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

Abstract

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. 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.

Dynamics of a nonlinear quantum oscillator under non-Markovian pumping

“…Let's consider an ensemble of cold bosonic particles, where small fraction belongs to some single state, while the remaining part is characterized by narrow but continuous energy spectrum and can be considered as precondensate. If number of particles is sufficiently large, we can invoke the semiclassical approximation, when amplitude of the state can be represented by a c-number [35][36][37][38][39][40][41]. Under certain conditions (which shall be discussed in Sec.…”

Spatial Phase Separation of a Binary Mixture in a Ring Trimer

“…Systems made up of two condensed species (be they heteronuclear [14] or homonuclear [15]) indeed offer a plethora of observable physical phenomena ranging from the dynamics of solitons [16,17,18] to the formation of entanglement between the species [19,20], not to mention the mechanisms that directly account for phase separation [21,22,23].…”

Phase separation can be stronger than chaos

“…Engineering of experimental setups capable of trapping boson mixtures [8][9][10] in optical lattices [11][12][13] has stimulated the interest of the theoretical community for the understanding of demixing effect in the presence of spatial fragmentation. In this context, beyond phase separation [14][15][16], a rich variety of phenomena have been highlighted including (but not limited to) the formation of boson currents in ring lattices, [17], the appearance of novel phases exhibiting magnetic-like properties [18,19], quantum emulsions [20], the emergence of polaron excitations [21,22], the entanglement between the species [23,24], the collision of a condensate with impurities [25][26][27], the formation of immiscible solitons [28] and the modulation instability in the phase separation [29]. Systems consisting of two bosonic species and optical lattices with ring geometry are within the reach of current experimental setups.…”