Effective potentials for dilute Bose-Einstein condensates
Effective potentials for dilute Bose-Einstein condensates
复制标题
稀释玻色-爱因斯坦凝聚态的有效电势
DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
C. Greene
中科院分区：
文献类型：
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作者：
J. Bohn;B. Esry;C. Greene
基于普通薛定谔量子力学，给出了零温下玻色-爱因斯坦凝聚体(BEC)的理论公式。通过适当选择坐标和变分试探波函数，我们将多原子问题简化为一个比BEC理论中通常的非线性薛定谔方程更易于处理和解释的线性薛定谔方程。然后，普通量子力学半定量地再现了零温度BEC的许多主要特征，包括具有负散射长度的凝聚体中的临界原子数量。这一过程在结果上类似于最近求解非线性薛定谔方程的变分方法，但在本质上完全不同。此外，本程序代表了一种系统的替代方法中的一步，该方法用于计算被捕获的玻色子原子的定量准确的波函数。
We present a theoretical formulation of trapped, dilute Bose-Einstein condensates (BEC's) at zero temperature based on ordinary Schr\"odinger quantum mechanics. By a judicious choice of coordinates and of a variational trial wave function we reduce the many-atom problem to a linear Schr\"odinger equation that is easier to handle and interpret than the usual nonlinear Schr\"odinger equation of BEC theory. Ordinary quantum mechanics then reproduces, semiquantitatively, many of the main features of zero-temperature BEC, including the critical number of atoms in a condensate with negative scattering length. The procedure is similar in results, but completely different in spirit, to recent variational approaches to solving the nonlinear Schr\"odinger equation. Moreover, the present procedure represents a step in a systematic alternative method for computing quantitatively accurate wave functions for trapped bosonic atoms.