Jaynes-Cummings interaction between low energy free-electrons and cavity photons

The Jaynes-Cummings Hamiltonian is at the core of cavity quantum electrodynamics, and is ubiquitous in a variety of quantum technologies. The ability to implement and control the various aspects of this Hamiltonian is thus of paramount importance. However, conventional implementations relying on bound-electron systems are fundamentally limited by the Coulomb potential that bounds the electron, in addition to suffering from practical limitations such as requiring cryogenic temperatures for operation and fabrication inhomogeneity. In this work, we propose theoretically a new approach to realize the Jaynes-Cummings Hamiltonian using low energy free-electrons coupled to dielectric microcavities, and exemplify several quantum technologies made possible by this approach. Our approach utilizes quantum recoil, which causes a large detuning that inhibits the emission of multiple consecutive photons, effectively transforming the free-electron into a two-level system coupled to the cavity mode. We show that this approach can be used for generation of single photons with unity efficiency and high fidelity. We then generalize the concept to achieve a multiple-level quantum emitter through a suitable design of cavity modes, allowing for deterministic photon-pair generation and even a quantum SWAP gate between a cavity photon and a free-electron qubit. An increase in coupling strength by a factor of \sqrt(N) can be achieved when an entangled symmetric state of N electrons is used to drive the cavity. Tunable by their kinetic energy and phase-matching to light waves, quantum free-electrons are inherently versatile emitters with an engineerable emission wavelength. As such, they pave the way towards new possibilities for quantum interconnects between photonic platforms at disparate spectral regimes.