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arXiv:2509.14506 · Nature Physics

Strong coupling of a microwave photon to an electron on helium

Gerwin Koolstra, E. O. Glen, N. R. Beysengulov, Heejun Byeon, Kyle E. Castoria, Michael J. Sammon, S. A. Lyon, D. G. Rees, J. Pollanen

Published Jun 15, 2026• 0 citations
arXivHTMLPDF
DOI
10.1038/s41567-026-03342-z

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Critical — Electron-On-Helium Photon Coupling As Spatial Check-Branch Custody — This article reads electron-on-helium microwave-photon coupling as a Spatial PTT check-branch custody problem. The source reports strong coupling between a resonator microwave field and the motional quantum state of a single electron on helium; the present work separates that physical coupling into payload, motional carrier, support, and photon metadata branch. The paper argues that the photon/resonator response is most useful when it remains branch-bound metadata rather than payload custody. It introduces the Bob incoming mismatch family for wrong, stale, shuffled, duplicated, time-shifted, role-converted, or unbound branches, and it identifies branch differentiation as the guardrail that prevents physically similar photon responses from cross-helping the wrong payload. The result is a bounded certification route: Strong payload and support can carry Strong-to-Weak check-branch custody with possible 0S0S0S-supported continuity, while valid endpoint collection requires both capsule match and branch match.
The in-plane motion of an electron on helium can couple to superconducting microwave resonators via electrical dipole coupling, offering a robust and rapid readout scheme. In previous efforts, microwave resonator designs for electrons on helium have lacked the coupling strength to reach the strong coupling regime, where coherent quantum effects outlast both electron and resonator decoherence rates. High-impedance superconducting microwave resonators offer a path to strong coupling, but integrating such resonators with electrons on helium remains an outstanding challenge. Here, we introduce a high-impedance resonator design compatible with strong coupling to electrons on helium. We fabricate and measure titanium nitride resonators with median internal quality factors of $3.9\ifmmode\times\else\texttimes\fi{}{10}^{5}$ and average impedance of 2.5 $\mathrm{k}\mathrm{\ensuremath{\Omega}}$, promising a sevenfold increase in coupling strength compared with standard 50-$\mathrm{\ensuremath{\Omega}}$ resonators. In addition, we develop a simplified resonator model from the capacitance matrix and sheet inductance that accurately predicts the mode frequencies, significantly simplifying the design process of future resonators for investigating quantum effects with electrons on helium.
Electrons on helium form a unique two-dimensional system on the interface of liquid helium and vacuum. A small number of trapped electrons on helium exhibits strong interactions in the absence of disorder, and can be used as a qubit. Trapped electrons typically have orbital frequencies in the microwave regime and can therefore be integrated with circuit quantum electrodynamics (cQED), which studies light-matter interactions using microwave photons. Here, we experimentally realize a cQED platform with the orbitals of single electrons on helium. We deterministically trap one to four electrons in a dot integrated with a microwave resonator, allowing us to study the electrons' response to microwaves. Furthermore, we find a single-electron-photon coupling strength of [Formula: see text] MHz, greatly exceeding the resonator linewidth [Formula: see text] MHz. These results pave the way towards microwave studies of Wigner molecules and coherent control of the orbital and spin state of a single electron on helium.