Globally linked vortex clusters in trapped wave fields

Abstract

We put forward the existence of a rich variety of fully stationary vortex structures, termed H clusters, made of an increasing number of vortices nested in paraxial wave fields confined by trapping potentials. However, we show that the constituent vortices are globally linked, rather than products of independent vortices. Also, they always feature a monopolar global wave front and exist in nonlinear systems, such as the Bose-Einstein condensates. Clusters with multipolar global wave fronts are nonstationary or, at best, flipping.

Few-particle vortex cluster equilibria in Bose–Einstein condensates: existence and stability

“…While earlier studies focused on the PDE approach attempting to infer conclusions for the vortex dynamics from the vicinity of the linear limit [22,23,24,25,26,27,28,29,30,32], our approach here has taken a complementary view whereby the vortices have been examined as interacting particle systems (as was done earlier chiefly for the dipole [33,34,35], but also for larger vortex numbers in the case where rotation is present [18] or absent [21] for cocirculating vortices). We have shown this approach to be fairly informative towards an understanding of the configurations that may arise for small vortex numbers N and the identification of their stability characteristics.…”

“…A very recent work has also produced sets of 2-, 3-, 4-vortices exploring their dynamics in the absence of a rotational angular momentum induced term [21]. These experimental works have, in turn, either had as a preamble [22,23,24,25,26,27,28,29,30] or subsequently motivated [31,32,33,34,35] studies on the statics, stability and dynamics of such vortex clusters (predominantly, in fact, the vortex dipole).…”

Elliptic vortices in composite Mathieu lattices

“…were also investigated [19][20][21][22][23][24]. Vortex dipoles, i.e., composite states with two embedded vortices of opposite topological charges (vortex-antivortex pairs), do exist as stationary soliton solutions to the effectively two-dimensional Gross-Pitaevskii equation for both symmetric and asymmetric traps.…”

Stable multiple vortices in collisionally inhomogeneous attractive Bose-Einstein condensates

“…The identification and experimental demonstration of more complex vortical structures, such as vortex dipoles [28,29] and quadrupoles [30,31], was confined to BEC with the self-repulsive nonlinearity. The most natural setting for hosting vortices is provided by a pancakeshaped axially symmetric BEC, which is strongly confined in one direction (z) and weakly confined in the transverse plane.…”