Real-time Monitoring of Neon Film Growth for Electron-on-Neon Qubits

TL;DR

The paper presents a real-time thickness monitor for neon films on superconducting circuits using a high-$T_c$ YBCO resonator, enabling control of Ne film growth near the triple point ($T_{TP}=24.56$ K). It compares liquid-phase and quench-condensation growth, revealing that solid films formed from liquid growth are highly stochastic in final thickness, while increasing microwave drive power reliably yields films under 100 nm due to localized heating. The findings reconcile triple-point wetting theory with observed Ne growth behavior and demonstrate a practical route to deterministic Ne films for electron-on-neon qubits. The approach also highlights the broader applicability of high-$T_c$ resonators for monitoring and controlling solid–gas interfaces in hybrid quantum systems.

Abstract

Electron-on-neon (eNe) charge states coupled to superconducting circuits are a promising platform for quantum computing. Control over the formation of these charge states requires techniques to track and control the growth of solid Ne films on the circuit surface. We demonstrate a real-time Ne film-growth monitor using high-transition-temperature (high-$T_c$) YBCO microwave resonators. The high $T_c$ enables tracking of the film thickness near Ne's triple temperature and below. Across more than 300 solidification experiments, we find that the final Ne thickness varies stochastically from a few nm to a few $μ$m for films solidified from the liquid phase. By increasing the driving power in the resonator, we consistently reduce the final thickness to below 100 nm. These results represent an important step toward controlled formation of Ne films for eNe qubits and highlight the broader utility of high-$T_c$ resonators for hybrid quantum systems.

Figures (5)

• Figure 1: Experimental setup to monitor cooling trajectories. (a) Diagram of the experimental setup in a 3 K cryostat. A capillary from room temperature feeds into the sample cell, enabling real-time Ne deposition and pressure monitoring. The sample cell is anchored to the low-temperature (3 K) stage of the cryostat. The capillary is heated with a nichrome wire, and the temperature of the sample cell is controlled by applying heat to the intermediate (40 K) stage of the cryostat, ensuring that the sample cell is the coldest part of the gas system. (b) The Ne phase diagram, with two illustrated deposition trajectories crossing the triple point (red dot) at 24.56 K; gas$\to$liquid$\to$solid is shown in blue, while gas$\to$solid is shown in orange. (c) The sample cell temperature rate of change versus temperature shows the effects of latent heat at different phase transitions. The gray dashed lines demark the condensation and deposition temperatures for the two trajectories. The spike in $dT/dt$ is the result of the latent heat of freezing while crossing the triple temperature.
• Figure 2: YBCO resonator thickness monitor. (a) Resonator design. The lower panel shows a (not to scale) cross-section of the chip with YBCO grown on a CeO$_2$ seed layer. The inset shows the corresponding lumped-element circuit diagram of a capacitor and an inductor in parallel to ground. (b) The resonator transmission $|S_{21}|^2$ versus frequency. (c) Measured $f_\mathrm{res}$ versus temperature. (d) Finite element modeling is used to estimate the Ne thickness from fractional frequency shifts of the resonator. Magenta is the conformal model, while green is the in-trench model. The dashed and solid lines correspond to liquid and solid phases, respectively. Side panels illustrate both Ne models on the chip surface. (e) Real-time tracking of Ne deposition onto the resonator at low temperature. At $t_\mathrm{start}$, Ne is injected via the gas manifold and $f_\mathrm{res}$ is recorded versus time. (f) Solid Ne thickness tracking over time, assuming a conformal growth morphology.
• Figure 3: Liquid and solid film growth monitoring. (a) The Ne phase diagram, (b) observed resonator frequency shifts, and (c) inferred film thickness versus temperature. Two initial gas quantities: 0.008 mol (blue) and 0.003 mol (orange) correspond to gas$\to$liquid$\to$solid and gas$\to$solid deposition trajectories respectively. The sample cell cooling rate is 0.07 K/min. The gray dashed lines denote approximate temperature regions of liquid film growth and solidification for the blue trajectory.
• Figure 4: Stochastic thickness of solid Ne films. (a) Five consecutive gas$\to$liquid$\to$solid deposition trajectories (0.006 mol Ne). For all trajectories, the onset of liquid condensation occurs at 25.5 K. The final film thickness varies significantly for the repeated trajectories. (b) Comparison of the solid film thickness (at 23.8 K) to the liquid film thickness (at 24.7 K) across different cooling rates. The resulting solid film varies between 10 nm and several tens of $\mu$m with weak dependence on the initial liquid thickness (correlation factor $r=0.6$, gray dashed line).
• Figure 5: Dependence of film dynamics on microwave driving power. (a) The observed resonance frequency shift as a function of driving power in the bare resonator, solid Ne film (thickness $\approx$ 300 nm, 23.8 K), and liquid film (thickness $\approx$ 1$~\mu$m, 24.7 K). (b) Resonator frequency shift for all three cases from (a) with green and blue traces corresponding to $-35$ dBm and 5 dBm respectively. (c) Abrupt reduction of the probe power results in near instantaneous changes in the profile for the bare and solid-Ne-covered resonator case. By contrast, we observe a slow relaxation of the frequency shift to its low power value for the liquid film. This behavior is accompanied by a relaxation of the sample cell temperature at a similar timescale. (d,e) Histograms of the final solid film thicknesses (at 23.8 K) when cooling with a $-54$ dBm and 5 dBm driving power.