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Chinese Physics Letters

Vortex Solitons in Atomic–Molecular Bose–Einstein Condensates with a Square-Optical-Lattice Potential

Yuan Zhao, Wan Liu, Linjia Wang, Zhuo Fan, Qin Zhou, Boris A. Malomed, Shunfang Chen, Si-Liu Xu

Published Jul 29, 2025• 12 citations
Publisher

Abstract

Abstract We propose a theoretical framework, based on the two-component Gross–Pitaevskii equation (GPE), for the investigation of vortex solitons (VSs) in hybrid atomic–molecular Bose–Einstein condensates under the action of the stimulated Raman-induced photoassociation and square-optical-lattice potential. Stationary solutions of the coupled GPE system are obtained by means of the imaginary-time integration, while the temporal dynamics are simulated using the fourth-order Runge–Kutta algorithm. The analysis reveals stable rhombus-shaped VS shapes with topological charges m = 1 and 2 of the atomic component. The stability domains and spatial structure of these VSs are governed by three key parameters: the parametric-coupling strength ( χ ), atomic-molecular interaction strength ( g 12 ), and the optical-lattice potential depth ( V 0 ). By varying χ and g 12 , we demonstrate a structural transition where four-core rhombus-shaped VSs evolve into eight-core square-shaped modes, highlighting the nontrivial nonlinear dynamics of the system. This work establishes a connection between interactions of cold atoms and topologically structured matter waves in hybrid quantum systems.

DOI
10.1088/0256-307x/42/9/090002

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Abstract We propose a theoretical framework, based on the two-component Gross–Pitaevskii equation (GPE), for the investigation of vortex solitons (VSs) in hybrid atomic–molecular Bose–Einstein condensates under the action of the stimulated Raman-induced photoassociation and square-optical-lattice potential. Stationary solutions of the coupled GPE system are obtained by means of the imaginary-time integration, while the temporal dynamics are simulated using the fourth-order Runge–Kutta algorithm. The analysis reveals stable rhombus-shaped VS shapes with topological charges m = 1 and 2 of the atomic component. The stability domains and spatial structure of these VSs are governed by three key parameters: the parametric-coupling strength ( χ ), atomic-molecular interaction strength ( g 12 ), and the optical-lattice potential depth ( V 0 ). By varying χ and g 12 , we demonstrate a structural transition where four-core rhombus-shaped VSs evolve into eight-core square-shaped modes, highlighting the nontrivial nonlinear dynamics of the system. This work establishes a connection between interactions of cold atoms and topologically structured matter waves in hybrid quantum systems.
Abstract Vortex solitons (VSs) in spin-orbit-coupled (SOC) quantum gases are of fundamental interest due to their unique topological properties and potential applications in quantum information processing. We investigate the existence and stability of two-dimensional (2D) matter-wave VSs in a binary SOC Bose-Einstein condensate (BEC) of Rydberg atoms, confined by a radially periodic potential. By employing the imaginary-time integration method, we numerically demonstrate the formation of three distinct types of matter-wave soliton pairs, ring-shaped, necklace-shaped, and crescent-shaped, carrying topological charges up to 7. Their stability is systematically verified through temporal evolution and fidelity analysis. The SOC strength is found to be critical for supporting VSs with high topological charges. However, the presence of the external potential imposes a constraint on the SOC interaction, suppressing the generation of VSs with very high charges. A repulsive Rydberg-Rydberg interaction is identified as essential for balancing the diffraction and the SOC effect. Furthermore, the phase structures of these solitons exhibit a periodic modulation in the radial direction, inherited from the external potential. This study provides significant promise for applications in quantum information processing and the design of novel topological devices.
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We studied the evolution of vortex solitons in two-component coupled Bose-Einstein condensates trapped in a harmonic potential. Using a two-dimensional coupled Gross-Pitaevskii equation model and a variational method, we theoretically derived the vortex soliton solution. Under an appropriate parametric setting, the derived vortex soliton radius was found to oscillate periodically. The derived quasi-stable states with typical nonlinear features are pictorially demonstrated and can be used to guide relevant experimental observations of vortex soliton phenomena in coupled ultracold atomic systems.
Abstract In ultracold atomic gases, optical lattices and spin-orbit coupling are two important and useful linear means to study and control the nonlinear and quantum dynamics of matter waves, and both have been well realized in experiments. Here, nonlinear localization of spin-orbit-coupled Bose-Einstein condensates in moiré optical lattices is revealed theoretically, stressing the existence and stability of localized modes of diverse types including fundamental, half-vortex matter-wave gap solitons, and full-vortex ones (of both components). Notably, to our knowledge, a new type of vector vortex gap solitons, which is composed of a gap vortex soliton (singular mode) and a rhombic-array gap vortex (quadruple mode), is predicted in our two-component theoretical framework. It is also found that the model exhibits unique linear Bloch band structures including band splitting and extremely-flat bands, because of which all the predicted localized modes tend to be robustly stable, backed by our direct perturbed simulations. Our results demonstrate that the moiré pattern (and its joint cooperation with spin-orbit coupling) provides great possibilities to explore flat-band and moiré physics in ultracold atoms, and to further investigate the nonlinear dynamics.
We study the dynamics of the atomic and molecular Bose-Einstein condensates (BECs) of 87Rb^{87}\text{R}\text{b}87Rb in a spherically symmetric trap coupled by stimulated Raman photoassociation process. Considering the higher order nonlinearity in the atom-atom interaction we analyze the dynamics of the system using coupled modified Gross-Pitaevskii (MGP) equations and compare it with mean-field coupled Gross-Pitaevskii (GP) dynamics. Considerable differences in the dynamics are obtained in these two approaches at large scattering length, i.e., for large values of peak-gas parameter ${x}_{pk}\ensuremath{\ge}{10}^{\ensuremath{-}3}$. We show how the dynamics of the coupled system is affected when the atom-molecule and molecule-molecule interactions are considered together with the atom-atom interaction and also when the strengths of these three interactions are increased. The effect of detuning on the efficiency of conversion of atomic fractions into molecules is demonstrated and the feasibility of maximum molecular BEC formation by varying the Raman detuning parameter at different values of time is explored. Thus by varying the Raman detuning and the scattering length for atom-atom interaction one can control the dynamics of the coupled atomic-molecular BEC system. We have also solved coupled Gross-Pitaevskii equations for atomic to molecular condensate formation through magnetic Feshbach resonance in a BEC of 85Rb^{85}\text{R}\text{b}85Rb. We found similar features for oscillations between atomic and molecular condensates noted in previous theoretical study and obtained fairly good agreement with the evolution of total atomic condensate observed experimentally.