用冷原子升降机方案填充陈绝缘体的拓扑保护边缘态及测量
Populating topologically protected edge states of a Chern insulator with the cold-atom elevator scheme and measurements
AI总结：
本文提出通过冷原子升降机方案填充陈绝缘体的边缘态，并引入瞬时投影测量，利用后选择提高手性边缘态中的粒子数或比例，同时发展了仅线性缩放于格点数的计算方法。
摘要：
二维陈绝缘体支持拓扑保护的手性边缘电流，这些电流可以在光晶格中的超冷原子实验中检测到。先前的研究表明，可以通过从储层转移粒子来填充陈绝缘体的一组选定边缘态。在这里，我们数值研究了在丢弃储层之前对储层进行瞬时投影测量的效果。通过这种方式，系统的最终状态是纯的，并由波函数描述。我们还表明，通过后选择，可能的测量结果有助于增加手性边缘态中的最终粒子数或百分比。如果没有测量步骤，物理可以用单粒子物理来描述。测量显著复杂化了描述。通过适当重写解析表达式，我们证明测量概率、期望值、期望值的平均值以及纯度仍然可以从测量前的状态计算，且对于固定粒子数，计算复杂度仅随格点数线性缩放。这使我们能够数值研究例如具有14个粒子和198个格点的设置。该方法普遍适用于守恒粒子数的无相互作用费米子模型。
英文摘要：
Two-dimensional Chern insulators support topologically protected, chiral edge currents, and these can be detected in experiments with ultracold atoms in optical lattices. It has previously been shown that one can populate a selected group of edge states of a Chern insulator by transferring particles from a reservoir. Here, we numerically investigate the effect of performing an instantaneous, projective measurement on the reservoir before the reservoir is discarded. In this way, the final state of the system is pure and described by a wavefunction. We also show that quite likely measurement outcomes can help to increase the final number or percentage of particles in the chiral edge states through postselection. Without the measurement step, the physics can be described in terms of single-particle physics. The measurement significantly complicates the description. By appropriately rewriting the analytical expressions, we show that measurement probabilities, expectation values, averages of expectation values, and purity can nevertheless be computed from the state before the measurement in a way that scales only linearly with the number of lattice sites for a fixed number of particles. This enables us to investigate a setup with, for instance, 14 particles and 198 lattice sites numerically. The approach applies generally to noninteracting, fermionic models that conserve the number of particles.
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