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Chaos An Interdisciplinary Journal of Nonlinear Science

Soliton evolution and associated sonic horizon formation dynamics in two-dimensional Bose–Einstein condensate with quintic-order nonlinearity

Ying Wang, Yujie Chen, Jun Dai, Zhao Li, Wen Wen, Wei Wang

Published Feb 1, 2021• 4 citations
Publisher

Abstract

This study explored the two-dimensional Bose-Einstein condensate with an inter-particle nonlinear interaction up to quintic order. Based on the two-dimensional Gross-Pitaevskii equation model with quintic-order nonlinearity, we first derived the bright soliton solution for the system based on the self-similar approach and the modified variational method. We identified that the kinematic quantities derived from the two methods agreed very well. The two-dimensional sonic horizon formation dynamics was then calculated based on the bright soliton solution that was obtained. The periodic formation and evolution patterns of the two-dimensional sonic horizon were quantitatively analyzed and pictorially illustrated. The results can be used to guide sonic black hole related phenomenon observations in a two-dimensional Bose-Einstein condensate with quintic-order nonlinearity.

DOI
10.1063/5.0031741

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This study explored the two-dimensional Bose-Einstein condensate with an inter-particle nonlinear interaction up to quintic order. Based on the two-dimensional Gross-Pitaevskii equation model with quintic-order nonlinearity, we first derived the bright soliton solution for the system based on the self-similar approach and the modified variational method. We identified that the kinematic quantities derived from the two methods agreed very well. The two-dimensional sonic horizon formation dynamics was then calculated based on the bright soliton solution that was obtained. The periodic formation and evolution patterns of the two-dimensional sonic horizon were quantitatively analyzed and pictorially illustrated. The results can be used to guide sonic black hole related phenomenon observations in a two-dimensional Bose-Einstein condensate with quintic-order nonlinearity.
Based on the Gross–Pitaevskii equation model that incorporates higher-order nonlinear interaction, we studied sonic black hole and sonic horizon formation involved in nonlinear dynamical evolution for Bose–Einstein condensates with higher-order nonlinear interaction. On the basis of the modified variational method and the scenario where the system starts dynamic evolution from ground state, we derived the typical system distribution width function, which is analytically formulated as periodic oscillation solution and monotonically damped variational oscillation solution under different parametric settings. We also calculated the criteria formula for sonic black hole horizon formation with regard to the two evolution modes: oscillation mode and monotonically decay mode, pictorially demonstrating the time interval of sonic horizon appearance. The theoretical results obtained here can be used to guide relevant experimental studies of sonic horizon and sonic black hole formation for Bose–Einstein condensates incorporating the higher-order nonlinear interaction effects.
We study the dynamics of sonic black hole horizon formation of quasi-one-dimensional (1D) Bose-Einstein condensate incorporating higher-order quintic nonlinear interaction. Based on the one dimensional Gross-Pitaevskii equation with nonlinearity up to the quintic order, we derived a novel analytical formula for the key dynamical variables of sonic horizon formation using the modified variational method and exact F-expansion method. We obtained good agreement between the key dynamical variables from the two different methods. The stabilization effects of higher-order nonlinear interaction along with the more precise location of the sonic horizon boundary were illustrated. The theoretical results obtained in this work can be used to guide relevant experimental observations of sonic black hole-related dynamics incorporating the effects of higher-order nonlinear interaction.
We study sonic horizon formation dynamics for Bose-Einstein condensate systems with higher-order nonlinear interaction. Based on the Gross-Pitaevskii equation incorporating higher-order nonlinear effects and through a variational method, we derived the criteria formula for sonic horizon occurrence. The key features of the sonic horizon are pictorially demonstrated, and we identified the stabilization and widening metastable effects of the higher-order nonlinear interaction, from which the quantitative results can be used to guide relevant experimental observations of sonic black holes with higher-order nonlinear effects.
We study the sonic horizon phenomena of the oscillating Bose-Einstein condensates in isotropic harmonic potential. Based on the Gross-Pitaevskii equation model and variational method, we derive the original analytical formula for the criteria and lifetime of the formation of the sonic horizon, demonstrating pictorially the interaction parameter dependence for the occur- rence of the sonic horizon and damping effect of the system distribution width. Our analytical results corroborate quantitatively the particular features of the sonic horizon reported in previous numerical study.
Abstract For Bose–Einstein condensates in two-dimensional scenarios, based on the Gross–Pitaevskii equation model with modified variational method, we studied first the oscillation and monotonic decay modes of isotropic vortices, then for asymmetric vortices, we studied the evolution modes with system isotropic potential and perturbations in angular direction. The corresponding stability of the rotating system with centrifugal potential is analyzed. We also calculated the criteria formula for the formation of sonic horizon corresponding to the occurrence of sonic black hole of isotropic Bose–Einstein condensate. For the asymmetric vortices evolution, we derived the corresponding oscillation and monotonously decay modes, calculated the stability features of the system under rotation, demonstrating the oscillation damping and monotonously accelerating effects for the system with rotating centrifugal potential. The theoretical results derived here can be used to guide the corresponding isotropic and asymmetric vortices experimental observation in two-dimensional Bose–Einstein condensates.
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