# Gap solitons in Rabi lattices

## TL;DR

This paper introduces a two-component nonlinear Schrödinger system with a Rabi lattice, exploring the existence, stability, and dynamics of various gap solitons in a setting applicable to Bose-Einstein condensates and optical fibers.

## Contribution

It presents the first detailed analysis of gap solitons in a Rabi lattice system, including stability properties and semi-analytical solutions under strong asymmetry.

## Key findings

- Stable gap solitons predominantly in the first bandgap
- Unstable solitons evolve into breathers or turbulent modes
- Semi-analytical solutions are derived for strong asymmetry cases

## Abstract

We introduce a two-component one-dimensional system, which is based on two nonlinear Schr\"{o}dinger/Gross-Pitaevskii equations (GPEs) with spatially periodic modulation of linear coupling ("Rabi lattice") and self-repulsive nonlinearity. The system may be realized in a binary Bose-Einstein condensate, whose components are resonantly coupled by a standing optical wave, as well as in terms of the bimodal light propagation in periodically twisted fibers. The system supports various types of gap solitons (GSs), which are constructed, and their stability is investigated, in the first two finite bandgaps of the underlying spectrum. These include on- and off-site-centered solitons (the GSs of the off-site type are additionally categorized as spatially even and odd ones), which may be symmetric or antisymmetric, with respect to the coupled components. The GSs are chiefly stable in the first finite bandgap, and unstable in the second one. In addition to that, there are narrow regions near the right edge of the first bandgap, and in the second one, which feature intricate alternation of stability and instability. Unstable solitons evolve into robust breathers or spatially confined turbulent modes. On-site-centered GSs are also considered in a version of the system which is made asymmetric by the Zeeman effect, or by birefringence of the optical fiber. A region of alternate stability is found in the latter case too. In the limit of strong asymmetry, GSs are obtained in a semi-analytical approximation, which reduces two coupled GPEs to a single one with an effective lattice potential.