Gap solitons of the Wannier and Bloch types in spin-orbit-coupled Bose-Einstein condensates with a moir\'{e} lattice

TL;DR

This paper investigates the formation, stability, and transition mechanisms of gap solitons in spin-orbit-coupled Bose-Einstein condensates within moiré lattices, revealing how lattice and SOC parameters influence soliton properties.

Contribution

It introduces five Wannier-type gap soliton families in spinor BECs with moiré lattices and demonstrates reversible transitions between Wannier and Bloch types via lattice and SOC tuning.

Findings

Five Wannier-type GS families bifurcate from the lowest five bands.

Reducing lattice period and depth induces a transition to Bloch-type GSs.

Adjusting SOC strength modulates band flatness and soliton localization.

Abstract

Gap solitons (GSs) bifurcating from flat bands, which may be represented in terms of Wannier functions, have garnered significant interest due to their strong localization with extremely small norms. Moir\'{e} lattices (MLs), with multiple flat bands, offer an appropriate platform for creating such solitons. We explore the formation mechanism and stability of GSs in spin-1 Bose-Einstein condensates under the combined action of the Rashba spin-orbit coupling (SOC) and an ML potential. We identify five Wannier-type GS families bifurcating from the lowest five energy bands in the spectrum induced by the ML with sufficiently large period and depth. These fundamental GSs serve as basic elements for constructing more complex Wannier-type GS states. Reducing the lattice period and depth triggers a transition from the Wannier-type GSs to ones of the Bloch type, the latter exhibiting higher norm thresholds and pronounced spatial broadening near edges of the energy bands. In addition to tuning the lattice-potential parameters, adjusting the SOC strength can also modulate the flatness of energy bands and enhance the localization of gap solitons, enabling reversible transitions between the GSs of the Wannier and Bloch types. Distinctive properties of GSs in the quasiperiodic ML are uncovered too. Thus, we propose the theoretical foundation for the creation of and manipulations with strongly localized GSs.