Stable multiple vortices in collisionally inhomogeneous attractive Bose-Einstein condensates

We study the stability of solitary vortices in a two-dimensional trapped Bose-Einstein condensate (BEC) with a spatially localized region of self-attraction. Solving the respective Bogoliubov--de Gennes equations and running direct simulations of the underlying Gross-Pitaevskii equation reveals that vortices with a topological charge up to $S=6$ (at least) are stable above a critical value of the chemical potential (i.e., below a critical number of atoms, which sharply increases with $S$). The largest nonlinearity-localization radius admitting stabilization of higher-order vortices is estimated analytically and accurately identified in numerical form. To the best of our knowledge, this is the first example of a setting which gives rise to stable higher-order vortices, $Sg1$, in a trapped self-attractive BEC. The same setting may be realized in nonlinear optics too.