通过绝热哈密顿量的离散跳跃实现 Thouless 泵浦

中文摘要 AI 辅助

Thouless 泵浦是一种著名的拓扑效应，能够实现量子化的粒子输运，并在量子技术应用中具有前景。然而，标准的绝热泵浦理论要求在整个泵浦过程中哈密顿量必须连续且缓慢地变化。在本工作中，我们展示了仅通过对哈密顿量进行离散采样即可实现 Thouless 泵浦，从而消除了控制变量需连续且缓慢变化的传统约束。具体而言，我们选取哈密顿量的特定参数点进行常规的连续量子绝热演化，然后在这些参数点施加哈密顿量，从而诱导具有给定准动量的赝自旋的测地线演化。根据量子绝热演化的充要条件，这实现了用于 Thouless 泵浦的绝热演化。

英文摘要

Thouless pumping is a celebrated topological effect that enables quantized particle transport and holds promise for applications in quantum technologies. However, the standard adiabatic pumping theory dictate that the Hamiltonian must be varied continuously and slowly throughout the whole pumping process. In this work, we show that Thouless pumping can be realized by using only discrete sampling of the Hamiltonian, removing the conventional constraint of continuous and slow change of control. Specifically, we select particular parameter points of the Hamiltonian for conventional continuous quantum adiabatic evolution, and then apply the Hamiltonian at these parameter points which induces a geodesic evolution for the pseudospin with a given quasimomentum. This realizes an adiabatic evolution for the Thouless pumping according to a necessary and sufficient condition for quantum adiabatic evolution.

发表机构

• South China Normal University（华南师范大学）

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