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

• Published in: Communications in nonlinear science & numerical simulation 2017-02, Vol.43, p.227-238
• Main Authors: Makarov, D.V., Uleysky, M.Yu
• Format: Article
• Language: English
• Subjects: Bose–Einstein condensate; Chaos; Finite-time Lyapunov exponent; Nonlinear Schrödinger equation; Solitons
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2016.07.006

•Binary mixture of Bose–Einstein condensates with linear interspecies coupling can undergo spontaneous self-stabilization after the strongly chaotic transient regime.•The self-stabilization is accompanied by the onset of spatially separated immiscible solitons.•One of the most important conditions for self-stabilization is the reduction of condensate density due to emittance of ballistically propagating waves. Binary discrete nonlinear Schrödinger 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. Immiscible solitons are formed from initially non-separated states after transient chaotic regime. We calculate the finite-time Lyapunov exponent as a rate of wavepacket divergence in the Hilbert space. Appearance of immiscible solitons to spontaneous self-stabilization of the wavepacket. It is found that onset of chaos is accompanied by fast variations of interaction energy and energy of inter-site tunneling. Crossover to self-stabilization is accompanied by reduction of condensate density due to emittance of ballistically propagating waves.