93 research outputs found

    Spontaneous symmetry breaking of fundamental states, vortices, and dipoles in two- and one-dimensional linearly coupled traps with cubic self-attraction

    Full text link
    We introduce two- and one-dimensional (2D and 1D) systems of two linearly-coupled Gross-Pitaevskii equations (GPEs) with the cubic self-attraction and harmonic-oscillator (HO) trapping potential in each GPE. The system models a Bose-Einstein condensate with a negative scattering length, loaded in a double-pancake trap, combined with the in-plane HO potential. In addition to that, the 1D version applies to the light transmission in a dual-core waveguide with the Kerr nonlinearity and in-core confinement represented by the HO potential. The subject of the analysis is spontaneous symmetry breaking in 2D and 1D ground-state (GS, alias fundamental) modes, as well as in 2D vortices and 1D dipole modes (the latter ones do not exist without the HO potential). By means of the variational approximation and numerical analysis, it is found that both the 2D and 1D systems give rise to a symmetry-breaking bifurcation (SBB) of the supercrtical type. Stability of symmetric states and asymmetric ones, produced by the SBB, is analyzed through the computation of eigenvalues for perturbation modes, and verified by direct simulations. The asymmetric GSs are always stable, while the stability region for vortices shrinks and eventually disappears with the increase of the linear-coupling constant, Îș \kappa . The SBB in the 2D system does not occur if Îș\kappa is too large (at Îș>Îșmax⁥\kappa >\kappa_{\max }); in that case, the two-component system behaves, essentially, as its single-component counterpart. In the 1D system, both asymmetric and symmetric dipole modes feature an additional oscillatory instability, unrelated to the symmetry breaking. This instability occurs in several regions, which expand with the increase of Îș\kappa .Comment: 22 pages, 19 figures, Phys. Rev. A, in pres

    Josephson oscillations of chirality and identity in two-dimensional solitons in spin-orbit-coupled condensates

    Full text link
    We investigate dynamics of two-dimensional chiral solitons of semi-vortex (SV) and mixed-mode (MM) types in spin-orbit-coupled Bose-Einstein condensates with the Manakov nonlinearity, loaded in a dual-core (double-layer) trap. The system supports two novel manifestations of Josephson phenomenology: one in the form of persistent oscillations between SVs or MMs with opposite chiralities in the two cores, and another one demonstrating robust periodic switching (identity oscillations) between SV in one core and MM in the other, provided that the strength of the inter-core coupling exceeds a threshold value. Below the threshold, the system creates composite states, which are asymmetric with respect to the two cores, or suffer the collapse. Robustness of the chirality and identity oscillations against deviations from the Manakov nonlinearity is investigated too. These dynamical regimes are possible only in the nonlinear system. In the linear one, exact stationary and dynamical solutions for SVs and MMs of the Bessel type are found. They sustain Josephson self-oscillations in different modes, with no interconversion between them.Comment: to be published in Physical Review Researc
    • 

    corecore