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Jisuan wuli

Interference of Three Bose-Einstein Condensates in One-dimensional Time-dependent Gross-Pitaevskii Equation

SU Ming-hui

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

Symplectic method is applied to solve 1D time-dependent Gross-Pitaevskii(GP) equation numerically.Interference of three Bose-Einstein condensates(BECs) is investigated with or without a trapping potential.Elastic collisions of BECs occur as trapping potential exists.If trapping potential is zero at t=0,interference of three BECs is observed and oscillation of probability density is found.

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Symplectic method is applied to solve 1D time-dependent Gross-Pitaevskii(GP) equation numerically.Interference of three Bose-Einstein condensates(BECs) is investigated with or without a trapping potential.Elastic collisions of BECs occur as trapping potential exists.If trapping potential is zero at t=0,interference of three BECs is observed and oscillation of probability density is found.
The symplectic method is applied to solve numerically the 1D time-dependent Gross-Pitaevskii(GP) equation.The interaction of two Bose-Einstein condensates is investigated when the external potential is exist or the external potential is set to zero.The elastic collision will occur when the external potential is exist.If the external potential is set to zero at t=0,the interference is observed between two condensates.While if the external potential is set to zero at t=2,the interaction between two condensates is complex.
We study certain stationary and time-evolution problems of trapped Bose-Einstein condensates using the numerical solution of the Gross-Pitaevskii (GP) equation with both spherical and axial symmetries. We consider time-evolution problems initiated by suddenly changing the interatomic scattering length or harmonic trapping potential in a stationary condensate. These changes introduce oscillations in the condensate which are studied in detail. We use a time iterative split-step method for the solution of the time-dependent GP equation, where all nonlinear and linear non-derivative terms are treated separately from the time propagation with the kinetic energy terms. Even for an arbitrarily strong nonlinear term this leads to extremely accurate and stable results after millions of time iterations of the original equation.
A one-dimensional (1D) Gross-Pitaevskii (GP) equation which governs the dynamics of Bose-Einstein condensates (BECs) with time-dependent scattering length in a harmonic potential is considered. Through a modified phase imprint transformation into the macroscopic order parameter, we suitably generate a derivative cubic-quintic Gross-Pitaevskii (DCQ-GP) equation that describes the dynamics of condensates in the harmonic potential for both twoand three-body interatomic interactions in the presence of nonlinear dispersion. Employing a modified lens-type transformation, we reduce the DCQ-GP equation into a derivative cubic-quintic Ginzburg-Landau (DCQ-GL) equation that allows us to investigate the modulational instability (MI) of the system and study, through the analytical exact solutions of the considered 1D GP equation, the effects of the three-body interactions and nonlinear dispersion on the dynamics of the BECs. We observe that for BECs with repulsive two-body interatomic interactions, the attractive three-body interactions and the nonlinear dispersion have opposite effects on the condensate: (i) The attractive three-body interactions enhance the instability, while the nonlinear dispersion softens the instability of the system; (ii) the attractive three-body interactions contributes to the ejections of atoms from the condensates while the nonlinear dispersion contributes to the accumulation of atoms in the condensates; (iii) the attractive three-body interactions contributes to the broadening of the matter wave solitons, while the nonlinear dispersion contributes to the compression of the matter wave solitons.
Quantum phenomena appear in a macroscopic scale in Bose-Einstein condensates. The Gross-Pitaevskii (GP) equation describes the dynamics of the weakly interacting Bose-Einstein condensates. The GP equation has a form of the Schroedinger equation with self-interaction. The coupled Gross-Pitaevskii equations are used to describe some mixtures of Bose-Einstein condensates. In this paper, we will show some numerical results of coupled Gross-Pitaevskii equations without self-interaction, which has a form of nonlinearly-coupled Schroedinger equations. We demonstrate that the macroscopic oscillation and the interference of two quantum wave packets decay in time owing to mutual interaction, which is analogous to the decoherence in quantum mechanics of many particles.