Vortex force in compressible spin-orbit-coupled Bose-Einstein condensates

Using a (1+2)-dimensional boson-vortex duality between nonlinear electrodynamics and a two-component compressible Bose-Einstein condensate with spin-orbit (SO) coupling, we obtain hydrodynamic continuity and Euler equations where the phase defect and nondefect degrees of freedom enter separately, and a separate equation encompassing quantization of circulation. We obtain the generalized force on vortices under SO coupling, and associate the linear confinement of vortices due to SO coupling with instanton fluctuations of the dual theory.

Figure 1

The attractive force between a pair of opposite vortices along the $x$ axis induced by a small spin-orbit coupling (we ignore terms of order $k_0^3$ and higher). The vortex separation is $d$, the radial system size is $\mathrm{\Lambda }$, and we have set $\hslash \mathrm{\Omega }B/\left(cm\right)=1$. The force decreases rapidly when the vortices approach the cloud edge ($d/\mathrm{\Lambda }\approx 2$).