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Matter-Wave Gap Solitons and Vortices in Three-Dimensional Parity-Time-Symmetric Optical Lattices

Jiawei Li, Yanpeng Zhang, Jianhua Zeng

Published Jan 1, 2021• 20 citations
Publisher

Abstract

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.

DOI
10.1016/j.isci.2022.104026

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We overview our recent theoretical studies on nonlinear atom optics of the Bose-Einstein condensates (BECs) loaded into optical lattices. In particular, we describe the band-gap spectrum and nonlinear localization of BECs in one- and two-dimensional optical lattices. We discuss the structure and stability properties of spatially localized states (matter-wave solitons) in 1D lattices, as well as trivial and vortex-like bound states of 2D gap solitons. To highlight similarities between the behavior of coherent light and matter waves in periodic potentials, we draw useful parallels with the physics of coherent light waves in nonlinear photonic crystals and optically-induced photonic lattices.
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.