Bifurcations, stability, and dynamics of multiple matter-wave vortex states

Abstract

In the present work, we offer a unifying perspective between the dark soliton stripe and the vortex multipole (dipole, tripole, aligned quadrupole, quintopole, etc.) states that emerge in the context of quasi-two-dimensional Bose-Einstein condensates. In particular, we illustrate that the multivortex states with the vortices aligned along the (former) dark soliton stripe sequentially bifurcate from the latter state in a supercritical pitchfork manner. Each additional bifurcation adds an extra mode to the dark soliton instability and an extra vortex to the configuration; moreover, the bifurcating states inherit the stability properties of the soliton prior to the bifurcation. The critical points of this bifurcation are computed analytically via a few-mode truncation of the system, which clearly showcases the symmetry-breaking nature of the corresponding bifurcation. We complement this small(-er) amplitude, few mode bifurcation picture, with a larger amplitude, particle-based description of the ensuing vortices. The latter enables us to characterize the equilibrium position of the vortices, as well as their intrinsic dynamics and anomalous modes, thus providing a qualitative description of the nonequilibrium multivortex dynamics.

Vortex–bright-soliton dipoles: Bifurcations, symmetry breaking, and soliton tunneling in a vortex-induced double well

“…While the bright component remains roughly invariant as the transition point is crossed, the dark component develops two singular points in the phase corresponding to the density vanishings and the opposite circulation characteristic of a vortex dipole [40]. The relevant bifurcations occur approximately at the same critical N 1 (N cr 1 ≈ 40, with N 2 fixed at 20).…”

“…In the same spirit as in the work of [40] (see also e.g. [50] and references therein), the prototypical relevant bound state is the VB dipole.…”

“…The emergence of the dipole state branches can be thought of in terms of a bifurcation picture in an equivalent way to the one described for one-component BECs in [40]. The two possible dipole branches, distinguished from the presence or absence of the phase jump of π in the bright component, arise at critical values of N 1 from two states, which can be regarded as generalizations of the dark soliton stripe observed in one-component condensates [4].…”

“…This mode is illustrated by the square markers (which are red in the online version) in the relevant panel and is well-known to correspond to the precession of the vortex within the parabolic trap (see e.g. [40] and references therein). However, it is noteworthy that this mode decreases in frequency due to the presence of the bright component and ultimately crosses the zero frequency point.…”

“…Our aim here is to explore this potential beyond the level of a single vortex-bright soliton entity. In particular, recently in the one-component setting, we have examined the bifurcation of few-vortex clusters (see [40] and references therein), most notably the vortex dipole, but also the vortex tripole, quadrupole, vortex polygons and larger scale crystals [41]. It is then natural to expect that similar bifurcations will arise in the two-component setting and, in fact, that the bright solitons that are "trapped" within the vortex states will potentially bear different relative phases (e.g.…”