Abstract
We studied the evolutionary patterns of two-dimensional Bose-Einstein condensates incorporating higher-order nonlinear interactions in harmonic potential. Using the Gross-Pitaevskii equation model with higher-order nonlinear corrections, we derived the analytical solitary vortex solutions via the variational method. The impact of the higher-order nonlinear interaction on the vortex dynamics is quantitatively analyzed, showing its key nonlinear feature contribution in the asymmetric vortex evolution with more precise evolutionary pattern generated. We found that, for the circular symmetric solution, if the nonlinear strength is not high, the higher-order nonlinear corrections essentially have only a tiny perturbative effect on the system’s quasi-static oscillation state, whereas for asymmetric evolution of the solitary vortex, incorporating higher-order corrections will generate an evolution pattern that better matches the results of numerical simulation. The theoretical results derived here can be used to guide relevant experimental studies of higher-order nonlinear effects in ultracold atomic systems.
Highlights
Nonlinear phenomena are among the most fascinating topics in ultracold atomic physics and optical science,[1,2,3,4,5,6,7,8,9,10] and have been heavily investigated both experimentally and theoretically within the past several decades
The soliton and vortex are the focus of nonlinear physics research owing to their appealing nonlinear features
We identified the perturbative nature of the higher-order term for the symmetric vortex, showing the robustness of the symmetric vortex when the leading order nonlinear interaction is relatively weak
Summary
Nonlinear phenomena are among the most fascinating topics in ultracold atomic physics and optical science,[1,2,3,4,5,6,7,8,9,10] and have been heavily investigated both experimentally and theoretically within the past several decades. One particular concern regarding the occurrence of the vortex is the stability-related issues that have been investigated in competing nonlinear media.[12] With the successful implementation of the Feshbach resonance experimental technique,[13,14] the atomic system’s inter-particle nonlinear interaction strength can be modulated continuously from −∞ to + ∞ (where “ + ” and “−” represent repulsive and attractive interactions respectively) Both theoretical[15] and experimental studies[16] show that, in systems where the leading-order nonlinear interaction strength effect alone is dominant, the solitary vortex can be stable,[16] and the modulational instability[17] can be suppressed if the leading nonlinear interaction strength is kept below a certain threshold value.
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