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Results in Physics

Rydberg-dressed solitons in Bose-Einstein condensates with parity-time symmetry

Yuxi Xu, Yuan Zhao, Qihong Huang, De-Wei Wang, Zhuo Fan, L. Xue, Si-Liu Xu

Published May 10, 2023• 1 citation
Publisher

Abstract

Generating stable bright solitons in free space has been a long-standing goal in the study of matter waves in Bose-Einstein condensates (BECs). Rydberg-induced matter wave demonstrates an excellent effect in balancing the repulsive and attractive interactions between remote atoms. Parity-time (PT) symmetric lattices have been widely studied in controlling the flow of matter waves. In this study, we theoretically investigated the localization of nonlinear matter waves in the PT-symmetric Rydberg atomic BECs system. The numerical simulation method was used to obtain the stationary solutions of the wave function by solving the Gross-Pitaevskii equation (GPE) of the Rydberg-dressed BECs system. Fundamental, higher-order solitons and vortical ones were uncovered, and their stabilities were evaluated through linear-stability analysis and direct simulation with perturbation. Furthermore, the collision of solitons exhibited a quasi-elastic feature.

DOI
10.1016/j.rinp.2023.106534

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Generating stable bright solitons in free space has been a long-standing goal in the study of matter waves in Bose-Einstein condensates (BECs). Rydberg-induced matter wave demonstrates an excellent effect in balancing the repulsive and attractive interactions between remote atoms. Parity-time (PT) symmetric lattices have been widely studied in controlling the flow of matter waves. In this study, we theoretically investigated the localization of nonlinear matter waves in the PT-symmetric Rydberg atomic BECs system. The numerical simulation method was used to obtain the stationary solutions of the wave function by solving the Gross-Pitaevskii equation (GPE) of the Rydberg-dressed BECs system. Fundamental, higher-order solitons and vortical ones were uncovered, and their stabilities were evaluated through linear-stability analysis and direct simulation with perturbation. Furthermore, the collision of solitons exhibited a quasi-elastic feature.
Past decades have witnessed the emergence and increasing expansion of parity-time (PT )-symmetric systems in diverse physical fields and beyond as they license entirely all-real spectra, although being non-Hermitian. Nonlinear waves in low-dimensional PT -symmetric non-Hermitian systems have recently been explored broadly, whose understanding in higher dimensions remains abstruse and has yet to be revealed. We survey, theoretically and numerically, matter-wave nonlinear gap modes of Bose-Einstein condensates with repulsive interparticle interactions in three-dimensional PT optical lattices with emphasis on multidimensional gap solitons and vortices. Relying on direct perturbed simulations, we address the stability and instability areas of both localized modes in the underlying linearband gap spectra. Our study provides deep and consistent understandings of the formation, structural property, and dynamics of coherent localized matter waves supported by PT optical lattices in multidimensional space, opening a way for exploring and stabilizing three-dimensional localized gap modes in non-Hermitian systems.
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.
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.
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We investigate the properties of modulational instability in the Salerno equation in quasi-one dimension in Bose-Einstein condensate (BEC). We analyzed the regions of modulational instability of nonlinear plane waves and determine the conditions of its existence in BEC. The existence and stability of strongly localized modes in discrete media is investigated with the framework of the Salerno model by using a linear analysis method. The regions of stability and instability are determined. Also the existence of localized modes for different values of parameters is shown numerically by homoclinic orbits intersection method. The response of Bose–Einstein condensates is studied with strong dipole–dipole atomic interactions to periodically varying perturbation. The dynamics is governed by the Gross–Pitaevskii equation with an additional nonlinear term, corresponding to nonlocal dipolar interactions. A mathematical model, based on the variational approximation, has been developed and applied to study parametric excitation of the condensates due to coefficient of nonlocal nonlinearity varying periodically. The model predicts the waveform of solitons in dipolar condensates and describes their small amplitude dynamics quite accurately. Theoretical predictions are verified by numerical simulations of the nonlocal Gross–Pitaevskii equation and a good agreement between them is found. The results can lead to better understanding of the properties of ultra-cold quantum gases, such as 52Cr, 164Dy and 168Er, where the long-range dipolar atomic interactions dominate the usual contact interactions. Dynamics of a matter wave soliton bouncing on the reflecting surface (atomic mirror) under the effect of gravity has been studied by analytical and numerical means. The iv analytical description is based on the variational approach. Resonant oscillations of the soliton's center of mass and width, induced by appropriate modulation of the atomic scattering length and the slope of the linear potential are analyzed. In numerical experiments, we observe the Fermi type acceleration of the soliton when the vertical position of the reflecting surface is periodically varied in time. Analytical predictions are compared with the results of numerical simulations of the Gross-Pitaevskii equation and a qualitative agreement between them is found.