Deterministic Nucleation and Dynamics of Infilled Multiply-Charged Vortices in an Immiscible $^{87}\mathrm{Rb}$-$^{41}\mathrm{K}$ Mixture
We propose a method for controllably generating multiply-charged vortices in immiscible Bose-Einstein condensates. We achieve this by applying a laser stirring technique to a $^{87}\mathrm{Rb}$-$^{41}\mathrm{K}$ mixture, where the vortices generated are infilled by the secondary component. We numerically demonstrate that the charge of the vortex can be tuned reproducibly by varying the stirring parameters, allowing the deterministic generation of stable infilled vortices with high topological charge. We then consider the dynamics of these multiply-charged vortices in a circular trap; in contrast to single-component condensates, we observe long-lived precession of the multiply-charged vortices with a charge dependent frequency and collective breathing modes of the infilling component. For specific large winding numbers, we observe distinct dynamical instabilities leading to vortex dislocation.