Skyrmion-antiskyrmion pairs in ultracold atomic gases

We study theoretically the dynamics of two-component Bose-Einstein condensates in two dimensions, which admit topological excitations related to the skyrmions of nuclear physics. We investigate a branch of uniformly propagating solitary waves, which, at high momentum, can be viewed as skyrmion-antiskyrmion pairs. We study these solitary waves for a range of interaction regimes and show that, for experimentally relevant cases, there is a transition to spatially extended spin-wave states at low momentum. We explain how this can be understood by analogy to the two-dimensional ferromagnet. Finally, we discuss how such solitary waves can be generated and studied in experiment.

Figure 1

The energy dispersion of a two-component condensate for $\eta =0.015$ and 0.030 and ${\mathrm{c̃}}_2=0$. The energy for a system of free spin waves [Eq. (11)] is shown for comparison in the limit of an infinite system $\eta \to 0$.

Figure 2

The local spin vector $\mathrm{\ell ⃗}(\mathit{r})$ projected onto the $\mathit{xy}$ plane, and contours of the typical particle density in component 2 for $\eta =0.015$ and (a) $p=4.0$ and (b) $p=8.5$. For clarity, one spin in five is plotted. The direction of the velocity $\mathit{v}$ and momentum $\mathit{P}$ of the solitary wave is indicated.

Figure 3

The energy dispersion of a two-component condensate for ${\mathrm{c̃}}_2=-2.0$, 0.0, and 2.0 for $\eta =0.015$. Energy is measured relative to the uniform system $\chi ={\chi }_{\infty }$. The value ${\mathrm{c̃}}_2=-2.0$ is below ${\mathrm{c̃}}_2^{*}=-1.5$, and so solitary waves exist at all momenta $p$ for $\eta \to 0$. Inset: Enlargement of the bifurcation region for ${\mathrm{c̃}}_2=2.0$, within which we find two branches of excitations for the same momenta.