Chaos-assisted formation of immiscible matter-wave solitons and self-stabilization in the binary discrete nonlinear Schrödinger equation

Binary discrete nonlinear Schr\"odinger equation is used to describe dynamics of two-species Bose-Einstein condensate loaded into an optical lattice. Linear inter-species coupling leads to Rabi transitions between the species. In the regime of strong nonlinearity, a wavepacket corresponding to condensate separates into localized and ballistic fractions. Localized fraction is predominantly formed by immiscible solitons consisted of only one species. Initial states without spatial separation of occupied sites expose formation of immiscible solitons after a strongly chaotic transient. We calculate the finite-time Lyapunov exponent as a rate of wavepacket divergence in the Hilbert space. Using the Lyapunov analysis supplemented by Monte-Carlo sampling, it is shown that appearance of immiscible solitons after the chaotic transient corresponds to self-stabilization of the wavepacket. It is found that onset of chaos is accompanied by fast variations of kinetic and interaction energies. Crossover to self-stabilization is accompanied by reduction of condensate density due to emittance of ballistically propagating waves. It turns out that spatial separation of species should be a necessary condition for wavepacket stability in the presence of linear inter-species coupling.

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