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arXiv:2206.02294 · Laser & Photonics Review

Stable High‐Dimensional Weak‐Light Soliton Molecules and Their Active Control

Lu Qin, Chao Hang, Boris A. Malomed, Guoxiang Huang

Published Aug 7, 2022• 25 citations
arXivHTMLPDF

Abstract

Abstract Bound states of solitons, alias soliton molecules (SMs), are well known in 1D systems, while making stable bound states of multidimensional solitons is a challenging problem because of the underlying instabilities. Here, a scheme for the creation of stable (2+1)D and (3+1)D optical SMs in a gas of cold Rydberg atoms is proposed, in which electromagnetically induced transparency (EIT) is induced by a control laser field. It is shown that, through the interplay of the EIT and the strong long‐range interaction between the Rydberg atoms, the system gives rise to giant nonlocal Kerr nonlinearity, which in turn supports stable (2+1)D spatial optical SMs, as well as ring‐shaped soliton necklaces, including rotating ones. They feature a large size, low generation power, and can be efficiently manipulated by tuning the nonlocality degree of the Kerr nonlinearity. Stable (3+1)D spatiotemporal optical SMs, composed of fundamental or vortex solitons, with low power and ultraslow propagation velocity, can also be generated in the system. These SMs can be stored and retrieved through the switching off and on of the control laser field. The findings reported here suggest applications to data processing and transmission in optical systems.

DOI
10.1002/lpor.202100297

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Abstract Bound states of solitons, alias soliton molecules (SMs), are well known in 1D systems, while making stable bound states of multidimensional solitons is a challenging problem because of the underlying instabilities. Here, a scheme for the creation of stable (2+1)D and (3+1)D optical SMs in a gas of cold Rydberg atoms is proposed, in which electromagnetically induced transparency (EIT) is induced by a control laser field. It is shown that, through the interplay of the EIT and the strong long‐range interaction between the Rydberg atoms, the system gives rise to giant nonlocal Kerr nonlinearity, which in turn supports stable (2+1)D spatial optical SMs, as well as ring‐shaped soliton necklaces, including rotating ones. They feature a large size, low generation power, and can be efficiently manipulated by tuning the nonlocality degree of the Kerr nonlinearity. Stable (3+1)D spatiotemporal optical SMs, composed of fundamental or vortex solitons, with low power and ultraslow propagation velocity, can also be generated in the system. These SMs can be stored and retrieved through the switching off and on of the control laser field. The findings reported here suggest applications to data processing and transmission in optical systems.
We investigate the formation of stable (2+1)-dimensional spatial-domain optical soliton molecules and breather molecules in a gas of Rydberg atoms, highlighting the role of the nonlocal nonlinearity, which is generated by the electromagnetically induced transparency in the Rydberg medium. The setting supports diverse species of large-size polygonal soliton molecules, including rectangular and oblique rhombuses, checkerboard cells, and hexagons. The analysis identifies two distinct formation regimes. In the case of moderately nonlocality, the long-range interactions alone stabilize the soliton molecules in the static form. In contrast, in the strongly nonlocal regime, initially imposed rotation is required to generate a centrifugal force that counteracts the strong attraction, resulting in stably rotating soliton molecules. The rotation period can be controlled by adjusting the system parameters. Furthermore, appropriate initial velocities can induce inherent breathing dynamics in the solitons, leading to the formation of breather molecules. Tuning the initial velocity, one can control the evolution of soliton molecules and breather molecules and even realize their mutual conversion. Our study offers a new scheme for engineering soliton molecules and breather molecules, and suggests new possibilities for the design of data processing and transmission in optical systems.
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.
XXX waves are a special type of wave packet that can maintain their transverse profile of XXX shape during propagation, and they are of much interest for the study of fundamental physics and practical applications. Here we present a scheme to generate nonlinear XXX waves and realize their active control by using a cold gas of Rydberg atoms via electromagnetically induced transparency (EIT). We show that, due to the EIT effect contributed by a control laser field and the strong, nonlocal Kerr nonlinearity contributed by Rydberg-Rydberg interaction between atoms, the system supports high-dimensional, nonlocal, and nonlinear optical XXX waves, which have low propagation loss, ultraslow propagation velocity, and ultralow generation power. We also show that the stability domain of such XXX waves can be greatly enlarged by increasing the nonlocality degree of the Kerr nonlinearity, and their motion trajectory can be manipulated by using an external magnetic field. Our study opens a route for generating and controlling nonlocal ultraslow nonlinear optical XXX waves, which may have promising applications in optical information processing and transmission.
We propose a scheme to realize parity-time (PT\mathcal{PT}PT) symmetry and nonlocal optical solitons in a cold Rydberg atomic system with electromagnetically induced transparency. We show that a two-dimensional (2D) periodic optical potential with PT\mathcal{PT}PT symmetry can be obtained for the propagation of probe laser field by using an incoherent population pumping between two low-lying levels and spatial modulations of control and assistant laser fields. We also show that, based on the giant nonlocal Kerr nonlinearity originated from the strong, long-range atom-atom interaction, the system supports 2D nonlocal gap solitons with very low light intensity. In particular, we find that the degree of the nonlocality of the Kerr nonlinearity, which can be actively tuned in our system, can be used to manipulate the phase transition of the PT\mathcal{PT}PT symmetry and the behavior of the nonlocal optical solitons. Our study opens a route for developing non-Hermitian nonlinear optics, especially for realizing and controlling high-dimensional weak-light optical solitons through adjustable PT\mathcal{PT}PT symmetry and giant nonlocal optical nonlinearity.
We propose a scheme to generate stable vector spatiotemporal solitons through a Rydberg electromagnetically induced transparency (Rydberg-EIT) system. Three-dimensional vector monopole and vortex solitons have been found under three nonlocal degrees. The numerical calculation and analytical solutions indicate that these solitons are generated with low energy and can stably propagate along the axes. The behavior of vector spatiotemporal solitons can be manipulated by the local and nonlocal nonlinearities. The results show a memory feature as these solitons can be stored and retrieved effectively by tuning the control field.
We propose a scheme to realize an optical Bessel potential with parity-time (PT\mathcal{P}TPT) symmetry and investigate the existence, propagation, and manipulation of multidimensional optical solitons through the interplay among diffraction, Kerr nonlinearity, and potential confinement in a cold atomic gas under the condition of electromagnetically induced transparency (EIT). We show that the system supports not only two-dimensional stationary optical solitons but also rotary ones; the stability of such solitons can be actively controlled by the gain-loss component (imaginary part), while the rotary motions can be tuned by the refractive-index component (real part) of the PT\mathcal{P}TPT-symmetric potential. Moreover, we demonstrate that the system allows the existence of stable three-dimensional spatiotemporal optical solitons, i.e., optical bullets, which have ultraslow propagation velocity and display helicoidal motions with controllable propagation trajectories. Due to the Kerr nonlinearity enhanced by the EIT effect, extremely low power is needed to create these multidimensional optical solitons. The results reported here are useful not only for the generation and manipulation of high-dimensional solitons via PT\mathcal{P}TPT-symmetric potentials, but also for promising applications in optical information processing and transmission.