Bifurcations, stability, and dynamics of multiple matter-wave vortex states

Abstract

In the present work, we offer a unifying perspective between the dark soliton stripe and the vortex multipole (dipole, tripole, aligned quadrupole, quintopole, etc.) states that emerge in the context of quasi-two-dimensional Bose-Einstein condensates. In particular, we illustrate that the multivortex states with the vortices aligned along the (former) dark soliton stripe sequentially bifurcate from the latter state in a supercritical pitchfork manner. Each additional bifurcation adds an extra mode to the dark soliton instability and an extra vortex to the configuration; moreover, the bifurcating states inherit the stability properties of the soliton prior to the bifurcation. The critical points of this bifurcation are computed analytically via a few-mode truncation of the system, which clearly showcases the symmetry-breaking nature of the corresponding bifurcation. We complement this small(-er) amplitude, few mode bifurcation picture, with a larger amplitude, particle-based description of the ensuing vortices. The latter enables us to characterize the equilibrium position of the vortices, as well as their intrinsic dynamics and anomalous modes, thus providing a qualitative description of the nonequilibrium multivortex dynamics.