一维光晶格中玻色凝聚气体高斯宽度与光晶格势强度的关系

Relationship of the Gaussian width of Bose-condensed gas and the intensity of ID-optical lattices potential

对囚禁在由谐振势和一维光晶格势构成的组合势中的玻色凝聚气体,基于Gross-Pitaevskii理论,并运用G-P能量泛函和变分方法,研究了组合势中子凝聚体的高斯宽度与光晶格势强度之间的关系。在分析了无相互作用的理想玻色气体的高斯宽度的基础上,提出了考虑相互作用后的高斯近似模型,并求解出高斯宽度随光晶格势强度变化的解析表达式。然后,将所得到的解析结果与直接的数值计算进行比较,表明高斯近似模型与数值计算结果更加接近,并且随着光晶格势强度的增加两者趋于一致。

Based on the Gross-Pitaevskii theory, for a Bose-condensed gas confined in a harmonic trap and in a one-dimensional （1D） optical lattice, the relationship of the Gaussian width of the sub-condenses and the intensity of 1D-optical lattices potential is studied by using the G-P energy functional and the variational method. For the ideal non-interacting model, the Gaussian width of the sub-condenses is analyzed. Concerning interacting Bosecondensed atoms, the Gaussian approximate model is advanced and the analytic expression of the Gaussian width with the intensity of optical lattices potential is obtained. And then, those analytical results are compared with the straightforward numerical calculation. It indicates that the Gaussian approximate model is closer to the results of the numerical solution, and both are reaching unanimity with the intensity of 1D-optical lattices potential increasing.