Vortex nucleation in a dissipative variant of the nonlinear Schrödinger equation under rotation

•The theme of vortex nucleation in finite temperature BECs is revisited.•The dissipative GPE is used to reveal the relevant phenomenology.•BdG stability analysis is used to reveal numerically the instability mechanism.•An asymptotic analysis of the BdG problem is developed.•The most unstable mode scales like μ2/3μ2/3 where μμ is the chemical potential.

In the present work, we motivate and explore the dynamics of a dissipative variant of the nonlinear Schrödinger equation under the impact of external rotation. As in the well established Hamiltonian case, the rotation gives rise to the formation of vortices. We show, however, that the most unstable mode leading to this instability scales with an appropriate power of the chemical potential μμ of the system, increasing proportionally to μ2/3μ2/3. The precise form of the relevant formula, obtained through our asymptotic analysis, provides the most unstable mode as a function of the atomic density and the trap strength. We show how these unstable modes typically nucleate a large number of vortices in the periphery of the atomic cloud. However, through a pattern selection mechanism, prompted by symmetry-breaking, only few isolated vortices are pulled in sequentially from the periphery towards the bulk of the cloud resulting in highly symmetric stable vortex configurations with far fewer vortices than the original unstable mode. These results may be of relevance to the experimentally tractable realm of finite temperature atomic condensates.