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Modern Physics Letters B

Sonic horizon formation for coupled one-dimensional Bose–Einstein condensate in an elongated harmonic potential

Ying Wang, Shuyu Zhou

Published Sep 27, 2018• 0 citations
Publisher

Abstract

We theoretically studied the sonic horizon formation problem for coupled one-dimensional Bose–Einstein condensate trapped in an external elongated harmonic potential. Based on the coupled (1[Formula: see text]+[Formula: see text]1)-dimensional Gross–Pitaevskii equation and F-expansion method under Thomas–Fermi formulation, we derived analytical wave functions of a two-component system, from which the sonic horizon’s occurrence criteria and location were derived and graphically demonstrated. The theoretically derived results of sonic horizon formation agree pretty well with that from the numerically calculated values.

DOI
10.1142/s0217984918503529

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We theoretically studied the sonic horizon formation problem for coupled one-dimensional Bose–Einstein condensate trapped in an external elongated harmonic potential. Based on the coupled (1[Formula: see text]+[Formula: see text]1)-dimensional Gross–Pitaevskii equation and F-expansion method under Thomas–Fermi formulation, we derived analytical wave functions of a two-component system, from which the sonic horizon’s occurrence criteria and location were derived and graphically demonstrated. The theoretically derived results of sonic horizon formation agree pretty well with that from the numerically calculated values.
We study the phenomena of the sonic horizon in an ultracold atomic Fermi system in an elongated harmonic trap.Based on the one-dimensional Gross-Pitaevskii equation model and variational method combined with exact derivation approach, we derive an analytical formula which describes the occurrence of the sonic horizon and the associated Hawking radiation temperature.Using a pictorial demonstration of the key physical quantities we identify the features reported in prior numerical studies of a three-dimensional (3D) ultracold atomic system, proving the applicability of the theoretical model presented here.
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.
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.
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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