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Jisuan wuli

Dynamical Study on Interaction of Bose-Einstein Condensates

Xue‐Shen Liu

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

Symplectic method is applied to solve numerically 1D time-dependent Gross-Pitaevskii equation. Breathing of the condensate is numerically illustrated. Interaction of two Bose-Einstein condensates is investigated as external potential is zero at t=0. Interference between two condensates is observed. Evolution of density due to interference at various relative phases is studied.

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Symplectic method is applied to solve numerically 1D time-dependent Gross-Pitaevskii equation. Breathing of the condensate is numerically illustrated. Interaction of two Bose-Einstein condensates is investigated as external potential is zero at t=0. Interference between two condensates is observed. Evolution of density due to interference at various relative phases is studied.
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.
The interference between two condensates with repulsive interaction is investigated numerically by solving the one-dimensional time-dependent Gross–Pitaevskii equation. The periodic interference pattern forms in two condensates, which are prepared in a double-well potential consisting of two truncated harmonic wells centered at different positions. Dark solitons are observed when two condensates overlap. Due to the existence of atom–atom interactions, atoms are transferred among the ground state and the excited states, which coincides with the condensate energy change.
We review our recent theoretical advances in the dynamics of Bose-Einstein condensates with tunable interactions using Feshbach resonance and external potential. A set of analytic and numerical methods for Gross-Pitaevskii equations are developed to study the nonlinear dynamics of Bose-Einstein condensates. Analytically, we present the integrable conditions for the Gross-Pitaevskii equations with tunable interactions and external potential, and obtain a family of exact analytical solutions for one- and two-component Bose-Einstein condensates in one and two-dimensional cases. Then we apply these models to investigate the dynamics of solitons and collisions between two solitons. Numerically, the stability of the analytic exact solutions are checked and the phenomena, such as the dynamics and modulation of the ring dark soliton and vector-soliton, soliton conversion via Feshbach resonance, quantized soliton and vortex in quasi-two-dimensional are also investigated. Both the exact and numerical solutions show that the dynamics of Bose-Einstein condensates can be effectively controlled by the Feshbach resonance and external potential, which offer a good opportunity for manipulation of atomic matter waves and nonlinear excitations in Bose-Einstein condensates.
In this work we employ the split-step technique combined with a Legendre pseudospectral representation to solve various time-dependent GrossPitaevskii equations (GPE). Our findings based on the numerical accuracy of this approach applied for one-dimensional (1D) and two-dimensional (2D) problems show that it can provide accurate and stable solutions. Moreover, this approach has been applied to study the dynamics of the Bose-Einstein condensate which is modeled with the GPE. The breathing of condensate with a repulsive and attractive interactions trapped in 1D and 2D harmonic potentials has been simulated as well.