Theory of quantum-coherent interactions between free electrons and photons

The short De-Broglie wavelength of the sub-relativistic enable electron microscopes atomic-scale precision spectroscopy and imaging. Hence, the second quantum revolution brings this field an important motivation: if we find new (ideally exploitable) physics involving free electrons, we could natively apply it to nano- and atomic scale quantum systems.

Being charged particles, free electrons exchange energy and momentum with polaritons such as photons, plasmons, excitons, and more. In that context, the semiclassical description works surprisingly well. Assuming a sub-femtosecond passage of a fast point-charge in the polaritonic electric field can reproduce the interaction with energy resolutions down to a few milli-eV, which is counterintuitive considering the Heisenberg uncertainty limit ħ/2 ~ 0.3 eV·fs. Furthermore, the interaction should entangle the electron and polariton states. Thus, it becomes necessary to formulate a unifying description that captures the quantum phenomena and reproduces the measured semi-classical behavior at the proper limits.

This talk discusses photons and their quantum coupling with electrons [1] through the perspectives of spontaneous cathodoluminescence (CL) and electron energy-loss spectroscopy (EELS), as well as laser-driven temporal shaping of the electron wavefunction (PINEM – photon-induced nearfield eˉ-microscopy). I specifically address phase-sensitive (i.e. coherent) aspects of these processes, with a focus on photons since they can carry quantum information to distant detectors, serving as “flying qubits”. The talk addresses two quantum-coherent processes of electron-photon coupling: one is the transfer of phase information by an electron beam, in which the free particle serves as a nonlinear-optics communication channel. The second is the prospect of transferring quantum information through entangled electron-photon pairs. I discuss the basics and pros and cons for mapping such electron-photon pairs temporally and spatially, alongside the means of quantifying their entanglement.