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Two-dimensional matter-wave solitons and vortices in competing cubic-quintic nonlinear lattices

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Abstract

The nonlinear lattice — a new and nonlinear class of periodic potentials — was recently introduced to generate various nonlinear localized modes. Several attempts failed to stabilize two-dimensional (2D) solitons against their intrinsic critical collapse in Kerr media. Here, we provide a possibility for supporting 2D matter-wave solitons and vortices in an extended setting — the cubic and quintic model — by introducing another nonlinear lattice whose period is controllable and can be different from its cubic counterpart, to its quintic nonlinearity, therefore making a fully “nonlinear quasi-crystal”.

A variational approximation based on Gaussian ansatz is developed for the fundamental solitons and in particular, their stability exactly follows the inverted Vakhitov–Kolokolov stability criterion, whereas the vortex solitons are only studied by means of numerical methods. Stability regions for two types of localized mode — the fundamental and vortex solitons — are provided. A noteworthy feature of the localized solutions is that the vortex solitons are stable only when the period of the quintic nonlinear lattice is the same as the cubic one or when the quintic nonlinearity is constant, while the stable fundamental solitons can be created under looser conditions. Our physical setting (cubic-quintic model) is in the framework of the Gross–Pitaevskii equation or nonlinear Schrödinger equation, the predicted localized modes thus may be implemented in Bose–Einstein condensates and nonlinear optical media with tunable cubic and quintic nonlinearities.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 61690224, 61690222, and 11204151), the Youth Innovation Promotion Association of the Chinese Academy of Sciences (Grant No. 2016357), the CAS/SAFEA International Partnership Program for Creative Research Teams, and partially the Initiative Scientific Research Program of the State Key Laboratory of Transient Optics and Photonics.

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  1. State Key Laboratory of Transient Optics and Photonics, Xi’an Institute of Optics and Precision Mechanics of CAS, Xi’an, 710119, China

    Xuzhen Gao & Jianhua Zeng

  2. University of Chinese Academy of Sciences, Beijing, 100084, China

    Xuzhen Gao

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  1. Xuzhen Gao
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arXiv: 1706.02500.

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Gao, X., Zeng, J. Two-dimensional matter-wave solitons and vortices in competing cubic-quintic nonlinear lattices. Front. Phys. 13, 130501 (2018). https://doi.org/10.1007/s11467-017-0697-3

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