Three-mode resonant coupling of collective excitations in a Bose-Einstein condensate
Three-mode resonant coupling of collective excitations in a Bose-Einstein condensate
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玻色-爱因斯坦凝聚中集体激发的三模共振耦合
DOI：
10.1103/physreva.71.043609
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发表时间：
2005-04
影响因子：
2.9
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中科院分区：
文献类型：
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本文系统地研究了玻色-爱因斯坦凝聚体中零温集体激发的共振模耦合。(i)本文从Gross-Pitaevskii方程出发，用多尺度方法导出了三模共振相互作用（TMRI）的非线性耦合包络方程。(ii)我们计算的耦合矩阵元素的TMRI和显示，在以前的研究中出现的分歧，可以完全消除使用的束缚变分近似的基态波函数的凝聚。(iii)根据激发的对称性，我们给出了模-模相互作用过程[包括TMRI和二次谐波产生（SHG）]中的选择规则。(iv)通过求解非线性耦合包络方程，我们得到了TMRI和SHG过程的无发散非线性振幅，并表明我们关于凝聚体形状振荡的理论结果与实验结果符合得很好。我们还建议一个实验，以检查本研究的理论预测的集体激发在BEC的TMRI。
We make a systematic study of the resonant mode coupling of the collective excitations at zero temperature in a Bose-Einstein condensate (BEC). (i) Based on the Gross-Pitaevskii equation we derive a set of nonlinearly coupled envelope equations for a three-mode resonant interaction (TMRI) by means of a method of multiple scales. (ii) We calculate the coupling matrix elements for the TMRI and show that the divergence appearing in previous studies can be eliminated completely by using a Fetter-like variational approximation for the ground-state wave function of the condensate. (iii) We provide the selection rules in mode-mode interaction processes [including TMRI and second-harmonic generation (SHG)] according to the symmetry of the excitations. (iv) By solving the nonlinearly coupled envelope equations we obtain divergence-free nonlinear amplitudes for the TMRI and SHG processes and show that our theoretical results on the shape oscillations of the condensate agree well with the experimental ones. We suggest also an experiment to check the theoretical prediction of the present study on the TMRI of collective excitations in a BEC.