The emergence of vortex-bright soliton dipoles in two-component Bose-Einstein condensates through bifurcations from suitable eigenstates of the underlying linear system is examined. These dipoles can have their bright solitary structures be in phase (symmetric) or out of phase (anti-symmetric). The dynamical robustness of each of these two possibilities is considered and the out-of-phase case is found to exhibit an intriguing symmetry-breaking instability that can in turn lead to tunneling of the bright wave function between the two vortex ``wells.'' We interpret this phenomenon by virtue of a vortex-induced double-well system, whose spontaneous symmetry breaking leads to asymmetric vortex-bright dipoles, in addition to the symmetric and antisymmetric ones. The theoretical prediction of these states is corroborated by detailed numerical computations.
The emergence of vortex-bright soliton dipoles in two-component Bose-Einstein condensates through bifurcations from suitable eigenstates of the underlying linear system is examined. These dipoles can have their bright solitary structures be in phase (symmetric) or out of phase (anti-symmetric). The dynamical robustness of each of these two possibilities is considered and the out-of-phase case is found to exhibit an intriguing symmetry-breaking instability that can in turn lead to tunneling of the bright wave function between the two vortex ``wells.'' We interpret this phenomenon by virtue of a vortex-induced double-well system, whose spontaneous symmetry breaking leads to asymmetric vortex-bright dipoles, in addition to the symmetric and antisymmetric ones. The theoretical prediction of these states is corroborated by detailed numerical computations.
Models of two-dimensional (2D) traps, with double-well structure in the third direction, for Bose-Einstein condensates are introduced with attractive or repulsive interactions between atoms. The models are based on systems of linearly coupled 2D Gross-Pitaevskii equations, where the coupling accounts for tunneling between the wells. Each well carries an optical lattice (OL) (stable 2D solitons cannot exist without OLs). The linear coupling splits each finite band gap in the spectrum of the single-component model into two subgaps. The main subject of the work is spontaneous symmetry breaking (SSB) in two-component 2D solitons and localized vortices (SSB was not considered before in 2D settings). Using variational approximation (VA) and numerical methods, we demonstrate that, in a system with attraction or repulsion, SSB occurs in families of symmetric or antisymmetric solitons (or vortices), respectively. The corresponding bifurcation destabilizes the original solution branch and gives rise to a stable branch of asymmetric solitons or vortices. The VA provides for an accurate description of the emerging branch of asymmetric solitons. In the model with attraction, all stable branches eventually terminate due to the onset of collapse. Stable asymmetric solitons in higher finite band gaps and vortices with a multiple topological charge are found too. The models also give rise to first examples of embedded solitons and embedded vortices (the states located inside Bloch bands) in two dimensions. In the linearly coupled system with opposite signs of the nonlinearity in the two cores, two distinct types of stable solitons and vortices are found, dominated by either the self-attractive component or the self-repulsive one. In the system with a mismatch between the two OLs, a pseudobifurcation is found: when the mismatch attains its largest value $(\ensuremath{\pi})$, the bifurcation does not happen, as branches of different solutions asymptotically approach each other, but fail to merge.
Abstract We unravel the spontaneous generation of vortex-bright-soliton structures in binary Bose–Einstein condensates with a small mass imbalance between the species confined in a two-dimensional harmonic trap where one of the two species has been segmented into two parts by a potential barrier. To trigger the dynamics the potential barrier is suddenly removed and subsequently the segments perform a counterflow dynamics. We consider a relative phase difference of π between the segments, while a singly quantized vortex may be imprinted at the center of the other species. The number of vortex structures developed within the segmented species following the merging of its segments is found to depend on the presence of an initial vortex on the other species. In particular, a π phase difference in the segmented species and a vortex in the other species result in a single vortex-bright-soliton structure. However, when the non-segmented species does not contain a vortex the counterflow dynamics of the segmented species gives rise to a vortex dipole in it accompanied by two bright solitary waves arising in the non-segmented species. Turning to strongly mass imbalanced mixtures, with a heavier segmented species, we find that the same overall dynamics takes place, while the quench-induced nonlinear excitations become more robust. Inspecting the dynamics of the angular momentum we show that it can be transferred from one species to the other, and its transfer rate can be tuned by the strength of the interspecies interactions and the mass of the atomic species.
We study dark–bright (DB) ring solitons in two-component Bose–Einstein condensates. In the limit of large densities of the dark component, we describe the soliton dynamics by means of an equation of motion for the ring radius. The presence of the bright, 'filling' species is demonstrated to have a stabilizing effect on the ring dark soliton. Near the linear limit, we discuss the symmetry-breaking bifurcations of DB soliton stripes and vortex-bright soliton clusters from the DB ring and relate the stabilizing effect of filling to changes in the bifurcation diagram. Finally, we show that the stabilization by means of a second component is not limited to the radially symmetric structures, but can also be observed in a cross-like DB soliton configuration.
In the present work, we revisit two-component Bose-Einstein condensates in their fully three-dimensional (3D) form. Motivated by earlier studies of dark-bright solitons in the 1D case, we explore the stability of these structures in their fully 3D form in two variants. In one the dark soliton is planar and trapping a planar bright (disk) soliton. In the other case, a dark spherical shell soliton creates an effective potential in which a bright spherical shell of atoms is trapped in the second component. We identify these solutions as numerically exact states (up to a prescribed accuracy) and perform a Bogolyubov-de Gennes linearization analysis that illustrates that both structures can be dynamically stable in suitable intervals of sufficiently low chemical potentials. We corroborate this finding theoretically by analyzing the stability via degenerate perturbation theory near the linear limit of the system. When the solitary waves are found to be unstable, we explore their dynamical evolution via direct numerical simulations which, in turn, reveal wave forms that are more robust. Finally, using the SO(2) symmetry of the model, we produce multi-dark-bright planar or shell solitons involved in pairwise oscillatory motion.
We study dark–bright (DB) ring solitons in two-component Bose–Einstein condensates. In the limit of large densities of the dark component, we describe the soliton dynamics by means of an equation of motion for the ring radius. The presence of the bright, 'filling' species is demonstrated to have a stabilizing effect on the ring dark soliton. Near the linear limit, we discuss the symmetry-breaking bifurcations of DB soliton stripes and vortex-bright soliton clusters from the DB ring and relate the stabilizing effect of filling to changes in the bifurcation diagram. Finally, we show that the stabilization by means of a second component is not limited to the radially symmetric structures, but can also be observed in a cross-like DB soliton configuration.
We study stationary states of a two-dimensional (2D) Bose-Einstein condensate with both attractive and repulsive nonlinearities in a combination of a double-square-well potential in one direction and a perpendicular optical lattice. We look for dual-core solitons in this configuration, focusing on their symmetry-breaking bifurcations. For attractive interactions, without the lattice, a similar analysis was performed [M. Matuszewski et al., Phys. Rev. A 75, 063621 (2007)], where subcritical bifurcation transforming antisymmetric gap solitons into asymmetric ones was found. Here we focus on the effect of an optical lattice and the so created gap solitons. We discover that a phase transition occurs when the lattice depth increases and the additional dimension becomes strongly suppressed. The bifurcation type changes from subcritical (typical for a 2D system, with hysteresis) to supercritical (typical for a one-dimensional system). An additional advantage of the lattice is that gap solitons exist even for repulsive interactions. In this case we also discover bifurcation of a supercritical type. The analysis is based on a variational approximation, which is surprisingly well verified by numerical results.