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.
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.
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.
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.
Quantum reflection refers to a nonvanishing reflection probability in the absence of a classically turning point. Much attention has been paid to such reflections due to their fundamental, intriguing physics and potential practical applications. Here we propose a scheme to realize a quantum reflection of nonlocal nonlinear optical beams in a cold Rydberg atomic gas via electromagnetically induced transparency working in a dispersion regime. Based on the long-range interaction between Rydberg atoms, we found that the system supports low-power nonlocal optical solitons. Such nonlocal solitons can display a sharp transition between reflection, trapping, and transmission when scattered by a linear attractive potential, created by gate photons stored in another Rydberg state. Different from conventional physical systems explored up to now, the quantum reflection of the nonlocal optical solitons in the Rydberg atomic gas exhibits interesting anomalous behavior, which can be actively manipulated by tuning the incident velocity and intensity of the probe field, as well as the nonlocality of the Kerr nonlinearity inherent in the Rydberg atomic gas. The results reported here are not only useful for developing Rydberg nonlinear optics but also helpful for characterizing the physical property of the Rydberg gas and for designing novel nonlinear optical devices.
Abstract Rydberg atoms, characterized by their giant polarizability and strong long-range interactions, provide an ideal platform for exploring optical nonlinearities. By coupling light to ensembles of Rydberg atoms, one can map the strong and nonlocal interactions between Rydberg atoms and light fields. A particularly important scheme for realizing such nonlinearity is electromagnetically induced transparency (EIT). This article presents a review of the research progress in nonlinear optics based on Rydberg-EIT systems, particularly nonlinear light propagation in Rydberg atomic gases. We first introduce the fundamental properties of Rydberg atoms and the physical mechanism of EIT-enhanced nonlinearity, emphasizing how the Rydberg blockade effect endows the system with a giant nonlocal Kerr nonlinearity. Subsequently, we discuss some typical nonlinear optical phenomena in such a system with focusing and defocusing nonlocal nonlinearities. In the focusing regime, we discuss spatial solitons, vortex solitons, soliton cloning, soliton molecules, optical bullets, and self-induced transparency solitons. Other topics are also discussed. In the defocusing regime, we analyze pattern formation and shock wave dynamics. Finally, we provide an outlook on the future development of this field toward quantum control, hybrid-system integration, and novel functional devices.
We propose a scheme to realize parity-time (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 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 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 symmetry and giant nonlocal optical nonlinearity.
Spontaneous symmetry breaking and formation of self-organized structures in nonlinear systems are intriguing and important phenomena in nature. Advancing such research to new nonlinear optical regimes is of much interest for both fundamental physics and practical applications. Here we propose a scheme to realize optical pattern formation in a cold Rydberg atomic gas via electromagnetically induced transparency. We show that, by coupling two Rydberg states with a microwave field (microwave dressing), the nonlocal Kerr nonlinearity of the Rydberg gas can be enhanced significantly and may be tuned actively. Based on such nonlocal Kerr nonlinearity, we demonstrate that a plane-wave state of a probe laser field can undergo a modulation instability (MI) and hence spontaneous symmetry breaking, which may result in the emergence of various self-organized optical patterns. Especially, we find that a hexagonal lattice pattern (which is the only optical pattern when the microwave dressing is absent) may develop into several types of square lattice ones when the microwave dressing is applied; moreover, as an outcome of the MI the formation of nonlocal optical solitons is also possible in the system. The optical patterns and nonlocal optical solitons found here can be flexibly manipulated by adjusting the effective probe-field intensity, nonlocality degree of the Kerr nonlinearity, and strength of the microwave field. Our paper opens a route for versatile controls of self-organizations and structural phase transitions of laser light, which may have potential applications in optical information processing and transmission.