双玻色子原子约瑟夫森结
Atomic Josephson junction with two bosonic species
摘要：
研究了双阱中存在两个相互作用的玻色-爱因斯坦凝聚体的原子约瑟夫森结（AJJ）。我们假设不同种类的玻色子相互作用。两个组分的宏观波函数服从两个三维耦合的Gross-Pitaevskii方程（GPE）。我们写出系统的拉格朗日量，并由此导出一个耦合常微分方程组（ODE），其中耦合摆表示力学模拟。这些微分方程控制分数不平衡和每个玻色子分量的相对相位的动力学行为。我们在保持对称性的点附近进行稳定性分析，得到稳定点附近振荡频率的解析公式。这样的公式可以用作种间s波散射长度的间接测量。我们还研究了每个分数不平衡在零和非零附近的振荡-宏观量子自陷（MQST）-时间平均值。对于不同的物种间相互作用振幅值，我们进行了这项研究，通过直接求解两个GPE和通过求解相应的耦合摆方程。我们表明，在一定的条件下，这两种方法的预测是很好的协议。此外，我们还计算了种间相互作用幅度的交叉值，该交叉值标志着MQST的开始。
英文摘要：
We study an atomic Josephson junction (AJJ) in presence of two interacting Bose-Einstein condensates (BECs) confined in a double well trap. We assume that bosons of different species interact with each other. The macroscopic wave functions of the two components obey to a system of two 3D coupled Gross-Pitaevskii equations (GPE). We write the Lagrangian of the system, and from this we derive a system of coupled ordinary differential equations (ODE), for which the coupled pendula represent the mechanic analogous. These differential equations control the dynamical behavior of the fractional imbalance and of the relative phase of each bosonic component. We perform the stability analysis around the points which preserve the symmetry and get an analytical formula for the oscillation frequency around the stable points. Such a formula could be used as an indirect measure of the inter-species s-wave scattering length. We also study the oscillations of each fractional imbalance around zero and non zero - the macroscopic quantum self-trapping (MQST) - time averaged values. For different values of the inter-species interaction amplitude, we carry out this study both by directly solving the two GPE and by solving the corresponding coupled pendula equations. We show that, under certain conditions, the predictions of these two approaches are in good agreement. Moreover, we calculate the crossover value of the inter-species interaction amplitude which signs the onset of MQST.
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