光晶格中物质波的传播：几何效应和平带效应
Matter-wave propagation in optical lattices: geometrical and flat-band effects
摘要：
可以设计光晶格的几何形状，允许研究原子沿着以图案排列的路径的传输，否则在固态下难以探测。原子系统中一个容易理解的问题是，物质波的传播速度是晶格几何的函数。为了解决这个问题，我们从理论上研究了几种二维光晶格几何中无相互作用和弱相互作用超冷费米子原子的量子输运。我们发现，三角形晶格具有更高的传播速度相比，正方形晶格，尽管支持更长的路径。体心正方形晶格有更长的路径，但传播速度更快。这个明显的悖论来自于动量态的混合，这导致了量子系统中不同的群速度。标准能带理论提供了一种解释，并允许一种系统的方法来搜索和设计具有可控物质波传播的系统。此外，一个平带的存在，如在一个双腿梯形几何导致一个动态的密度不连续性，这对比移动和本地化的原子在量子输运的行为。我们的预测是可以实现目前的实验能力。
英文摘要：
The geometry of optical lattices can be engineered allowing the study of atomic transport along paths arranged in patterns that are otherwise difficult to probe in the solid state. A question readily accessible to atomic systems is related to the speed of propagation of matter-waves as a function of the lattice geometry. To address this issue, we have investigated theoretically the quantum transport of non-interacting and weakly-interacting ultracold fermionic atoms in several 2D optical lattice geometries. We find that the triangular lattice has a higher propagation velocity compared to the square lattice, despite supporting longer paths. The body-centered square lattice has even longer paths, nonetheless the propagation velocity is yet faster. This apparent paradox arises from the mixing of the momentum states which leads to different group velocities in quantum systems. Standard band theory provides an explanation and allows for a systematic way to search and design systems with controllable matter-wave propagation. Moreover, the presence of a flat band such as in a two-leg ladder geometry leads to a dynamical density discontinuity, which contrasts the behavior of mobile and localized atoms in quantum transport. Our predictions are realizable with present experimental capability.
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