Here we present a new paradigm of free-electron–bound-electron resonant interaction. This concept is based on a recent demonstration of the optical frequency modulation of the free-electron quantum electron wave function (QEW) by an ultrafast laser beam. We assert that pulses of such QEWs correlated in their modulation phase, interact resonantly with two-level systems, inducing resonant quantum transitions when the transition energy $\mathrm{\Delta }E=\hslash {\omega }_{21}$ matches a harmonic of the modulation frequency ${\omega }_{21}=n{\omega }_b$. Employing this scheme for resonant cathodoluminescence and resonant EELS combines the atomic level spatial resolution of electron microscopy with the high spectral resolution of lasers.

Do the prior history and the wave-packet size and form of a free electron have a physical effect in its interaction with light? Here we answer these fundamental questions on the interpretation of the electron quantum wave function by analyzing spontaneous and stimulated emissions of a quantum electron wave packet, interacting with a general, quantized radiation field. For coherent radiation (Glauber state), we confirm that stimulated emission and absorption of photons depends on the preinteraction-history-dependent size, exhibiting spectral cutoff when it exceeds the interacting radiation wavelength. Furthermore, stimulated emission of an optically modulated electron wave packet has a characteristic harmonic emission spectrum beyond the cutoff, which depends on the modulation features. In either case, there is no wave-packet-dependent radiation of the Fock state, and particularly the vacuum state spontaneous emission is wave-packet independent. The classical-to-quantum transition of radiation from the point-particle to the plane-wave limits, and the effects of wave-packet modulation indicate a way of measuring the wave-packet size of a single electron wave function, and suggest an alternative direction for exploring light-matter interaction.

We reveal the classical and quantum regimes of free electron interaction with radiation, common to the general variety of radiation sources (e.g., a Smith-Purcell radiation), the dielectric laser accelerator, and photo-induced near-field electron microscopy (PINEM). Modeling the electron with initial conditions of a coherent quantum electron wave packet, its topology in phase space uniquely defines a universal distinction of three interaction regimes: point-particle-like acceleration, a quantum wave function (PINEM), and a newly reported regime of anomalous PINEM (APINEM). The quantum interference beat of APINEM is capable of improving the spectral resolution of postselective electron microscopy. The particle-wave duality transition between regimes reveals the history-dependent nature of quantum electron interaction with light.

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.

Current shot-noise for a relativistic electron beam—proportional to the average current and frequency bandwidth of the beam—can be suppressed below the shot-noise limit at optical frequencies, through the exploitation of collective Coulomb interactions. The current shot-noise of an electron beam is proportional to its average current and the frequency bandwidth. This is a consequence of the Poisson distribution statistics of particles emitted at random from any source. Here we demonstrate noise suppression below the shot-noise limit in optical frequencies for relativistic electron beams. This process is made possible by collective Coulomb interaction between the electrons of a cold intense beam during beam drift1. The effect was demonstrated by measuring a reduction in optical transition radiation power per unit of electron-beam pulse charge. This finding indicates that the beam charge homogenizes owing to the collective interaction, and its distribution becomes sub-Poissonian. The spontaneous radiation emission from such a beam would also be suppressed (Dicke’s subradiance2). Therefore, the incoherent spontaneous radiation power of any electron-beam radiation source (such as free-electron lasers3,4) can be suppressed, and the classical coherence limits5 of seed-injected free-electron lasers6 may be surpassed.

We present a comprehensive theory for interrogation of the quantum state of a two-level system (TLS) based on a free-electron–bound-electron resonant interaction scheme. The scheme is based on free electrons, whose quantum electron wavefunction is preshaped or optically modulated by lasers in an electron microscope setup and then inelastically scattered by a quantum TLS target (e.g., atom, quantum dot, and crystal defect center) upon traversing in proximity to the target. Measurement of the postinteraction energy spectrum of the electrons probes and quantifies the full Bloch sphere parameters of a pre-excited TLS and enables coherent control of the qubit states. The exceptional advantage of this scheme over laser-based ones is atomic-scale spatial resolution of addressing individual TLS targets. Thus, this scheme opens horizons for electron microscopy in material interrogation and quantum information technology.