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Modern Physics Letters B

Sonic horizon formation for two-dimensional Bose–Einstein condensates with higher-order nonlinear interaction

Xia Yu, Xiaoning Liu, Yubin Jiao, Ying Wang, Xiangyu Ran, Chunchen Tang

Published Aug 24, 2023• 0 citations
Publisher

Abstract

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.

DOI
10.1142/s0217984923502147

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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.
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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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