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arXiv:2608.16292

Quantum Wave-Particle Duality in Free-Electron--Free-Electron Entanglement

Du Ran, Jing-Yi Liu, Dan Jin, Peng-Yu Su, Reuven Ianconescu, Shuai Liu, Avraham Gover

quant-phSubmitted Aug 17, 2026• Announced Aug 18, 2026• 0 citations
v1 · Aug 17, 2026v2 · Aug 18, 2026
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Abstract

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.

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8 pages, 3 figures

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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\Gee\Gee and the logarithmic negativity \EN=arsinh⁡(\Gee)/ln⁡2\EN=\operatorname{arsinh}(\Gee)/\ln2\EN=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.
We present a comprehensive relativistic quantum-mechanical theory for interaction of a free electron with a bound electron in a model, where the free electron is represented as a finite-size quantum electron wave packet (QEW) and the bound electron is modeled by a quantum two-level system (TLS). The analysis reveals the wave-particle duality nature of the QEW, delineating the point-particle-like and wavelike interaction regimes and manifesting the physical reality of the wave function dimensions when interacting with matter. This QEW size dependence may be used for interrogation and coherent control of superposition states in a TLS and for enhancement of cathodoluminescence and electron energy-loss spectroscopy in electron microscopy.
Free-Electron Bound-Electron Resonant Interaction (FEBERI) is the resonant inelastic interaction of periodically density-bunched free electrons with a quantum two level system. We present a comprehensive relativistic quantum mechanical theory for this interaction in a model in which the electrons are represented as quantum electron wavepackets (QEW). The analysis reveals the wave-particle duality nature of the QEW, delineating the point-particle-like and wave-like interaction regimes, and manifesting the physical reality of the wavefunction dimensions and its density modulation characteristics in interaction with matter. The analysis comprehends the case of laser-beam-modulated multiple QEWs that are modulation-phase correlated. Based on the Born interpretation of the electron wavefunction we predict quantum transitions enhancement proportional to the number of electrons squared, analogous to superradiance.
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In this study, we investigate the effect of the Lorentz transformation on the measures of quantum coherence in an entangled atomic system. Here, we consider the effect of this relativistic boosts on two-particle entangled generalized Gaussian wave packets in two scenarios. In the first scenario, we consider that the relativistic boost affects the one particle and other remains unaffected while in the second scenario, we consider that both the particles are affected by the effect of the relativistic boost. The coherence of the wave function as measured by the boosted observer is studied as a function of the boost parameter and the width of the Gaussian wave packets. Using various formulations of coherence, it is shown that in general the coherence decays with increase in the width of the Gaussian wave packet, higher values of boost parameter, and the number of particles on which boost is applied.
The modulation and engineering of the free-electron wave function bring new ingredients to the electron-matter interaction. We consider the dynamics of a free-electron passing by a two-level system fully quantum mechanically and study the enhancement of interaction from the modulation of the free-electron wave function. In the presence of resonant modulation of the free-electron wave function, we show that the electron energy loss and gain spectrum is greatly enhanced for a coherent initial state of the two-level system. Thus, a modulated electron can function as a probe of the atomic coherence. We further find that distantly separated two-level atoms can be entangled through interacting with the same free electron. Effects of modulation-induced enhancement can also be observed using a dilute beam of modulated electrons.