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Stable three-dimensional solitons in spin-orbit-coupled atomic-molecular condensates

Chao Kong1,2, Jinqing Li1,2, Guihua Chen3, Guilong Li4, Zhaopin Chen5, Haiming Deng1,2,*, Boris A. Malomed6, and Yongyao Li7

  • *Contact author: woshidenghaiming@126.com
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Phys. Rev. Research 8, 033278 – Published 4 September, 2026

DOI: https://doi.org/10.1103/zm5l-1q4w

Abstract

We elaborate a mechanism for the creation of stable three-dimensional (3D) solitons in spin-orbit-coupled (SOC) atomic-molecular Bose-Einstein condensates, modeled by the mean-field equations with the quadratic three-wave interaction, characterized by mismatch α. The planar (effectively two-dimensional) SOC is applied to the soliton’s atomic component, structuring it as a mixed mode (MM) or semivortex (SV). The molecular component of the SV soliton is shaped as a 3D vortex, while the molecular component in the MM soliton is an MM too. The solitons exist up to a critical value of α. The system demonstrates a relatively large norm share of the vortex components, exceeding 50% of the total norm, which is an essential feature of SOC-supported solitons. This is a scheme for realizing stable vortex solitons in free space with the quadratic nonlinearity.

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Phys. Rev. Research 8, 033278– Published 4 September, 2026
  • Received 12 March 2026
  • Accepted 10 July 2026
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