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Electrons trapped on the surface of cryogenic substrates (liquid helium, solid neon or hydrogen) are an emerging platform for quantum information processing made attractive by the inherent purity of the electron environment, the scalability of trapping devices and the predicted long lifetime of electron spin states. Here we demonstrate the spatial control and detection of single electrons above the surface of liquid helium at temperatures above 1 K. A superconducting coplanar waveguide resonator is used to read out the charge state of an electron trap defined by gate electrodes beneath the helium surface. Dispersive frequency shifts are observed as the trap is loaded with electrons, from several tens down to single electrons. These frequency shifts are in good agreement with our theoretical model that treats each electron as a classical oscillator coupled to the cavity field. This sensitive charge readout scheme can aid efforts to develop large-scale quantum processors that require the high cooling powers available in cryostats operating above 1 K., Comment: 12 pages, 6 figures

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., Comment: 15 pages, 7 figures, 2 tables

We describe a helium source cell for use in cryogenic experiments that is hermetically sealed $in$ $situ$ on the cold plate of a cryostat. The source cell is filled with helium gas at room temperature and subsequently sealed using a cold weld crimping tool before the cryostat is closed and cooled down. At low temperature the helium condenses and collects in a connected experimental volume, as monitored via the frequency response of a planar superconducting resonator device sensitive to small amounts of liquid helium. This on-cryostat helium source negates the use of a filling tube between the cryogenic volumes and room temperature, thereby preventing unwanted effects such as such as temperature instabilities that arise from the thermomechanical motion of helium within the system. This helium source can be used in experiments investigating the properties of quantum fluids or to better thermalize quantum devices., Comment: 5 pages, 3 figures