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Physical review. E

Stable three-dimensional vortex solitons of high topological charge in a Rydberg-dressed Bose-Einstein condensate with spin-orbit coupling

Yanchao Zhang, Chao Hang, Boris A. Malomed, Guoxiang Huang

Published Feb 11, 2025• 7 citations
Publisher

Abstract

Stable vortex solitons (VSs) are objects of great interest for fundamental studies and various applications, including particle trapping, microscopy, data encoding, and matter-wave gyroscopes. However, three-dimensional (3D) VSs with high topological charges, supported by self-attractive nonlinearities, are unstable against fragmentation, which eventually leads to internal blowup (supercritical collapse) of the fragments. Here, we propose a scheme for realizing stable 3D VSs with topological charges up to 5 and 6 in the two components of a binary, Rydberg-dressed Bose-Einstein condensate with spin-orbit coupling (SOC). We show that, if the SOC strength exceeds a critical value, the rotational symmetry of the VSs in the transverse plane gets broken, resulting in a separation of the two components. Nevertheless, the VSs with the broken symmetry remain stable. The VS stability domains are identified in the system's parameter space. Moreover, application of torque to the stable VSs sets them in the state of robust gyroscopic precession.

DOI
10.1103/physreve.111.024205

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Stable vortex solitons (VSs) are objects of great interest for fundamental studies and various applications, including particle trapping, microscopy, data encoding, and matter-wave gyroscopes. However, three-dimensional (3D) VSs with high topological charges, supported by self-attractive nonlinearities, are unstable against fragmentation, which eventually leads to internal blowup (supercritical collapse) of the fragments. Here, we propose a scheme for realizing stable 3D VSs with topological charges up to 5 and 6 in the two components of a binary, Rydberg-dressed Bose-Einstein condensate with spin-orbit coupling (SOC). We show that, if the SOC strength exceeds a critical value, the rotational symmetry of the VSs in the transverse plane gets broken, resulting in a separation of the two components. Nevertheless, the VSs with the broken symmetry remain stable. The VS stability domains are identified in the system's parameter space. Moreover, application of torque to the stable VSs sets them in the state of robust gyroscopic precession.
Stable vortex solitons (VSs) are objects of great interest for fundamental studies and various applications, including particle trapping, microscopy, data encoding, and matter-wave gyroscopes. However, three-dimensional (3D) VSs with high topological charges, supported by self-attractive nonlinearities, are unstable against fragmentation, which eventually leads to internal blowup (supercritical collapse) of the fragments. Here, we propose a scheme for realizing stable 3D VSs with topological charges up to 555 and 666 in the two components of a binary, Rydberg-dressed Bose-Einstein condensate (BEC) with spin-orbit coupling (SOC). We show that, if the SOC strength exceeds a critical value, the rotational symmetry of the VSs in the transverse plane gets broken, resulting in separation of the two components. Nevertheless, the VSs with the broken symmetry remain stable. The VS stability domains are identified in the system's parameter space. Moreover, application of torque to the stable VSs sets them in the state of robust gyroscopic precession.
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.
Abstract We present a novel approach for generating stable three-dimensional (3D) spatiotemporal solitons (SSs) within a rotating Bose–Einstein condensate, incorporating spin–orbit coupling (SOC), a weakly anharmonic potential and cold Rydberg atoms. This intricate system facilitates the emergence of quasi-stable 3D SSs with topological charges | m | ≤ 3 in two spinor components, potentially exhibiting diverse spatial configurations. Our findings reveal that the Rydberg long-range interaction, spin–orbit coupling, and rotational angular frequency exert significant influence on the domains of existence and stability of these solitons. Notably, the Rydberg interaction contributes to a reduction in the norm of topological solitons, while the SOC plays a key role in stabilizing the SSs with finite topological charges. This research of SSs exhibits potential applications in precision measurement, quantum information processing, and other advanced technologies.
We elaborate a mechanism for the creation of stable three-dimensional (3D) solitons in spin-orbit-coupled (SOC) atomic-molecular Bose-Einstein condensate, modeled by the mean-field equations with the quadratic three-wave interaction, characterized by mismatch ααα. The planar (effectively two-dimensional) SOC is applied to the soliton's atomic component, structuring it as a mixed mode (MM) or semi-vortex (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 ααα. The system demonstrates a relatively large norm share of the vortex components, exceeding 50%50\%50% of the total norm, which is an essential feature of SOC-supported solitons. This is scheme for realizing stable vortex solitons in free space with the quadratic nonlinearity.
We present numerical results for three-dimensional (3D) solitons with symmetries of the semi-vortex (SV) and mixed-mode (MM) types, which can be created in spinor Bose-Einstein condensates of Rydberg atoms under the action of the spin-orbit coupling (SOC). By means of systematic numerical computations, we demonstrate that the interplay of SOC and long-range spherically symmetric Rydberg interactions stabilize the 3D solitons, improving their resistance to collapse. We find how the stability range depends on the strengths of the SOC and Rydberg interactions and the soft-core atomic radius.
It is commonly known that two-dimensional mean-field models of optical and matter waves with cubic self-attraction cannot produce stable solitons in free space because of the occurrence of collapse in the same setting. By means of numerical analysis and variational approximation, we demonstrate that the two-component model of the Bose-Einstein condensate with the spin-orbit Rashba coupling and cubic attractive interactions gives rise to solitary-vortex complexes of two types: semivortices (SVs, with a vortex in one component and a fundamental soliton in the other), and mixed modes (MMs, with topological charges 0 and ±1 mixed in both components). These two-dimensional composite modes can be created using the trapping harmonic-oscillator (HO) potential, but remain stable in free space, if the trap is gradually removed. The SVs and MMs realize the ground state of the system, provided that the self-attraction in the two components is, respectively, stronger or weaker than the cross attraction between them. The SVs and MMs which are not the ground states are subject to a drift instability. In free space (in the absence of the HO trap), modes of both types degenerate into unstable Townes solitons when their norms attain the respective critical values, while there is no lower existence threshold for the stable modes. Moving free-space stable solitons are also found in the present non-Galilean-invariant system, up to a critical velocity. Collisions between two moving solitons lead to their merger into a single one.