broaden the solitons and suppress the transverse snake instability. We discuss ways of observing these phenomena in cold-atom experiments.

Figure 1

Density profiles of a dark soliton at different relative spin imbalances $n_I=0,0.15,0.33$ [Eq. (8)]. The solid blue curves show the total density $n_{\uparrow }+n_{\downarrow }$ and the dashed orange curves show the density difference $n_{\uparrow }-n_{\downarrow }$. The densities are plotted as a function of $x$ after integrating over the $y$ and $z$ directions and normalizing by the asymptotic density $n_o$.

Figure 2

Dynamics of the snaking instability of dark solitons in the presence of excess spins. Dark colors are regions of small $\left|\mathrm{\Delta }(x,y,z=0)\right|/{\mathrm{\Delta }}_o$, where ${\mathrm{\Delta }}_o$ is the value of $\mathrm{\Delta }$ far from the soliton core at time $t=0$. The relative spin imbalances $n_I$ at the core of the soliton [Eq. (8)] are $n_I=0,0.18,0.40$ for columns (a)–(c), respectively. The transverse length is $L_{\perp }{k}_F\approx 18$.

Figure 3

Time scale $\tau$ for the decay of a dark soliton via a transverse snaking instability as a function of the relative spin imbalance $n_I$ [Eq. (8)] at the core of the soliton. The different colors and shapes represent different transverse lengths $L_{\perp }$. The dashed curves show guides for the eye.