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Physical Review A

Optical solitons and optical patterns controlled by a moiré lattice potential in a Rydberg atomic gas

Zeyun Shi, Lu Qin, Yuan Zhou, Yu Zhong, Guanghui Wang, Haibo Huang

Published Aug 12, 2024• 5 citations
Publisher

Abstract

We investigate the optical soliton and patterns within a system exhibiting a ladder-type Rydberg electromagnetically induced transparency configuration, controlled by a moir\'e lattice potential. By designing theoretically the optical moir\'e lattice, we study its localization-delocalization transition and numerically demonstrate the conditions for stable high-dimensional solitons in a commensurate and an incommensurate moir\'e lattice, respectively. Through modulation instability analysis and numerical simulations, on the one hand, we find that the solitons and vortices exhibit exceptional stability in the self-focusing Kerr nonlinear system. On the other hand, our simulations further reveal the emergence of various extended structures, including polygonal, hexagonal, square, annular, and droplet patterns in self-defocusing Kerr nonlinear system. We also demonstrate various structural phase transitions of the optical patterns by actively manipulating the moir\'e lattice constant and the strength of nonlinear interactions, resulting in a diverse range of ground-state patterns. Our paper provides a versatile platform for manipulating and controlling light-matter interactions in Rydberg atomic ensembles, opening avenues for future research in designing and controlling complex light structures using Rydberg atomic systems.

DOI
10.1103/physreva.110.023513

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We investigate the optical soliton and patterns within a system exhibiting a ladder-type Rydberg electromagnetically induced transparency configuration, controlled by a moir'e lattice potential. By designing theoretically the optical moir'e lattice, we study its localization-delocalization transition and numerically demonstrate the conditions for stable high-dimensional solitons in a commensurate and an incommensurate moir'e lattice, respectively. Through modulation instability analysis and numerical simulations, on the one hand, we find that the solitons and vortices exhibit exceptional stability in the self-focusing Kerr nonlinear system. On the other hand, our simulations further reveal the emergence of various extended structures, including polygonal, hexagonal, square, annular, and droplet patterns in self-defocusing Kerr nonlinear system. We also demonstrate various structural phase transitions of the optical patterns by actively manipulating the moir'e lattice constant and the strength of nonlinear interactions, resulting in a diverse range of ground-state patterns. Our paper provides a versatile platform for manipulating and controlling light-matter interactions in Rydberg atomic ensembles, opening avenues for future research in designing and controlling complex light structures using Rydberg atomic systems.
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.
We propose a physical setup to realize parity-time (PT) symmetric moiré optical lattices (ML) and nonlocal optical solitons in a cold Rydberg atomic system with electromagnetically induced transparency (EIT). We also show that based on the PT symmetry lattice strength and giant nonlocal Kerr nonlinearity originated from the strong, long-range atom–atom interaction, the system supports two-dimension (2D) nonlocal solitons with very low light intensity. By using numerical simulation method, we uncover the formation, properties, and dynamics of higher-order solitons and vortical ones. 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-symmetric moiré lattice parameters and giant nonlocal optical nonlinearity.
We investigate the formation and control of stationary optical patterns in a cold Rydberg atomic gas via double electromagnetically induced transparency. We show that, through the modulational instability of the plane-wave state of a laser field with two polarization components, the system undergoes a spontaneous symmetry breaking and hence the emergence of plentiful self-organized spatial optical structures, which can be manipulated by the ratio between the cross- and self-Kerr nonlinearities, the nonlocality degree of the Kerr nonlinearities, and the populations initially prepared in the two atomic ground states. Interestingly, a crossover from mixture to separation in space (optical phase separation) of the two polarization components occurs when the ratio between the cross- and self-Kerr nonlinearities exceeds a critical value. We also show that the system supports nonlocal two-component spatial optical solitons and vortices when the parameters of the system are selected suitably. The rich diversity and active controllability of the self-organized optical structures reported here provide a way for realizing novel optical patterns and solitons and their structural phase transitions based on Rydberg atomic gases.
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.
Realizing single light solitons that are stable in high dimensions is a long-standing goal in research of nonlinear optical physics. Here, we address a scheme to generate stable two-dimensional solitons in a cold Rydberg atomic system with a parity-time (PT) symmetric moiré optical lattice. We uncover the formation, properties, and their dynamics of fundamental and two-pole gap solitons as well as vortical ones. The PT symmetry, lattice strength, and the degrees of local and nonlocal nonlinearity are tunable and can be used to control solitons. The stability regions of these solitons are evaluated in two numerical ways: linear-stability analysis and time evolutions with perturbations. Our results provide an insightful understanding of solitons physics in combined versatile platforms of PT-symmetric systems and Rydberg–Rydberg interaction in cold gases.
Spontaneous pattern formation from a spatially homogeneous background of nonlinear systems driven out of equilibrium is a widespread phenomenon in nature. However, similar phenomena and their physical realization in nonlinear systems with external potentials of gain and loss remain a challenge. We propose a scheme to realize a new type of spatial pattern formation through the self-organization of laser light in a Rydberg-dressed atomic gas with self-defocusing Kerr nonlinearity as well as non-Hermitian optical potentials. We show that by a suitable design of control and assistant laser fields, non-Hermitian optical potentials with or without parity-time (PT) symmetry for the probe laser field can be created. We find that through the nonlocal Kerr nonlinearity contributed by the long-range atom–atom interaction, a constant-intensity wave (CIW) may undergo modulation instability and induce spontaneous symmetry breaking, resulting in the emergence of various self-organized optical structures, which can be actively manipulated by tuning the nonlocality degree of the Kerr nonlinearity and by designing the non-Hermitian optical potentials. The results reported here open a door for developing non-Hermitian nonlinear optics.