Stability and dynamics of vortex clusters in nonrotated Bose-Einstein condensates

Abstract

We study stationary clusters of vortices and antivortices in dilute pancake-shaped Bose-Einstein condensates confined in nonrotating harmonic traps. Previous theoretical results on the stability properties of these topologically nontrivial excited states are seemingly contradicting. We clarify this situation by a systematic stability analysis. The energetic and dynamic stability of the clusters is determined from the corresponding elementary excitation spectra obtained by solving the Bogoliubov equations. Furthermore, we study the temporal evolution of the dynamically unstable clusters. The stability of the clusters and the characteristics of their destabilizing modes only depend on the effective strength of the interactions between particles and the trap anisotropy. For certain values of these parameters, there exist several dynamical instabilities, but we show that there are also regions in which some of the clusters are dynamically stable. Moreover, we observe that the dynamical instability of the clusters does not always imply their structural instability, and that for some dynamically unstable states annihilation of the vortices is followed by their regeneration, and revival of the cluster.

Three-vortex configurations in trapped Bose-Einstein condensates

“…The fact that our setup is not really quasi-2D indicates that the results of Ref. [7] are valid well beyond the pancake-shape limit. It is expected [7] that the tripole survives for a time of the order of ω −1 0 , which for our case is about 10 ms, well within the 20 ms of waiting time before releasing the atoms from the magnetic potential.…”

“…[7] are valid well beyond the pancake-shape limit. It is expected [7] that the tripole survives for a time of the order of ω −1 0 , which for our case is about 10 ms, well within the 20 ms of waiting time before releasing the atoms from the magnetic potential. Thus tripole decay has a chance to reduce the number of observations of tripole configurations, as discussed further below.…”

Emergence and stability of vortex clusters in Bose–Einstein condensates: A bifurcation approach near the linear limit

“…More elaborate states, such as dipoles, tripoles and quadrupoles, were considered in Refs. [24,25]. Dynamics of such few vortex states in the weakly-interacting limit were performed in Ref.…”

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.…”