Dimension-dependent stimulated radiative interaction of a single electron quantum wavepacket

Highlights: • We analyze theoretically and numerically stimulated interaction of a single electron quantum-wavepacket with coherent radiation when passing through a grating. • Net synchronous acceleration of a single electron is fundamentally impossible beyond a critical pre-interaction drift length of the electron. • Below this range, such wavepacket-dependent acceleration is possible, approaching the limit of classical 'point-particle' acceleration. • In quantum wave limit, our analysis emulates the FEL gain formula and exhibits quantum momentum recoil sidebands characteristics of PINEM. • We propose a method for experimental measurement of electron wavepacket size, which is a fundamental question in modern physics. - Abstract: In the foundation of quantum mechanics, the spatial dimensions of electron wavepacket are understood only in terms of an expectation value – the probability distribution of the particle location. One can still inquire how the quantum electron wavepacket size affects a physical process. Here we address the fundamental physics problem of particle–wave duality and the measurability of a free electron quantum wavepacket. Our analysis of stimulated radiative interaction of an electron wavepacket, accompanied by numerical computations, reveals two limits. In the quantum regime of long wavepacket size relative to radiation wavelength, one obtains only quantum-recoil multiphoton sidebands in the electron energy spectrum. In the opposite regime, the wavepacket interaction approaches the limit of classical point-particle acceleration. The wavepacket features can be revealed in experiments carried out in the intermediate regime of wavepacket size commensurate with the radiation wavelength.