Half-vortex soliton lattices in spin-orbit-coupled Bose-Einstein condensates with a quasi-flat band

TL;DR

This paper explores the formation, stability, and diverse geometries of half-vortex soliton lattices in spin-orbit-coupled Bose-Einstein condensates with a quasi-flat band, revealing their potential for low-atom-number excitation and symmetry-driven properties.

Contribution

It introduces the concept of half-vortex soliton lattices in a quasi-flat band system and analyzes their existence, stability, and geometric configurations within the Gross-Pitaevskii framework.

Findings

Half-vortex solitons can be confined within a single lattice cell in a quasi-flat band.

Arrays of half-vortex solitons exhibit diverse geometric profiles and enhanced stability near the linear regime.

The study demonstrates the formation of a super-half-vortex soliton with nonlinear symmetry breaking.

Abstract

Periodic potentials with flat bands in their spectra support strongly localized nonlinear excitations. Although a perfectly flat band cannot exist in a continuous system, a spin-orbit-coupled Bose-Einstein condensate loaded in a Zeeman lattice can realize the quasi-flat lowest band with an extremely narrow bandwidth. In such a quasi flat band, half vortex solitons become confined within a single lattice cell, enabling the formation of arrays of coupled half vortex solitons arranged of various spatial geometries. In this work, we study the existence and stability of these lattices within the framework of the two-component Gross-Pitaevskii equation. We demonstrate that, near the quasi-flat band, half-vortex solitons and their arrays can be excited with a nearly negligible number of atoms and are constrained by their local symmetries, which are isomorphic to a dihedral group of order 8. This allows observation of the respective field patterns in the nearly linear regime where they exhibit enhanced stability. The constructed lattices may have diverse geometric profiles, and in particular create a composite super-half-vortex soliton with nonlinear symmetry breaking.