Spontaneous symmetry breaking in a nonlinear double-well structure

Abstract

We propose a model of a nonlinear double-well potential (NDWP), alias a double-well pseudopotential, with the objective to study an alternative implementation of the spontaneous symmetry breaking (SSB) in Bose-Einstein condensates (BECs) 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 both 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 the 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 the subcritical to supercritical type. Antisymmetric solutions may also get stabilized in the NDWP structure of the general type, 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. Experimental observation of the predicted effects should be possible in BEC formed by several hundred atoms.Comment: submitted to Physical Review

One- and two-dimensional solitons supported by singular modulation of quadratic nonlinearity

“…Similar to other models with two separated symmetric peaks of the local χ (2) [22] and χ (3) [11,33,34] nonlinearity strength , the asymmetric solitons are generated from the symmetric ones by the spontaneous-symmetrybreaking bifurcation [27], which occurs with the increase of separation 2∆ between the peaks, if other parameters are fixed. The bifurcation is illustrated by Fig.…”

Spontaneous chiral symmetry breaking in metamaterials

“…Well-known examples include spontaneous magnetization 3 , the symmetry breaking in strong interaction that is responsible for the bulk of mass of nucleons 4,5 , the recently discovered Higgs boson [6][7][8][9][10] and the breaking of chiral symmetry in biochemistry that is crucially important for the homochirality of biomolecules [11][12][13] . Recent studies of spontaneous symmetry breaking in nonlinear optical systems [14][15][16] and Bose-Einstein condensates 17,18 further underline its ubiquity.…”

Switch between the Types of the Symmetry Breaking Bifurcation in Optically Induced Photorefractive Rotational Double-Well Potential

“…Among many kinds of nonlinear systems, double-well potential (DWP) or dual-core system is the most essential model employed to study the phase transition and SSB of the nonlinear states [2][3][4][5][6][7][8][9]. In DWP system, the important process relating to the phase transition and SSB is symmetric breaking bifurcation (SBB), which determines the process of symmetric states transiting to the asymmetric ones [10][11][12][13][14][15][16][17]. There are two kinds of SBB, subcritical and super critical, which are tantamount to the phase transition of the first and second kind respectively.…”