Quantum electron-photon coupling has emerged from two seemingly distinct interactions of free-electron beams with light: stimulated energy gain- and loss driven by strong lasers, and spontaneous radiative electron-energy loss. The strength of the quantum coupling theory was their unification into one theoretical phenomenon, governed by one coupling amplitude, gQu. As a result, existing theory focuses almost exclusively on inelastic processes.

In this talk, I introduce a complementary regime: elastic quantum coupling between electrons and light. In this regime, the interaction leads to phase exchange between the quantum fields of the electrons and photons. Hence it is governed by a profoundly different coupling, gϕ. We develop a theoretical framework that reveals new perspectives on familiar phenomena. For example, we predict (i) photonic phase kickback in Kapitza-Dirac scattering, (ii) a fast electron acting as a birefringent refractive medium, and (iii) cumulative optical phase shifts from multi-electron transits. Additionally, we show quantitatively that well-designed optical resonators can preform quantum non-demolition (QND) measurements and thus form multi-electron states with sub-Poisson statistics.

Looking ahead, elastic interactions may open a route toward electron-number states with indistinguishable particles, which would push the performance of electron microscopes to below the shot-noise limit.