High-impedance resonators for strong coupling to an electron on helium

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 $3.9\times 10^5$ and average impedance of 2.5 k$\Omega$, promising a seven-fold increase in coupling strength compared with standard 50$\Omega$ resonators. Additionally, 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.