自由电子-自由电子纠缠中的量子波粒二象性
Quantum Wave-Particle Duality in Free-Electron--Free-Electron Entanglement
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中文总结 AI 辅助
该研究通过相对论两电子波包理论，建立自由电子量子波包尺寸与电磁耦合产生的纠缠的直接联系，发现自由漂移可增大QEW宽度以增强纠缠，确立了自由电子波粒二象性与二分纠缠的关联。
中文摘要 AI 辅助
电子-电子相互作用的点粒子描述忽略了自由电子量子波包（QEW）的相干纵向延展。相对论两电子波包理论将QEW纵向尺寸确定为相互电磁耦合产生纠缠的直接控制参数。对于空间路径分离的两个电子，二次相互作用相位给出无量纲纠缠参数$\tilde{G}$，对数负性$\tilde{E}_N=\text{arsinh}(\tilde{G})/\text{ln}2$。含时薛定谔方程全计算证实了窄QEW的标度关系，并揭示了更大空间延展下的高阶库仑效应。自由漂移会增大相互作用点处的QEW宽度，同时保持动量概率分布，从而增强后续产生的纠缠。该结果建立了自由电子波粒二象性与二分纠缠的直接关联。
英文摘要
Point-particle descriptions of electron-electron interaction omit the coherent longitudinal extent of a free-electron quantum wave packet (QEW). A relativistic two-electron wave-packet theory identifies the longitudinal QEW size as a direct control parameter for entanglement generated by mutual electromagnetic coupling. For two electrons in spatially separated paths, the quadratic interaction phase gives a dimensionless entangling parameter $\Gee$ and the logarithmic negativity $\EN=\operatorname{arsinh}(\Gee)/\ln2$. Full time-dependent Schrödinger equation calculations confirm the scaling for narrow QEWs and reveal higher-order Coulomb effects at larger spatial extent. Free drift increases the interaction-point QEW width while preserving the momentum probability distribution, thereby enhancing the subsequently generated entanglement. The results establish a direct connection between free-electron wave-particle duality and bipartite entanglement.
