arXiv 2103.142052021-03cond-mat.quant-gasphysics.atom-ph

动量态晶格的Gross-Pitaevskii方程描述：陷阱和多体相互作用的作用

A Gross-Pitaevskii-equation description of the momentum-state lattice: roles of the trap and many-body interactions

Tao Chen, Dizhou Xie, Bryce Gadway, Bo Yan

备注：: 8 pages, 7 figures

摘要：

我们报告了一个理论描述的合成动量态晶格与三维Gross-Pitaevskii方程（GPE），其中外部陷阱势和平均场的空间密度依赖的多体相互作用自然包括和准确处理。GPE模型表现出更好的性能比紧束缚模型来描绘实验观察。由于陷阱修改了自由粒子的色散关系，并形成了导致非均匀相互作用的空间密度分布，因此即使在短时间内也会出现退相干（阻尼振荡）。我们对两态振荡的参数计算表明，我们应该在弱相互作用机制中使用相对较浅的陷阱，特别是当考虑长期动力学时。平均场相互作用的影响，即，研究了有限多态晶格链中的自陷行为、输运动力学和拓扑相变。这种非均匀相互作用的精确处理允许进一步调查的相互作用与无序，对关联动力学，和热化过程中的动量空间。

英文摘要：

We report a theoretical description of the synthetic momentum-state lattices with a 3D Gross-Pitaevskii equation (GPE), where both the external trap potential and the mean-field spatial-density-dependent many-body interactions are naturally included and exactly treated. The GPE models exhibit better performance than the tight-binding model to depict the experimental observations. Since the trap modifies the dispersion relation for free particles and shapes the spatial density distribution that leads to inhomogeneous interactions, decoherences (damping oscillation) appear even for a short-time evolution. Our parametric calculations for the two-state oscillation suggest that we should work with a relatively shallow trap in the weakly interacting regime, especially when the long-term dynamics are concerned. The impact of the mean-field interaction, i.e., the self-trapping behavior, on the transport dynamics and the topological phase transition in a finite multiple-state lattice chain is also specifically investigated. Such an accurate treatment of the inhomogeneous interactions allows for further investigations on the interplay with disorder, the pair correlation dynamics, and the thermalization process in momentum space.

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英文摘要：

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