Spontaneous symmetry breaking in Schrödinger lattices with two nonlinear sites

Abstract

We introduce discrete systems in the form of straight (infinite) and ring-shaped chains, with two symmetrically placed nonlinear sites. The systems can be implemented in nonlinear optics (as waveguiding arrays) and BEC (by means of an optical lattice). A full set of exact analytical solutions for symmetric, asymmetric, and antisymmetric localized modes is found, and their stability is investigated in a numerical form. The symmetry-breaking bifurcation (SBB), through which the asymmetric modes emerge from the symmetric ones, is found to be of the subcritical type. It is transformed into a supercritical bifurcation if the nonlinearity is localized in relatively broad domains around two central sites, and also in the ring of a small size, i.e., in effectively nonlocal settings. The family of antisymmetric modes does not undergo bifurcations, and features both stable and unstable portions. The evolution of unstable localized modes is investigated by means of direct simulations. In particular, unstable asymmetric states, which exist in the case of the subcritical bifurcation, give rise to breathers oscillating between the nonlinear sites, thus restoring an effective dynamical symmetry between them.

To appear in PRA

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• Pinned modes in lossy lattices with local gain and nonlinearity
• Spontaneous symmetry breaking of binary fields in a nonlinear double-well structure
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• Pinned modes in two-dimensional lossy lattices with local gain and nonlinearity
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• Symmetric and antisymmetric nonlinear modes supported by dual local gain in lossy lattices
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• Symmetric and asymmetric localized modes in linear lattices with an embedded pair of ${\chi }^{(2)}$-nonlinear sites
• Symmetry breaking in binary chain with nonlinear sites
• $\mathcal{P}\mathcal{T}$-symmetric ladders with a scattering core
• Solitons supported by singular modulation of the cubic nonlinearity
• Self trapping transition for a nonlinear impurity within a linear chain
• Bifurcations and dynamics emergent from lattice and continuum models of bioactive porous media
• Localized modes in two-dimensional Schroedinger lattices with a pair of nonlinear sites
• Frequency comb generation for wave transmission through the nonlinear dimer
• Spontaneous Symmetry Breaking In Nonlinear Binary Periodic Systems