171 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
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