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Register a new userSymbiotic two-component gap solitons
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Added by
Thawatchai Mayteevarunyoo
Publication date
2012
fields
Physics
and research's language is
English
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We consider a two-component one-dimensional model of gap solitons (GSs), which is based on two nonlinear Schrodinger equations, coupled by repulsive XPM (cross-phase-modulation) terms, in the absence of the SPM (self-phase-modulation) nonlinearity. The equations include a periodic potential acting on both components, thus giving rise to GSs of the symbiotic type, which exist solely due to the repulsive interaction between the two components. The model may be implemented for holographic solitons in optics, and in binary bosonic or fermionic gases trapped in the optical lattice. Fundamental symbiotic GSs are constructed, and their stability is investigated, in the first two finite bandgaps of the underlying spectrum. Symmetric solitons are destabilized, including their entire family in the second bandgap, by symmetry-breaking perturbations above a critical value of the total power. Asymmetric solitons of intra-gap and inter-gap types are studied too, with the propagation constants of the two components falling into the same or different bandgaps, respectively. The increase of the asymmetry between the components leads to shrinkage of the stability areas of the GSs. Inter-gap GSs are stable only in a strongly asymmetric form, in which the first-bandgap component is a dominating one. Intra-gap solitons are unstable in the second bandgap. Unstable two-component GSs are transformed into persistent breathers. In addition to systematic numerical considerations, analytical results are obtained by means of an extended (tailed) Thomas-Fermi approximation (TFA).
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We consider a one-dimensional model of a two-component Bose-Einstein condensate in the presence of periodic external potentials of opposite signs, acting on the two species. The interaction between the species is attractive, while intra-species interactions may be attractive too [the system of the right-bright (BB) type], or of opposite signs in the two components [the gap-bright (GB) model]. We identify the existence and stability domains for soliton complexes of the BB and GB types. The evolution of unstable solitons leads to the establishment of oscillatory states. The increase of the strength of the nonlinear attraction between the species results in symbiotic stabilization of the complexes, despite the fact that one component is centered around a local maximum of the respective periodic potential.
Nonlinear periodic systems, such as photonic crystals and Bose-Einstein condensates (BECs) loaded into optical lattices, are often described by the nonlinear Schrodinger/Gross-Pitaevskii equation with a sinusoidal potential. Here, we consider a model based on such a periodic potential, with the nonlinearity (attractive or repulsive) concentrated either at a single point or at a symmetric set of two points, which are represented, respectively, by a single {delta}-function or a combination of two {delta}-functions. This model gives rise to ordinary solitons or gap solitons (GSs), which reside, respectively, in the semi-infinite or finite gaps of the systems linear spectrum, being pinned to the {delta}-functions. Physical realizations of these systems are possible in optics and BEC, using diverse variants of the nonlinearity management. First, we demonstrate that the single {delta}-function multiplying the nonlinear term supports families of stable regular solitons in the self-attractive case, while a family of solitons supported by the attractive {delta}-function in the absence of the periodic potential is completely unstable. We also show that the {delta}-function can support stable GSs in the first finite gap in both the self-attractive and repulsive models. The stability analysis for the GSs in the second finite gap is reported too, for both signs of the nonlinearity. Alongside the numerical analysis, analytical approximations are developed for the solitons in the semi-infinite and first two finite gaps, with the single {delta}-function positioned at a minimum or maximum of the periodic potential. In the model with the symmetric set of two {delta}-functions, we study the effect of the spontaneous symmetry breaking of the pinned solitons. Two configurations are considered, with the {delta}-functions set symmetrically with respect to the minimum or maximum of the potential.
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