Electron microscopes provide a powerful platform for exploring physical phenomena with nanoscale resolution, based on the interaction of free electrons with the excitations of a sample such as phonons, excitons, bulk plasmons, and surface plasmons. The interaction usually results in the absorption or emission of such excitations, which can be detected directly through cathodoluminescence or indirectly through electron energy loss spectroscopy (EELS). However, as we show here, the underlying interaction of a free electron and an arbitrary optical excitation goes beyond what was predicted or measured so far, due to the interplay of entanglement and decoherence of the electron-excitation system. The entanglement of electrons and optical excitations can provide new analytical tools in electron microscopy. For example, it can enable measurements of optical coherence, plasmonic lifetimes, and electronic length scales in matter (such as the Bohr radius of an exciton). We show how these can be achieved using common configurations in electron diffraction and EELS, revealing significant changes in the electron’s coherence, as well as in other quantum information theoretic measures such as purity. Specifically, we find that the purity after interaction with nanoparticles can only take discrete values, versus a continuum of values for interactions with surface plasmons. We quantify the post-interaction density matrix of the combined electron-excitation system by developing a framework based on macroscopic quantum electrodynamics. The framework enables a quantitative account of decoherence due to excitations in any general polarizable material (optical environment). This framework is thus applicable beyond electron microscopy. Particularly in electron microscopy, our work enriches analytical capabilities and informs the design of quantum information experiments with free electrons, allowing control over their quantum states and their decoherence by the optical environment.

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电子显微镜中的量子相关性

电子显微镜提供了一个强大的平台，可以基于自由电子与诸如声子，激子，体等离激元和表面等离激元的样品的激发相互作用，以纳米级分辨率探索物理现象。相互作用通常导致这种激发的吸收或发射，可以直接通过阴极发光或通过电子能量损失谱（EELS）进行间接检测。但是，正如我们在此处所示，由于电子激发系统的纠缠和去相干的相互作用，自由电子和任意光激发之间的潜在相互作用超出了迄今为止的预测或测量。电子和光激发的纠缠可以为电子显微镜提供新的分析工具。例如，它可以测量物质的光学相干性，等离子体寿命和电子长度标度（例如激子的玻尔半径）。我们展示了如何使用电子衍射和EELS中的常见配置实现这些目标，揭示了电子相干性以及其他量子信息理论方法（例如纯度）的重大变化。具体而言，我们发现与纳米粒子相互作用后的纯度只能取离散值，而不是与表面等离子体激元相互作用的连续值。我们通过开发基于宏观量子电动力学的框架来量化组合电子激发系统的相互作用后密度矩阵。该框架能够定量分析由于在任何普通可极化材料（光学环境）中的激发而引起的退相干。因此，该框架适用于电子显微镜以外的领域。特别是在电子显微镜中，我们的工作丰富了分析能力，并为自由电子的量子信息实验设计提供了信息，从而可以通过光学环境控制其量子态和去相干性。