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Journal of Modern Optics

Vector vortex solitons in two-component Bose–Einstein condensates with modulated nonlinearities and a harmonic trap

Si-Liu Xu, Wang Ze-qiang, Jun-Rong He, Li Xue, Milivoj R. Belić

Published Apr 6, 2018• 3 citations
Publisher

Abstract

We introduce vector solitary waves in two-component Bose–Einstein condensates with spatially modulated nonlinearity coefficients and a harmonic trapping potential. Using the self-similarity method, novel vector solitary waves are built with the help of Whittaker function, including multipole solutions and necklace rings. The stability of vortex soliton pairs is examined by direct numerical simulation; the results show that a new class of stable low-order vortex soliton pairs with n = 2 and m ≤ 3 can be supported by the spatially modulated interaction in the harmonic trap. Higher order vector-vortex soliton is found unstable over prolonged distances.

DOI
10.1080/09500340.2018.1455915

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The novel phenomena arising from Bose-Einstein condensates with spatially and spatiotemporally modulated nonlinearities in external potential is reviewed from a theoretical viewpoint. We first present theoretical analysis and numerical studies of the localized nonlinear matter waves in one-dimensional single and two-component BECs with spatially and spatiotemporally modulated nonlinearities, respectively. It is shown that the spatially or spatiotemporally modulated nonlinearity can support stable novel localized nonlinear matter waves such as the breathing solitons and moving solitons. Then the quasi-two-dimensional BEC with spatially modulated nonlinearity is investigated and we show that all of the BECs, similar to the linear harmonic oscillator, can have an arbitrary number of localized nonlinear matter waves with discrete energies. Their properties are determined by the principal quantum number and secondary quantum number. Moreover, we investigate the quantized vortices in a rotating BEC with spatiotemporally modulated interaction in harmonic and anharmonic potentials, respectively. The exact quantized vortex and giant vortex solutions are constructed explicitly by similarity transformation. Their stability behavior is examined by numerical simulation, which shows that a new series of stable vortex states which are defined by radial and angular quantum numbers, can be supported by the spatiotemporally modulated interaction in this system. We find that there exist stable quantized vortices with large topological charges in repulsive condensates with spatiotemporally modulated interaction.
Abstract We systematically construct vector solitary waves in harmonically trapped one-dimensional two-component Bose–Einstein condensates with unequal dispersion coefficients by a numerical continuation in chemical potentials from the respective analytic low-density linear limits to the high-density nonlinear Thomas-Fermi regime. The main feature of the linear states herein is that the component with the larger quantum number has instead a smaller linear eigenenergy, enabled by suitable unequal dispersion coefficients, leading to new series of solutions compared with the states similarly obtained in the equal dispersion setting. Particularly, the lowest-lying series gives the well-known dark-anti-dark waves, and the second series yields the dark-multi-dark states, and the following series become progressively more complex in their wave structures. The Bogoliubov-de Gennes spectra analysis shows that most of these states bear unstable modes, but they can be long-lived and remarkably all of them can be fully stabilized in suitable parameter regimes.
We introduce matter-wave vector azimuthons, i.e., spatially localized vortex states with azimuthal modulations of density, in multicomponent Bose-Einstein condensates. These localized states generalize spatially modulated vortex solitons introduced earlier in nonlinear optics [A. S. Desyatnikov, A. A. Sukhorukov, and Yu. S. Kivshar, Phys. Rev. Lett. 95, 203904 (2005)] and Bose-Einstein condensates [V. M. Lashkin, Phys. Rev. A 77, 025602 (2008)]. We find, numerically, nonrotating and rotating two-component azimuthons in a Bose-Einstein condensate with a negative scattering length confined by a quasi-two-dimensional parabolic trap.