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Physical Review A

Vortex light bullets in Rydberg atoms trapped in twisted PT -symmetric waveguide arrays

Si-Liu Xu, Junhao Li, Yiheng Hou, Jun-Rong He, Zhou Fan, Yuan Zhao, Liangwei Dong

Published Aug 6, 2024• 19 citations
Publisher

Abstract

We present a theoretical scheme for generating vortex light bullets (LBs) in a Rydberg atomic system. The stability property and propagation dynamics of vortex LBs with different topological charges are investigated in twisted circular waveguide arrays with a parity-time ($\mathcal{PT}$) symmetry. The numerical solutions of the corresponding nonlinear Schr\"odinger equation are obtained by the modified square operator method and split-step Fourier method. The longitudinal twist changes the stabilities of six-core vortex LBs and enriches the modulation diversity as the states with the opposite charges degenerate by the introducing of rotation frequency. Specifically, we reveal that the energy exchange between waveguides and media gives rise to the formation of necklace breathers, which is crucial for implementing light storage. These unique characteristics arise from the balance or quasibalance among the rotation frequency, the Rydberg-Rydberg interaction, and the nonequivalent gain/loss distribution along the azimuthal direction. We thus provide examples of robust high-charge vortex LBs and necklace breathers in the Rydberg atomic system with a $\mathcal{PT}$ symmetry.

DOI
10.1103/physreva.110.023508

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We present a theoretical scheme for generating vortex light bullets (LBs) in a Rydberg atomic system. The stability property and propagation dynamics of vortex LBs with different topological charges are investigated in twisted circular waveguide arrays with a parity-time (PT\mathcal{PT}PT) symmetry. The numerical solutions of the corresponding nonlinear Schr"odinger equation are obtained by the modified square operator method and split-step Fourier method. The longitudinal twist changes the stabilities of six-core vortex LBs and enriches the modulation diversity as the states with the opposite charges degenerate by the introducing of rotation frequency. Specifically, we reveal that the energy exchange between waveguides and media gives rise to the formation of necklace breathers, which is crucial for implementing light storage. These unique characteristics arise from the balance or quasibalance among the rotation frequency, the Rydberg-Rydberg interaction, and the nonequivalent gain/loss distribution along the azimuthal direction. We thus provide examples of robust high-charge vortex LBs and necklace breathers in the Rydberg atomic system with a PT\mathcal{PT}PT symmetry.
A scheme is proposed to generate stable light bullets (LBs) in a cold Rydberg atomic system with a parity-time (PT) symmetric potential, by utilizing electromagnetically induced transparency (EIT). Using an incoherent population pumping between two low-lying levels and spatial modulations of control and auxiliary laser fields, we obtain a two-dimensional (2D) periodic optical potential with PT symmetry. Based on PT symmetry potential and the long-range Rydberg-Rydberg atomic interaction, the system may support slow LBs with low light intensity. Further, it is found that the local and non-local nonlinear coefficients and PT-symmetric potential can be tuned and used to manipulate the behavior of LBs.
Abstract We propose an approach for generating robust two-dimensional (2D) vortex clusters (VCs) in a Rydberg atomic system by utilizing parity-time ( P T ) symmetric optical Bessel potential. We show that the system supports novel multi-core VCs with four and eight cores, corresponding to topological charges 2 and 4, respectively. The stability of these VCs can be dynamically adjusted through the manipulation of the gain-loss component, Kerr nonlinearities, and the degree of nonlocality inherent in the Rydberg atoms. These VCs are confined within the first lattice well of the Bessel potential, and both the power and width of lights undergo a quasi-periodic breathing phenomenon, which is attributed to the power exchange between the light fields and Bessel potential. Both self-attractive and self-repulsive Kerr interactions can sustain robust VCs within this system. The insights presented here not only facilitate the creation and manipulation of 2D VCs through P T -symmetric potentials but also pave the way for potential applications in optical information processing and transmission.
Rydberg electromagnetically-induced transparency has been widely studied as a medium supporting light propagation under the action of nonlocal nonlinearities. Recently, optical potentials based on moiré lattices (MLs) were introduced for exploring unconventional physical states. Here, we predict a possibility of creating fully three-dimensional (3D) light bullets (LBs) in cold Rydberg gases under the action of ML potentials. The nonlinearity includes local self-defocusing and long-range focusing terms, the latter one induced by the Rydberg-Rydberg interaction. We produce zero-vorticity LB families of the fundamental, dipole, and quadrupole types, as well as vortex LBs. They all are gap solitons populating finite bandgaps of the underlying ML spectrum. Stable subfamilies are identified utilizing the combination of the anti-Vakhitov-Kolokolov criterion, computation of eigenvalues for small perturbations, and direct simulations.
Realizing single light bullets and vortices that are stable in high dimensions is a long-standing goal in the study of nonlinear optical physics. On the other hand, the storage and retrieval of such stable high dimensional optical pulses may offer a variety of applications. Here we present a scheme to generate such optical pulses in a cold Rydberg atomic gas. By virtue of electromagnetically induced transparency, strong, long-range atom-atom interaction in Rydberg states is mapped to light fields, resulting in a giant, fast-responding nonlocal Kerr nonlinearity and the formation of light bullets and vortices carrying orbital angular momenta, which have extremely low generation power, very slow propagation velocity, and can stably propagate, with the stability provided by the combination of local and the nonlocal Kerr nonlinearities. We demonstrate that the light bullets and vortices obtained can be stored and retrieved in the system with high efficiency and fidelity. Our study provides a new route for manipulating high-dimensional nonlinear optical processes via the controlled optical nonlinearities in cold Rydberg gases.
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.
In recent years, vortex light, a distinctive form of structured light, has attracted considerable attention owing to its unique properties and the rich physical phenomena arising from its interaction with matter. In this paper, we investigate the propagation dynamics of vortex beams in a symmetry-broken three-level system based on forward and backward three-wave mixing (TWM) processes. We find that both processes enable the transfer of high-gain vortex light, with the associated topological charges obeying identical algebraic relations. The forward process exhibits periodic oscillatory transmission and modulates the transverse spatial profile of the generated signal vortex field, whereas the backward process features stable transmission and produces a signal field with higher gain and improved fidelity. Under the Autler-Townes splitting (ATS) regime, the probe field detuning in both schemes has a negligible influence on the gain. Optical depth influences only the rate at which the gain approaches its maximum, while the peak value remains unchanged. These results constitute a meaningful extension of the work reported in reference [40] and may provide a feasible approach for quantum communication, quantum computation, and the generation of high-gain, high-fidelity vortex light.