NbTiN Nanowire Resonators for Spin-Photon Coupling on Solid Neon

TL;DR

This work addresses scalable spin qubits by coupling an electron on solid neon to microwave photons in a high-impedance NbTiN nanowire resonator. It experimentally demonstrates that neon and electron depositions do not degrade the resonator quality and, from a design perspective, couples charge to photons with a strong potential for spin–photon coupling via local magnetic gradients. The authors show a viable micromagnet geometry that yields b_perp ≈ 2π×1 GHz and, with typical parameters, a spin–photon cooperativity C ≳ 10^6, enabling strong coupling; they predict single- and two-qubit gate fidelities approaching or exceeding 99.9% using natural neon, with potential to reach >99.999% for single-qubit gates through optimization. These results point toward scalable spin qubit networks with electrons on neon, balanced by strategies to preserve resonator Q in integrated devices.

Abstract

Electrons floating on a solid neon exhibit long charge coherence times, making them attractive for hybrid quantum systems. When combined with high-quality, high-impedance superconducting resonators and a local magnetic field gradient, this platform enables strong charge--photon and spin--charge coupling-key ingredients for scalable spin qubit architectures. In this work, we demonstrate that NbTiN nanowire resonators maintain high quality factors around 10^5 after depositing solid neon onto the resonators and subsequently loading electrons onto the neon surface, validating their suitability for electrons-on-neon platforms. Building on these experimental results, we theoretically analyze micromagnet designs and coupling strategies that can enable spin-photon interactions in this platform. Our analysis outlines performance targets for next-generation devices, showing that, at the charge sweet spot, spin qubit gate fidelities exceeding 99.99% for single-qubit operations and 99.9% for two-qubit operations are achievable with natural neon.

Figures (9)

• Figure 1: (a) Schematic overview of the electrical setup within the dilution refrigerator and at room temperature (RT). Input lines are attenuated with attenuators by $60\,\text{dB}$ in total, with output lines equipped with an LNF-LNC4_8C amplifier at $4\,\text{K}$ and an LNF-LNR4_8ART amplifier at RT. The diagram also includes an optical micrograph of the measured device on the $10\,\mathrm{mK}$ plate, showing three resonators—Resonator 1, Resonator 2, and Resonator 3—all sharing a single microwave (MW) feed line. (b) Conceptual illustration of Resonator 1. The nanowire resonator is shown in pink. Two black rounded squares represent grounded regions, with both the interior of the squares and the surrounding exterior connected to ground. SEM images of the enlarged areas highlight the two ends of the resonator. A schematic illustration of vertical cross-sections along line P is also presented. (c) Transmission response of Resonator 1 measured at $10\,\mathrm{mK}$ with a Vector Network Analyzer (VNA). The blue lines represent the measured $S_{21}$ in linear amplitude and phase before the deposition of solid neon or electrons. The orange lines are constructed from the best fit using the method described in Refs. Probst2015-gsProbst2024resonator.
• Figure 2: (a) Resonance peaks of Resonator 2 measured at $3.4\,\mathrm{K}$ over time. The vertical red dashed lines indicate the moments when electrons were emitted, with the applied filament voltages shown next to each. The red crosses mark the resonance peaks used to extract the resonance frequency shift and $Q_\mathrm{int}$ in (b) and (c), respectively. The inset displays the I-V curve of the filament. (b) The resonance frequency shift $\Delta f$, where the errors are smaller than the data points. (c) The inverse quality factor $1/Q_\mathrm{int}$. The error bars correspond to 95% confidence.
• Figure 3: (a) Addition of Co magnets (gray) near the gap between the two ends of Resonator 1. In the cross-sectional view, the black line schematically represents the electrical potential experienced by the electron. (b) The magnetic field gradient in the $z$-direction along the $y$-axis, $\frac{\partial B_z}{\partial y}$, is shown as a function of the vertical distance $\Delta z$ between the center position of the Co magnet and the electron, for various Co thicknesses ranging from $20\,\text{nm}$ to $100\,\text{nm}$. (c) The absolute values of the offsets of the $y$- and $z$-components of the magnetic field at the electron’s position (i.e., at the potential minima), as well as the $y$- and $z$-components at the position of the NbTiN resonator, are plotted as functions of the Co thickness. For each Co thickness, the Ti thickness is optimized to maximize $\frac{\partial B_z}{\partial y}$.
• Figure 4: (a) Single-qubit gate error as a function of the spin--charge coupling strength $\Lambda$. For Scenario 1, the green and red dotted lines show $1 - F_1(0)$ and $1 - \overline{F_1}$, with the minimum at $\Lambda = 0.40$ (vertical green dashed line). For Scenarios 2 and 3, the blue and cyan lines show $1 - F_1(0)$, respectively. For Scenario 2, the error is minimized at $\Lambda = 0.057$, as indicated by the vertical blue dashed line. (b) iSWAP gate error $1 - F_2$ as a function of $\Lambda$, calculated from Eq. \ref{['eq:iSWAP']}, for Scenario 1 (green line) with a minimum at $\Lambda = 0.37$ (vertical green dashed line), and for Scenarios 2 and 3 (blue and cyan lines) with a minimum at $\Lambda = 0.22$ (vertical blue dashed line). The parameter $\beta = \Delta_s / g_s$ is set to 10, and $\kappa / 2\pi = 0.1\,\mathrm{MHz}$ in all cases.
• Figure 5: (a) Resonance peaks measured for the bare Resonator 1 at $7\,\mathrm{mK}$ (red), with neon at $3.4\,\mathrm{K}$ (blue), and with neon and electrons at $7.5\,\mathrm{mK}$ (green). The corresponding internal quality factors ($Q_\mathrm{int}$: $2.34 \times 10^5$, $4.66 \times 10^3$, $2.22 \times 10^5$), external quality factors ($Q_\mathrm{ext}$: $3.19 \times 10^4$, $4.33 \times 10^3$, $3.36 \times 10^4$), and resonance frequencies ($f_\mathrm{r}$: $4.854\,\mathrm{GHz}$, $4.82\,\mathrm{GHz}$, $4.808\,\mathrm{GHz}$) are given for red, blue, and green, respectively. (b) Resonance peaks measured for the bare Resonator 2 at $7\,\mathrm{mK}$ (red), with neon at $3.4\,\mathrm{K}$ (blue), and with neon and electrons at $7.5\,\mathrm{mK}$ (green). The corresponding internal quality factors ($Q_\mathrm{int}$: $1.91 \times 10^5$, $3.9 \times 10^3$, $1.42 \times 10^5$), external quality factors ($Q_\mathrm{ext}$: $2.16 \times 10^4$, $3.49 \times 10^3$, $1.97 \times 10^4$), and resonance frequencies ($f_\mathrm{r}$: $5.959\,\mathrm{GHz}$, $5.918\,\mathrm{GHz}$, $5.906\,\mathrm{GHz}$) are given for red, blue, and green, respectively. (a, b) The dotted lines represent the fits. (c) Resonance frequency shift obtained from the COMSOL simulation as a function of the neon thickness. The vertical dotted and dashed lines represent the maximum measured resonance frequency shifts of Resonators 1 and 2 caused by the neon and electron deposition, $-0.94\%$ and $-0.86\%$, respectively. Resonance frequency shifts for Resonator 1 are simulated using 3D RF model.