Spontaneous symmetry breaking of binary fields in a nonlinear double-well structure

Abstract

We introduce a one-dimensional two-component system with the self-focusing cubic nonlinearity concentrated at a symmetric set of two spots. Effects of the spontaneous symmetry breaking (SSB) of localized modes were previously studied in the single-component version of this system. In this work, we study the evolution (in the configuration space of the system) and SSB scenarios for two-component modes of three generic types, as concerns the spatial symmetry of each component: symmetric-symmetric (Sm-Sm), antisymmetric-antisymmetric (AS-AS), and symmetric-antisymmetric (S-AS) ones. In the limit case of the nonlinear potential represented by two -functions, solutions are obtained in a semi-analytical form. They feature novel properties, in comparison with the previously studied single-component model. In particular, the SSB of antisymmetric modes is possible solely in the two-component system, and, obviously, S-AS states exist only in the two-component system too. In the general case of the symmetric pair of finite-width nonlinear potential wells, evolution scenarios are very complex. In this case, new results are reported, first, for the single-component model. These are pairs of broken-antisymmetry modes, and of twin-peak symmetric ones, which are generated by saddle-mode bifurcations separated from the transformations previously studied in the the single-component setting. With regard to these findings, complex scenarios of the evolution of the two-component solution families are realized in terms of links connecting pairs of modes of three simplest types: (A) two-component ones with unbroken symmetries; (B) single-component modes featuring density peaks in both potential wells; (C) single-component modes which are trapped, essentially, in a single well.

22 pages, 18 figures; Physica D, in press

References in corpus (17)

• Theory of ultracold Fermi gases
• Solitons in nonlinear lattices
• Spontaneous symmetry breaking in a nonlinear double-well structure
• Symmetry Breaking in Symmetric and Asymmetric Double-Well Potentials
• Realization of a single Josephson junction for Bose-Einstein condensates
• Spontaneous symmetry breaking of solitons trapped in a double-channel potential
• Symmetric and asymmetric solitons in linearly coupled Bose-Einstein condensates trapped in optical lattices
• Nonlinear modes for the Gross-Pitaevskii equation -- demonstrative computation approach
• Solitons supported by localized nonlinearities in periodic media
• Spontaneous symmetry breaking of gap solitons in double-well traps
• Spontaneous symmetry breaking in Schrödinger lattices with two nonlinear sites
• Two-Component Nonlinear Schrodinger Models with a Double-Well Potential
• Spinor BECs in a double-well: population transfer and Josephson oscillations
• Rabi-Josephson oscillations and self-trapped dynamics in atomic junctions with two bosonic species
• Spatial quadratic solitons guided by narrow layers of a nonlinear material
• Spontaneous symmetry breaking of photonic and matter waves in two-dimensional pseudopotentials
• Transfer and scattering of wave packets by a nonlinear trap

Cited by in corpus (9)

• A solvable model for solitons pinned to a PT-symmetric dipole
• Solitons and vortices in nonlinear potential wells
• Spatial control of the competition between self-focusing and self-defocusing nonlinearities in one- and two-dimensional systems
• One- and two-dimensional solitons supported by singular modulation of quadratic nonlinearity
• Symmetric and asymmetric localized modes in linear lattices with an embedded pair of ${\chi }^{(2)}$-nonlinear sites
• Symmetry breaking in competing single-well linear-nonlinear potentials
• Solitons supported by singular modulation of the cubic nonlinearity
• Ring modes supported by concentrated cubic nonlinearity
• Symmetry breakings in dual-core systems with double-spot localization of nonlinearity