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Physical Review A

Parity-time symmetry along with nonlocal optical solitons and their active controls in a Rydberg atomic gas

Chao Hang, Guoxiang Huang

Published Oct 19, 2018• 37 citations
Publisher

Abstract

We propose a scheme to realize parity-time ($\mathcal{PT}$) 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 $\mathcal{PT}$ 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 $\mathcal{PT}$ 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 $\mathcal{PT}$ symmetry and giant nonlocal optical nonlinearity.

DOI
10.1103/physreva.98.043840

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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 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.
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.
Due to its myriad applications in many fields of science and technology, novel light diffraction from specially designed optical gratings is a subject of great interest. Here, we propose a scheme to realize the linear and nonlinear Bragg diffractions from an electromagnetically induced grating (EIG) with parity-time (PT)(\mathcal{PT})(PT) symmetry in a cold Rydberg atomic gas, where the Rydberg-Rydberg interaction between atoms are mapped to strong and long-range interaction between photons, characterized by a giant nonlocal Kerr nonlinearity. We show that a probe laser beam with very low light intensity incident upon the PT\mathcal{PT}PT-symmetric EIG can display distinctive asymmetric diffraction patterns, which can be actively manipulated through tuning the gain-absorption coefficient of the EIG and the input power of the laser beam. We also show that the intensity distribution among different diffraction orders depends significantly on the PT\mathcal{PT}PT-symmetry property of the EIG and on the magnitude and nonlocality degree of the Kerr nonlinearity. In addition, we demonstrate that such Bragg diffraction patterns can be controlled by an external gradient magnetic field, which provides a different way of diffraction control. The research results reported here are not only useful for understanding the unique properties of linear and nonlinear Bragg diffractions by PT\mathcal{PT}PT-symmetric gratings but may also be promising for designing optical devices applicable 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.
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.
Understanding and manipulating the non-Hermitian optical property based on coherent atomic gases is of great importance and has attracted much theoretical and experimental attentions. Advancing this study to the nonlinear optics regime is highly desirable due to its importance in fundamental physics and potential applications. In this work, we propose to realize a tunable electromagnetically induced grating (EIG) with parity-time (PT\mathcal{PT}PT) symmetry in a cold gas of Rydberg atoms, where interatomic interactions between Rydberg states are mapped to strong and long-range optical interactions, and investigate nonlinear light diffractions in this system. We show that for far-field diffraction, laser beams incident upon the PT\mathcal{PT}PT-symmetric EIG display distinctive asymmetric diffraction fringes, which can be actively manipulated through tuning the gain-absorption coefficient of the EIG, the incident intensity of the laser beam, and the nonlocality provided by Rydberg atoms. For near-field diffraction, the nonlinear Talbot diffraction carpets emerge and can be modulated by PT\mathcal{PT}PT symmetry in the presence of strong nonlocal interactions, allowing the realization of controllable optical self-imaging. The results are not only imperative for the study of non-Hermitian nonlinear optics but also useful for characterizing the interatomic interaction in Rydberg gases and for designing new optical devices useful in optical information processing and transmission.