Ultrafast quantum gates with fully quantized free-electron quantum optics

TL;DR

This work addresses realizing fully quantized free-electron quantum optics and universal quantum computing with flying electrons. It develops a cavity-free, grating-based platform where photon–electron interactions map onto Jaynes–Cummings and Tavis–Cummings models via Floquet–Bloch analysis, yielding the fully quantized PINEM Hamiltonian $\mathcal{H}_{\text{PINEM}}$ and a tunable coupling $g$. The authors demonstrate ultrafast single-qubit gates in the Bragg regime and two-qubit entangling gates, such as iSWAP, in the dispersive regime, achieving fidelities around $F \approx 0.99$ and gate times from tens of femtoseconds to a few picoseconds (e.g., $T_{\pi} = 43.3~\mathrm{fs}$; $T_{\text{iSWAP}} \sim 7.8~\mathrm{ps}$), enabling deterministic preparation of multi-qubit states like the $|W\rangle$ state. They outline scalable architectures with multiple flying electrons, readout via momentum-sideband detection by EELS, and applications in quantum simulation, sensing, and hybrid quantum technologies, outlining a path toward universal free-electron quantum computing.

Abstract

Free-electron quantum optics provides a versatile platform for manipulating electrons at the quantum level with potential applications in quantum information technologies. We propose a grating-based architecture for fully quantized free-electron quantum optics, in which photon-electron interactions map onto Jaynes-Cummings and Tavis-Cummings models via Bloch-Floquet analysis. Within this framework, we design ultrafast single- and two-qubit gates with cavity-free flying electrons, enabling universal quantum computing in experimentally accessible setups. More broadly, this framework establishes a platform for probing free-electron quantum optics and advancing quantum technologies in simulation, sensing, and information processing.

Figures (5)

• Figure 1: Schematic setup of the photon-electron interaction realizing an effective Jaynes-Cummings model. A free electron enters the near-field interaction region, generating a light-induced synthetic dimension. The on-site energy spacing restricts the momentum sidebands to form an effective two-level electron qubit. This configuration allows coherent quantum control and the implementation of gate operations within the Jaynes-Cummings framework.
• Figure 2: Numerical simulation of populations on momentum sidebands. (a) A resonant $\pi$-pulse flips the population $|g\rangle\rightarrow|e\rangle$ of a low-energy electron ($E_0 = 100~\mathrm{eV}$) using coherent light $|\alpha|=10$ in the UV regime ($\hbar\omega_L=6.20~\mathrm{eV}$). The dynamics closely follow the ideal Jaynes-Cummings model, with a strong vacuum field amplitude $\tilde{E}_z=7.48\times 10^6~\mathrm{V/m}$ at the diffraction limit, achieving an ultrafast gate time $T_\pi=43.3~\mathrm{fs}$ and fidelity of 0.994. The two-level approximation remains valid for slow electrons, with negligible leakage, as indicated by the dashed and dotted curves, even under a hundredfold increase of $\tilde{E}_z$. (b) Dispersive iSWAP gate mediated by a slightly detuned virtual photon of energy $6.24~\mathrm{eV}$ exchanges the populations $|eg\rangle \leftrightarrow |ge\rangle$ with a relative phase, following the Tavis-Cummings dynamics. The operation completes in $T_{\text{iSWAP}} = 7.81~\mathrm{ps}$ with $\tilde{E}_z=7.58\times 10^6~\mathrm{V/m}$, achieving a fidelity of 0.991.
• Figure 3: Density matrices of a three-qubit state after applying the first and second $\mathrm{iSWAP}(\theta_k)$ gates, targeting a $W$-state. The system starts from $|egg\rangle$ with $\theta_1=\arcsin(1/\sqrt{3})$ and $\theta_2=\pi/4$. Ideal matrix elements are shown as transparent boxes. The ultrafast gate sequence prepares the $W$-state with a fidelity of 0.992 within $8.65~\mathrm{ps}$. A relative phase on the second qubit can be removed by a virtual $\mathrm{R_z}(\pi/2)$ rotation to obtain a standard $W$-state.
• Figure S1: Quantum dynamics showing collapse and revival in the Bragg regime. The dispersion curvature of the slow electron ($\beta = 0.02$) suppresses higher and lower momentum sidebands, ensuring dynamics that follow the Jaynes-Cummings model exactly.
• Figure S2: Quantum dynamics showing collapse and revival in the Raman-Nath regime. For the faster electron ($\beta = 0.05$), the dispersion curvature no longer suppresses the higher and lower momentum sidebands, leading to collapse-revival behavior characteristic of a multilevel system rather than the standard Jaynes-Cummings or quantum Rabi model in the ultrastrong coupling regime without the RWA.