On the characterization of vortex configurations in the steady rotating Bose–Einstein condensates

Abstract

Motivated by experiments in atomic Bose-Einstein condensates (BECs), we compare predictions of a system of ordinary differential equations (ODE) for dynamics of one and two individual vortices in the rotating BECs with those of the partial differential equation (PDE). In particular, we characterize orbitally stable vortex configurations in a symmetric harmonic trap due to a cubic repulsive interaction and the steady rotation. The ODE system is analyzed in details and the PDE model is approximated numerically. Good agreement between the two models is established in the semi-classical (Thomas-Fermi) limit that corresponds to the BECs at the large chemical potentials.

Bifurcations of Multi-Vortex Configurations in Rotating Bose–Einstein Condensates

“…The asymmetric pair is stable in numerical simulations and coexist for rotating frequencies above the threshold value with the stable symmetric vortex pair located at the smaller-than-critical distances [26]. The symmetric pair is a local minimizer of energy above the threshold value, whereas the asymmetric pair is a local constrained minimizer of energy, where the constraint again eliminates the rotational degree of freedom [18].…”

Platonic solids and symmetric solutions of the $N$-vortex problem on the sphere

“…The importance of the model is usually associated with geophysical fluid dynamics since it describes the interaction of hurricanes on the Earth. Interestingly, similar models of vortices are also relevant in the study of Bose-Einstein condensates [20], while the steady solutions of the problem have applications in semiconductors [4] and reaction-diffusion models [44]. We refer the reader to the papers by Aref et al [1], Aref [2] and the book by Newton [38] for a general overview of the N-vortex problem and for an extensive bibliography on the subject.…”