Three-dimensional solitons supported by the spin-orbit coupling and Rydberg-Rydberg interactions in PT-symmetric potentials

TL;DR

This paper proposes a novel stabilization method for 3D solitons in binary Bose-Einstein condensates by combining spin-orbit coupling, Rydberg-Rydberg interactions, and PT-symmetric potentials, enabling stable excited states with complex structures.

Contribution

It introduces a stabilization strategy for 3D excited solitons using SOC, RRI, and PT-symmetric potentials, extending stability to states previously considered unstable.

Findings

Stable 3D solitons with high vorticity S=4 identified.

Interwoven necklace-like structures in MM solitons demonstrated.

Regions of effective stability mapped as functions of potential and interaction parameters.

Abstract

Excited states (ESs) of two- and three-dimensional (2D and 3D) solitons of the semivortex (SV) and mixed-mode (MM) types, supported by the interplay of the spin-orbit coupling (SOC) and local nonlinearity in binary Bose-Einstein condensates, are unstable, on the contrary to the stability of the SV and MM solitons in their fundamental states. We propose a stabilization strategy for these states in 3D, combining SOC and long-range Rydberg-Rydberg interactions (RRI), in the presence of a spatially-periodic potential, that may include a parity-time (PT)-symmetric component. ESs of the SV solitons, which carry integer vorticities S and S+1 in their two components, exhibit robustness up to S= 4. ESs of MM solitons feature an interwoven necklace-like structure, with the components carrying opposite fractional values of the orbital angular momentum. Regions of the effective stability of the 3D solitons of the SV and MM types (both fundamental ones and ESs), are identified as functions of the imaginary component of the PT-symmetric potential and strengths of the SOC and RRI terms.