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

Abstract

The Jaynes-Cummings Hamiltonian is at the core of cavity quantum electrodynamics; however, it relies on bound-electron emitters fundamentally limited by the binding Coulomb potential. In this work, we propose theoretically a new approach to realizing the Jaynes-Cummings model using low-energy free electrons coupled to dielectric microcavities and exemplify several quantum technologies made possible by this approach. Using quantum recoil, a large detuning inhibits the emission of multiple consecutive photons, effectively transforming the free electron into a few-level system coupled to the cavity mode. We show that this approach can be used for generation of single photons, photon pairs, and even a quantum SWAP gate between a photon and a free electron, with unity efficiency and high fidelity. Tunable by their kinetic energy, quantum free electrons are inherently versatile emitters with an engineerable emission wavelength. Hence, they pave the way toward new possibilities for quantum interconnects between photonic platforms at disparate spectral regimes.

Strongly correlated multielectron bunches from interaction with quantum light

“…The use of free electrons for quantum computing has several unique advantages over using photon-based or bound electron–based systems. Free electrons readily propagate information across macroscopic distances and are thus a potential candidate for “flying qubits” ( 68 , 69 ), for instance via the phenomenon of free electron–polariton blockade, made possible by leveraging quantum recoil ( 70 , 71 ). These flying qubits are a core component of designing a potential quantum network or quantum internet, which has motivated implementations thus far in semiconductor systems and bound-electron systems ( 68 ).…”

Strong Coupling and Single-Photon Nonlinearity in Free-Electron Quantum Optics

“…), each electron emits on average |g Q | 2 photons, in a Poissonian distribution, while in the nonlinear regime 2 NL , we should expect a sub-Poissonian distribution, and vacuum Rabi oscillations as a function of |g Q |. 11 In Section S6, we calculate the total coupling efficiency for a general mode family (labeled by = s TM , TE , HE ij ij ij ), for a transition between initial and final transverse electron eigenstates (labeled "i" and "f"), for mth order phase-matching, and for the two types of phase-matching points, as…”

“…For a choice of nonlinearity 2κ = 1.5Δ, the electron excites a single cavity mode and is detuned from the rest, as can be seen in the cavity mode population (Figure 5e) and the evolution of the average photon numbers (Figure 5f), displaying a distinct vacuum Rabi oscillation. This is the so-called Jaynes− Cummings regime, 11 where the electron reduces to an effective two-level emitter interacting with a single mode. Another choice, this time of 2κ = Δ, makes sure that following every recoil, the electron is always phase-matched to a neighboring mode.…”

“…2,3,5,6,18−22 Specifically, measurement of free electrons' energy can be used for the heralded generation of quantum light, such as Fock states, 1,4,8,10,23−25 squeezed states 26 and even cat and GKP states. 9 More recently, it was predicted that free electrons could serve as ancillary qubits for quantum computation 15,16 and provide a platform for nonlinear electron dynamics 27,28 and deterministic single-photon nonlinearities 11,29,30 emerging from quantum recoil. 31,32 Owing to the nature of free-electron emitters, the anticipated single photon nonlinearity can span a vast spectral range 33,34 and operate on femtosecond-temporal and subwavelength-spatial resolution, 35−37 allowing new paradigms in quantum optical technologies.…”

Toward Optimum Coupling between Free Electrons and Confined Optical Modes

“…Several theoretical works have explored the use of free electrons to herald the production of single photons, entangled photons, and other nonclassical light states, − while a recent experiment has demonstrated Fock photon-state generation in optical resonators correlated with energy losses of the electron . A large electron–photon coupling is then required at the single-electron/single-photon level, which is currently achieved in such resonators by matching the phases of the electron excitation current and the light propagating inside a curved waveguide over an interaction distance of several microns .…”