Symbiotic two-component gap solitons

TL;DR

This paper investigates symbiotic two-component gap solitons in a nonlinear Schrödinger model with a periodic potential, analyzing their stability, types, and transformations, with applications in optics and quantum gases.

Contribution

It introduces a model of symbiotic gap solitons with repulsive XPM interactions, constructs fundamental solutions, and analyzes their stability and bifurcations, including analytical approximations.

Findings

Symmetric solitons destabilized by symmetry-breaking perturbations.

Asymmetric solitons have limited stability regions, especially in the second bandgap.

Unstable solitons evolve into persistent breathers.

Abstract

We consider a two-component one-dimensional model of gap solitons (GSs), which is based on two nonlinear Schr\"odinger 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).