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
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, . The SBB in the 2D system does not occur
if is too large (at ); 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
.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
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
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