飞行时间图像中隐藏的陈数
Chern numbers hiding in time-of-flight images
摘要：
提出了一种从超冷原子的飞行时间图像中检测拓扑不变量--陈数的方法。我们证明了格点费米子的整数量子霍尔态的陈数在原子的动量分布中留下了它们的指纹。我们分析表明，在两个极限情况下，大跳跃各向异性和连续极限的动量分布的局部极大值的数量是等于陈数。此外，我们的数值模拟超过这两个限制表明，这些局部最大值持续的参数范围。因此，冷原子实验中的日常观测值可以作为一个有用的工具来表征和可视化具有非平凡拓扑结构的量子态。
英文摘要：
We present a technique for detecting topological invariants -- Chern numbers -- from time-of-flight images of ultra-cold atoms. We show that the Chern numbers of integer quantum Hall states of lattice fermions leave their fingerprints in the atoms' momentum distribution. We analytically demonstrate that the number of local maxima in the momentum distribution is equal to the Chern number in two limiting cases, for large hopping anisotropy and in the continuum limit. In addition, our numerical simulations beyond these two limits show that these local maxima persist for a range of parameters. Thus, an everyday observable in cold atom experiments can serve as a useful tool to characterize and visualize quantum states with non-trivial topology.
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