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 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.
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 5 and 6 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 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.
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.
Applying an imaginary time evolution method (AITEM) to the system of Gross–Pitaevskii equations, we find two-dimensional stable solitons in binary atomic Bose–Einstein condensates with spin–orbit coupling (SOC) and the Rydberg–Rydberg interaction (RRI). The stability of 2D solitons by utilizing their norm and energy is discussed in detail. Depending on the SOC and Rydberg–Rydberg interaction, we find stable zero-vorticity and vortical solitons. Furthermore, we show that the solitons can be effectively tuned by the local and nonlocal nonlinearities of this system.
Solitons are self-trapped modes existing in various nonlinear systems. Creating stable solitons in two- and three-dimensional settings is a challenging goal in various branches of physics. Several methods have been developed theoretically and experimentally to achieve this, but few of them can support stable multi-dimensional solitons in free space. Recently, a new scheme using spin-orbit-coupling (SOC) has been proposed to create stable 2D solitons in Bose–Einstein condensates (BECs). This paper reviews recent theoretical progress on creating stable 2D solitons in spinor dipolar BEC with SOC, combined with long-range dipole-dipole interaction (DDI), Zeeman splitting (ZS) and contact nonlinearity, in free space. The continuous family of stable symmetric vortex solitons (SVS), asymmetric vortex solitons (AVS), as well as gap solitons (GS) is found via different settings. Their existence and stability conditions are summarized and discussed in detail. The mobility properties of these types of solitons are also addressed. For SVS, a potential method to manipulate its shape and mobility is investigated. These results are supposed to enrich our understanding of 2D solitons and help create multi-dimensional solitons in experiments.