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arXiv:2010.15756

Resonant Interaction of Modulation-correlated Quantum Electron Wavepackets with Bound Electron States

Avraham Gover, Bin Zhang, Du Ran, Reuven Ianconescu, A. Friedman, Jacob Scheuer, Amnon Yariv

Published Oct 29, 2020• 6 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2010.15756

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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.
We present a fully quantum model for the excitation of a bound electron based on the “free-electron bound-electron resonant interaction” (FEBERI) scheme. The bound electron is modeled as a quantum two-level system (TLS) at any initial quantum (qubit) state, and the free electron is presented as a pre-shaped quantum electron wavepacket (QEW). In the case that the QEW is short or modulated at optical frequency, the TLS quantum state may be coherently controlled with multiple modulation-correlated QEWs. For this case, we derive the transition probability of the TLS due to interaction with a multi-particle beam based on an analytical approximate solution of the Schrodinger equation that amounts to using Born’s probabilistic interpretation of the quantum electron wavefunction. We verify the credibility of the analytical model at its validity ranges using a fully quantum density matrix computation procedure. It is shown that the transition probability can grow quadratically with the number of correlated QEWs and exhibit Rabi oscillation. The study indicates a possibility of engineering the quantum state of a TLS by utilizing a beam of shaped QEWs.
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.
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.
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.
It has been shown that the spontaneous emission rate of photons by free electrons, unlike stimulated emission, is independent of the shape or modulation of the quantum electron wavefunction (QEW). Nevertheless, here we show that the quantum state of the emitted photons is non-classical and does depend on the QEW shape. This non-classicality originates from the shape dependent off-diagonal terms of the photon density matrix. This is manifested in the Wigner distribution function and would be observable experimentally through Homodyne detection techniques as a squeezing effect. Considering a scheme of electrons interaction with a single microcavity mode, we present a QED formulation of spontaneous emission by multiple modulated QEWs through a build-up process. Our findings indicate that in the case of a density modulated QEWs beam, the phase of the off-diagonal terms of the photon state emitted by the modulated QEWs is the harbinger of bunched beam superradiance, where the spontaneous emission is proportional to N_e^2. This observation offers a potential for enhancement of other quantum electron interactions with quantum systems by a modulated QEWs beam carrying coherence and quantum properties of the modulation.
It has been shown that the spontaneous emission rate of photons by free electrons, unlike stimulated emission, is independent of the shape or modulation of the quantum electron wavefunction (QEW). Nevertheless, here we show that the quantum state of the emitted photons is non-classical and does depend on the QEW shape. This non-classicality originates from the shape dependent off-diagonal terms of the photon density matrix. This is manifested in the Wigner distribution function and would be observable experimentally through homodyne detection techniques as a squeezing effect. Considering a scheme of electrons interaction with a single microcavity mode, we present a QED formulation of spontaneous emission by multiple modulated QEWs through a build-up process. Our findings indicate that in the case of a density modulated QEWs beam, the phase of the off-diagonal terms of the photon state emitted by the modulated QEWs is the harbinger of bunched beam superradiance, where the spontaneous emission is proportional toNe2. This observation offers a potential for enhancement of other quantum electron interactions with quantum systems by a modulated QEWs beam carrying coherence and quantum properties of the modulation.