A model of a nonlinear double-well potential (NDWP) is proposed, with the objective to study a new implementation of the spontaneous symmetry breaking (SSB) in Bose-Einstein condensates and optical media, under the action of a potential with two symmetric minima. In the limit case when the NDWP structure is induced by the local nonlinearity coefficient represented by a set of two delta-functions, a fully analytical solution is obtained for symmetric, antisymmetric and asymmetric states. In this solvable model, the SSB bifurcation has a fully subcritical character. Numerical analysis, based on direct simulations and computation of stability eigenvalues, demonstrates that, while the symmetric states are stable up to the SSB bifurcation point, both symmetric and emerging asymmetric states, as well as all antisymmetric ones, are unstable in the model with the delta-functions. In a general model with a finite width of the nonlinear-potential wells, the asymmetric states quickly become stable, simultaneously with the switch of the SSB bifurcation from subcritical to supercritical. Antisymmetric solutions may also get stabilized in the finite-width NDWP structure, which gives rise to a bistability between them and asymmetric states. The symmetric states require a finite norm for their existence, an explanation to which is given. A full diagram for the existence and stability of the trapped states in the model is produced.


Seminar, 30th of September, 12:00h. Conference Room

Hosted by Prof. Maciej Lewenstein