Dynamics of a Few Corotating Vortices in Bose-Einstein Condensates

Abstract

We study the dynamics of small vortex clusters with few (2-4) co-rotating vortices in Bose-Einstein condensates by means of experiments, numerical computations, and theoretical analysis. All of these approaches corroborate the counter-intuitive presence of a dynamical instability of symmetric vortex configurations. The instability arises as a pitchfork bifurcation at sufficiently large values of the angular momentum that induces the emergence and stabilization of asymmetric rotating vortex configurations. The latter are quantified in the theoretical model and observed in the experiments. The dynamics is explored both for the integrable two-vortex system, where a reduction of the phase space of the system provides valuable insight, as well as for the non-integrable three-(or more) vortex case, which additionally admits the possibility of chaotic trajectories.

Multidimensional Josephson vortices in spin-orbit-coupled Bose-Einstein condensates: Snake instability and decay through vortex dipoles

“…The latter, in particular, opens up an interesting way to study the snake instability in twocomponent condensates, in the same manner as it is currently being the case of DS decay in scalar condensates [45,46]. Besides, the decay of JVs in SO coupled condensates provides an excellent playground to investigate the rich dynamics of vortex dipoles as has been previously done in scalar BECs [47,48].…”

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

“…(21) It should be noted here that in the present work the precession frequency of a single vortex will be assumed to be constant, an assumption that is fairly accurate between the center of the trap confining the BEC and half of its radial extent (the latter is often referred to as the Thomas-Fermi radius). More general position dependent precession frequency expressions can be used also in connection to experiments, such as most notablyΩ j = Ω/(1 − r 2 j ) [14,19,21]. However we have checked that these do not modify the existence or stability conclusions for the solutions presented in this paper.…”

“…In the latter case, the rotation imposed by the precession is only enhanced by the rotation induced by the interaction and hence the vortices cannot find themselves in a situation of genuine equilibrium. Rather, in the latter case, one can only talk about rigidly rotating states as was examined in the recent work of [21] for N = 2, 3 and 4. For large N , the latter setting has been examined too, with a recent example being the work of [40]; see also therein for relevant references.…”

“…However, in parallel, a growing fraction of the literature has been advocating [19,21,30,34,35] the usefulness of a particle model corroborating the two principal features of the vortex motion. These are that each of the vortices has a precessional motion (dictated by its charge, distance from the origin of the parabolic trap confining the BEC and characteristics of the BEC, namely its background density at the center characterizing the so-called chemical potential µ and the trap confinement frequency Ω) and also has a relative position dependent interaction with other vortices present in the BEC.…”

“…However, in more recent experimental efforts, states with two vortices in the form of a counter-circulating vortex dipole [12,14,19], as well as vortex tripoles [20] (with two vortices of one sign, and one vortex of the opposite sign) have been produced and their dynamics monitored. 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).…”