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Journal of applied physical science international

The Study of Formation of Sonic Black Hole in One-Dimensional Bose-Einstein Condensate

Haoquan Xu, Qingru Wang, Ying Wang, Qi Zhang, Xiaomei Liu, Chaohui Li

Published Oct 10, 2023• 0 citations
Publisher

Abstract

Based on the one-dimensional Gross-Pitaevskii equation (GPE) model, this work studies the formation of acoustic black holes in one-dimensional Bose Einstein condensate (BEC) in harmonic oscillator external potential, and extending the applicable scenarios of the GPE model for its specific application of simulating the formation conditions of acoustic black holes in one-dimensional systems. At the same time, We deepen the understanding of the analytical formula for determining the production conditions of acoustic black holes and the evolution formula of the radius of acoustic black holes.

DOI
10.56557/japsi/2023/v15i28411

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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 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 In this article, we study the dynamics of a Bose–Einstein condensate (BEC) with the idea of finding solutions that could possibly correspond to the so-called acoustic (or Unruh) black/white holes. These are flows with horizons where the speed of the flow changes from sub-sonic to super-sonic. This is because sound cannot return from the supersonic to the subsonic regions. The speed of sound plays the role of the speed of light in a gravitational black hole, with an important difference being that there are excitations that can go faster than the speed of sound and therefore can escape the sonic black hole. Here, the motion of the BEC is described by the Gross–Pitaevskii equation (GPE). More specifically, we discuss singular Stationary solutions of GPE in 2D (with circular symmetry) and 3D (with spherical symmetry). We use these solutions to study the local speed of sound and magnitude of flow velocity of the condensate to determine whether they cross, indicating the potential existence of a sonic analog of a black/white hole. We discuss the numerical techniques used and also study the semi-analytical Laplace–Borel resummation of asymptotic series solutions to see how well they agree with numerical solutions. We also study how the resurgent transseries plays a role in these solutions.
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.
In a previous article, we studied stationary solutions to the dynamics of a Bose-Einstein condensate corresponding to acoustic (or Unruh) black or white holes, namely, configurations where the flow becomes supersonic, creating a horizon for phonons. In this paper, we consider again the Gross-Pitaevskii equation, but looking for stationary numerical solutions in the case where the couplings are position dependent in a prescribed manner. Initially, we consider a two-dimensional quantum gas in a funnel-like spatial metric. We then reinterpret this solution as a solution in a flat metric but with spatially dependent coupling and external potential. In these solutions, the local speed of sound and the magnitude of flow velocity cross, indicating the existence of a supersonic region and therefore of sonic analogs of black and white holes and wormholes. We discuss the numerical techniques used. We also study phase (and density) fluctuations in these solutions and derive approximate acoustic metric tensors. For certain external potentials, we find uniform-density acoustic-black-hole configurations and obtain their Hawking temperature.
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.