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.
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.
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.
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.
We study the phenomena of long-wave and short-wave modulation instabilities (LMI and SMI) in Rydberg atomic gases within the framework of the nonlocal nonlinear Schrödinger equations in the local and nonlocal regions (characterized by the ratio of beam radius to radius of Rydberg blockade sphere), respectively. We further reveal the rich soliton dynamics arising from interactions of nonlinear waves triggered by LMI. We also show the variety of spatial self-organization pattern formations and their active manipulation due to SMI. Through a synthesis of theoretical analysis and numerical simulations, the self-organized optical structures reported here provide a way for realizing what we believe to be novel optical patterns and solitons based on Rydberg atomic gases.
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.
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 self-organized pattern formation in nonlinear systems are fundamental phenomena with broad implications. Studying these effects in cold atomic gases, particularly through the optical control of laser-dressed Rydberg atoms, bridges atomic physics and modern optics. Here, we investigate the ground-state matter-wave pattern formation in cold Rydberg-dressed Bose-Einstein condensates (BECs) with considerations of the Lee-Huang-Yang (LHY) correction and Raman-induced spin-orbit coupling (SOC). A surprising discovery is that the combination of these effects can induce spontaneous symmetry breaking in a plane-wave state of matter waves, giving rise to a variety of exotic self-organized structures, including stripes, positive and negative hexagons, squares, black-eye patterns, and quasi-lattices, among others. Furthermore, we uncover intriguing structural behaviors by considering inter- and intra-specific nonlocal interactions and the hard-core (contact, short-range) and soft-core (long-range) interactions. Our findings advance optical control of quantum matter, with potential applications in atomic-based information processing.