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**Free-electron–bound-electron resonant interaction**

*Physical Review Letters*( IF 8.385 )

**Pub Date :**

Avraham Gover and Amnon Yariv

Here we present a new paradigm of Free Electron Bound-Electron Resonant Interaction (FEBERI) . This concept is based on recent demonstration of optical frequency modulation of free electron Quantum Electron Wavefunction (QEW) by an ultra-fast laser beam. We assert that a pulse of such QEWs that are correlated in their modulation phase, interact resonantly with two-level systems, inducing resonant quantum transitions when the transition energy $E=

更新日期：2020-01-14
*{21} $matches an harmonic of the modulation frequency: $*{21} =n*{b} $. Employing this scheme for Resonant Cathodoluminescence (RCL) and Resonant EELS combines the atomic level spatial resolution of electron microscopy with the high spectral resolution of lasers. The reality of the quantum electron wavefunction and its interpretation, have been a matter of debate since the inception of quantum theory [1,2]. Recent developments in ultrafast electron microscopy, and particularly Photon-Induced Near Field Electron Microscopy (PINEM) [3-10] demonstrated the possibility of modulating the energy spectrum of single Quantum Electron Wavepackets (QEW) at discrete energy sidebands $E*{n} =n*{b} $ by interaction with a laser beam of frequency$*{b} $. The interaction is made possible by a multiphoton emission/absorption process in the near field of a nanostructure [9, 11], a foil [10,8] or a laser-beat (pondermotive potential) [12, 37]. It was also shown that due to the nonlinear energy dispersion of electrons in free space drift, the discrete energy modulation of the QEW turns into tight bunching density modulation at attosecond short levels, corresponding to high spectral harmonics contents $*{n} =n*{b} $ in the expectation value of the QEW density:$ $. The physical reality of this sculpting of the QEW in the time and space (propagation coordinate – z) dimensions, can be demonstrated in the interaction of such modulated QEWs with radiation [13,14]. Such bunching-phase-sensitive resonant stimulated radiative interactions (acceleration/deceleration) of QEW have been demonstrated recently experimentally with a second laser beam, phase-locked to the bunching frequency or its harmonic [10,12,35,36]. Here we propose a new concept of Free-Electron Bound-Electron Resonant Interaction (FEBERI) based on the idea that optical frequency density modulated QEWs can interact resonantly with quantum electron transitions in matter at harmonics of its modulation frequency. Such interaction is shown schematically in Fig. 1a,b for the simple case of interaction with a single two-level system (2-LS) of a bound electron, e.g. in an atom, quantum-dot structure, defect center in crystal, etc. The interaction would lead to resonant transitions between the quantum levels 1 and 2 and corresponding energy loss/gain in the free electron energy. The resonant interaction can be monitored by measurement of the Electron Energy Loss/Gain Spectrum (EELS, EEGS) [19], or by measuring the fluorescence due to excitation of the bound electron to the upper level 2 and its radiative relaxation to the lower level 1 or possible other levels. In this sense, the effect will be a Resonant Cathodoluminescence (RCL) effect, showing enhanced CL [15] emission of the sample when the harmonic frequency of the interacting QEW $n…