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arXiv:1702.04628

Dynamics of the localized nonlinear waves in spin-1 Bose-Einstein condensates with time-space modulation

Yuqin Yao, Wei Han, Li, Ji, Hui-Lan Wu, Wu‐Ming Liu

Published Feb 9, 2017• 1 citation
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Abstract

We investigate the dynamics of the localized nonlinear matter wave in spin-1 Bose-Einstein condensates with trapping potentials and nonlinearities dependent on time and space. We solve the three coupled Gross-Pitaevskii equation by similarity transformation and obtain two families of exact matter wave solutions in terms of Jacobi elliptic functions and Mathieu equation. The localized states of the spinor matter wave describe the dynamics of vector breathing solitons, moving breathing solitons, quasibreathing solitons and resonant solitons. The results of stability show that one order vector breathing solitons, quasibreathing solitons, resonant solitons, and the moving breathing solitons ψ_{\pm1} are all stable but the moving breathing solitons ψ_0 is unstable. We also present the experimental parameters to realize these phenomena in the future experiments.

DOI
10.48550/arxiv.1702.04628

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We investigate the dynamics of the localized nonlinear matter wave in spin-1 Bose-Einstein condensates with trapping potentials and nonlinearities dependent on time and space. We solve the three coupled Gross-Pitaevskii equation by similarity transformation and obtain two families of exact matter wave solutions in terms of Jacobi elliptic functions and Mathieu equation. The localized states of the spinor matter wave describe the dynamics of vector breathing solitons, moving breathing solitons, quasibreathing solitons and resonant solitons. The results of stability show that one order vector breathing solitons, quasibreathing solitons, resonant solitons, and the moving breathing solitons ψ_{\pm1} are all stable but the moving breathing solitons ψ_0 is unstable. We also present the experimental parameters to realize these phenomena in the future experiments.
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The time- and space-modulated nonlinearity is the important character of the Bose–Einstein condensates (BECs). Many works have been done on atomic BECs with spatially modulated nonlinearity, but there is little work on atomic–molecular BECs. In this paper, we construct one family of explicitly exact solutions of the atomic–molecular BECs with time- and space-modulated nonlinearities and trapping potential by similarity transformations. We discuss the dynamics of matter waves including breathing solitons, quasi-breathing solitons, resonant solitons and moving solitons. We analyze the linear stability of the solutions by adding various initial stochastic noise. We also provide the experimental parameters to produce these phenomena in future experiments.
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.
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