Spontaneous and stimulated radiative emission of modulated free-electron quantum wavepackets—semiclassical analysis

Abstract

Here we present a semiclassical analysis of spontaneous and stimulated radiative emission from unmodulated and optically-modulated free-electron quantum wavepackets. We show that the radiative emission/absorption and corresponding deceleration/acceleration of the wavepackets depend on the controllable 'history-dependent' wavepacket size. The characteristics of the radiative interaction when the wavepacket size (duration) is short relative to the radiation wavelength, are close to the predictions of the classical point-particle modelling. On the other hand, in the long-sized wavepacket limit, the interaction is quantum-mechanical, and it diminishes exponentially at high frequency. We exemplify these effects through the scheme of Smith-Purcell radiation, and demonstrate that if the wavepacket is optically-modulated and periodically-bunched, it exhibits finite radiative emission at harmonics of the modulation frequency beyond the limit of high-frequency cutoff. Besides, the radiation analysis is further extended to the cases of superradiant emission from a beam of phase-correlated modulated electron wavepackets. The features of the wavepacket-dependent radiative emission explain the classical-to-quantum transition, and indicate a way for measuring the quantum electron wavepacket size. This suggests a new direction for exploring light-matter interaction.

Free-Electron–Bound-Electron Resonant Interaction

“…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 a tight bunching density modulation at attosecond short levels, corresponding to high spectral harmonics contents ω n ¼ nω b in the expectation value of the QEW density hjΨðr; tÞj 2 i. 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 [14,15]. Such bunching-phase-sensitive resonant stimulated radiative interactions (acceleration or deceleration) of QEW have been demonstrated recently experimentally with a second laser beam, phase-locked to the bunching frequency or its harmonic [10,12,16,17].…”

“…In this Letter we neglect the effect of the 2-LS dipole moment on the QEWs (neglecting their interaction quantum recoil), and assume that the bound electron transition is governed by the Schrödinger equation e −inω b t , and B n are the coefficients of the harmonics. Maximal tight density bunching is attained after drift time t D;max ¼ T b =ð2Δp m =p 0 Þ past the laser modulation point, where T b ¼ 2π=ω b , and Δp m =p 0 is the momentum modulation amplitude of the electron relative to the average momentum [9,15]. Substantially high amplitude (B n > 0.3) harmonics are attainable up to the 20th harmonic [15] and beyond [25] (see Supplemental Material [24] SM-B).…”

“…Maximal tight density bunching is attained after drift time t D;max ¼ T b =ð2Δp m =p 0 Þ past the laser modulation point, where T b ¼ 2π=ω b , and Δp m =p 0 is the momentum modulation amplitude of the electron relative to the average momentum [9,15]. Substantially high amplitude (B n > 0.3) harmonics are attainable up to the 20th harmonic [15] and beyond [25] (see Supplemental Material [24] SM-B).…”

“…1(c)], is similar to the case of superradiance of a bunched electron beam. In this case PHYSICAL REVIEW LETTERS 124, 064801 (2020) the bunching of the electrons is modeled in terms of point particles [28] or quantum wave packets [15], and the bunched beam radiates at all harmonics nω b of the bunching frequency in proportion to N 2 e , similarly to Dicke's atomic superradiance [29,30].…”

Anomalous Photon-Induced Near-Field Electron Microscopy

“…Defining the point-particle-like acceleration regime as the regime where the damping of the QEW acceleration due to the Gaussian decay factor is less than Simulation Setup -To confirm our observations beyond perturbation analysis, we demonstrate the quantum characteristics of electron-light interaction in phase-space through numerical solution (see sup. B) of the Schrodinger equation for the example of stimulated SPR interaction of a QEW with the near field of a grating that we have analyzed earlier with semiclassical [17] and quantum electrodynamics formulations [16]. It is necessary to stress the significance of the quantum interference fringes in producing the PINEM and APINEM spectra.…”