A charge qubit on solid neon in a spin-qubit compatible circuit QED platform

This paper demonstrates a charge qubit formed by a single electron on solid neon coupled to a magnetic-field-compatible NbTiN resonator, achieving high-speed coherent control and readout while characterizing position uncertainties to confirm the feasibility of future spin-qubit implementations.

The Gist

Imagine a tiny, lonely electron floating in a vacuum, hovering just above a block of frozen neon gas. Because it's floating in empty space, it's perfectly isolated from the messy, dirty atoms of the solid world below it. This makes it a very clean, quiet place to store information. Scientists call this a "qubit," the basic unit of a future quantum computer.

This paper describes a successful experiment where researchers built a "playground" for this floating electron and taught it to dance to the tune of microwaves. Here is how they did it, broken down into simple concepts:

1. The Stage: A Superconducting Wire

The researchers built a tiny, superconducting wire (made of a special metal called NbTiN) right under the neon. Think of this wire as a giant, invisible trampoline that vibrates at a specific radio frequency.

• Why this wire? Most superconductors stop working if you put a magnet near them. But this specific wire is tough; it keeps vibrating even in strong magnetic fields. This is crucial because the scientists want to eventually use magnets to control the electron's "spin" (its internal compass), which is the key to making a better type of qubit.

2. The Actor: The Floating Electron

The electron isn't stuck to the neon; it floats about 1–2 nanometers above it (that's thinner than a human hair by a factor of a million).

• The Problem: The surface of the frozen neon isn't perfectly smooth. It's like a bumpy, icy landscape with tiny hills and valleys. The electron gets stuck in one of these "valleys" by accident. The researchers couldn't force it to sit exactly where they wanted it, which made the experiment tricky.
• The Solution: Even though they couldn't see the electron directly, they could "feel" where it was. By turning knobs (voltage) on different electrodes around the wire, they noticed how strongly the electron reacted. It was like trying to find a hidden person in a dark room by shouting and listening for the echo; the direction and loudness of the echo told them exactly where the electron was hiding.

3. The Dance: Making the Qubit Talk

Once they found the electron, they started talking to it using microwaves (the same kind of waves your phone uses, but tuned to a very specific frequency).

• The Conversation: They sent a microwave pulse to the wire. If the electron was in a "sleeping" state (0), the wire vibrated one way. If the electron was in an "awake" state (1), the wire vibrated slightly differently. By listening to the wire, they could tell if the electron was 0 or 1.
• The Dance Moves (Rabi Oscillations): They didn't just listen; they made the electron dance. By hitting it with the right microwave pulse, they could flip it from 0 to 1 and back again. They did this incredibly fast—up to 76 million times a second. This is ten times faster than previous experiments with similar setups.

4. The Surprise: The "Heavy" Dance

When they turned the microwave power up really high, something strange happened. The electron's dance frequency slowed down and shifted.

• The Analogy: Imagine a swing. If you push it gently, it swings at a normal speed. But if you push it with a massive, chaotic force, the air resistance and the weight of the pusher might actually slow the swing down or change its rhythm.
• The Cause: The researchers think the intense microwave field created a "crowd" of photons (light particles) in the wire. This crowd pushed on the electron, changing its energy levels. It's like the electron got "heavy" from all the microwave energy hitting it.

5. The Result: A Promise for the Future

The electron didn't stay in the perfect spot the scientists wanted, and the "dance" didn't last as long as they hoped (it lost its rhythm after about 200 nanoseconds). However, the experiment proved two major things:

1. It Works: You can trap an electron on solid neon and control it with a superconducting wire that works in magnetic fields.
2. The Potential: Even with the electron in a "messy" spot, the researchers did some math to predict what would happen if they added tiny magnets to the setup. They calculated that a spin-based qubit (a more advanced version of this electron) could still achieve a success rate of 99.5%.

In short: The scientists built a high-tech stage, found a floating electron that was hiding in a slightly bumpy spot, and successfully taught it to dance to microwaves. Even though the electron wasn't in the perfect spot, the dance was so fast and the setup so robust that they are confident this platform can eventually host the next generation of quantum computers.

Technical Summary

Technical Summary: A Charge Qubit on Solid Neon in a Spin-Qubit Compatible Circuit QED Platform

Problem and Motivation
Electrons floating in vacuum above cryogenic substrates offer a pristine environment for quantum information processing, isolated from the material defects and impurities inherent in solid-state systems. While electrons on liquid helium have been extensively studied, recent progress has shifted focus to electrons on solid neon, which has demonstrated long coherence times even for charge qubits ($T_2^* = 50$ µs). However, realizing spin qubits on this platform requires coupling the electron to a superconducting resonator that remains operational in magnetic fields while maintaining high quality factors. Furthermore, a significant challenge in the solid-neon platform is the deterministic positioning of electrons; surface roughness and microscopic morphology create uncontrolled electrostatic disorder, making it difficult to trap electrons at specific, optimal locations for maximum coupling.

Methodology
The authors fabricated a device based on a superconducting Niobium Titanium Nitride (NbTiN) nanowire resonator, chosen for its robustness in magnetic fields and large kinetic inductance, which enhances zero-point voltage fluctuations and charge-photon coupling. The device features four DC electrodes (G1–G4) positioned near the resonator's center to tune the electrostatic potential and control the electron's orbital energy levels.

The experimental procedure involved:

1. Device Characterization: Measuring the resonator's bare resonance ($f_r \approx 5.345$ GHz) and quality factors before and after depositing solid neon and loading electrons.
2. Electron Selection: Sweeping DC voltages on the electrodes and resonator while monitoring microwave transmission to identify electrons whose orbital energy splitting resonates with the cavity.
3. Spectroscopy and Control: Performing microwave spectroscopy to map the qubit frequency as a function of DC voltages. The team utilized two-tone spectroscopy to extract coupling strengths and infer the electron's position based on differential coupling to the electrodes.
4. Coherent Operations: Implementing Rabi oscillations, Ramsey interferometry, and Hahn-echo sequences to characterize coherence times ($T_1$, $T_2^*$, $T_2$) and demonstrate coherent control.
5. Post-Processing: Annealing the neon film by warming the system to 8.6 K and re-depositing electrons to observe changes in relaxation times and coupling parameters.
6. Theoretical Estimation: Using the experimentally derived electron position and coupling parameters to model the feasibility of Electric Dipole Spin Resonance (EDSR) by integrating ferromagnets (Co/Ti stack) into the device architecture.

Key Results

• Charge Qubit Realization: The authors successfully realized a charge qubit using a single electron on solid neon coupled to an NbTiN nanowire resonator. They demonstrated microwave readout and coherent control.
• High-Speed Control: Rabi frequencies up to 76 MHz were achieved, an order of magnitude larger than in previous studies on this platform.
• Coupling and Positioning: The electron-resonator coupling strength was extracted as $g/2\pi = 2.1 \pm 0.2$ MHz. By analyzing the coupling to multiple electrodes, the authors inferred the electron's position to be approximately $(x, y) = (5.37, 0.57)$ nm relative to the resonator center, with a double-well potential separation of $d=100$ nm. This position was not the intended optimal trap but was sufficient for operation.
• Coherence Times: The measured coherence times were $T_2^* = 91 \pm 23$ ns and $T_2 = 202 \pm 5$ ns (Hahn-echo). These values are significantly shorter than previously reported for electrons on solid neon, suggesting the presence of broadband (white) noise, potentially from stray electrons. The energy relaxation time was measured at $T_1 = 3.06$ µs.
• Nonlinear Effects: Under strong driving, a downward shift in the qubit transition frequency was observed. The authors attribute this partially to a dispersive shift caused by the high photon number in the resonator and potentially to a ponderomotive effect modifying the trapping potential.
• Annealing Effects: After annealing the neon film and re-depositing electrons, a new qubit realization showed a significantly longer relaxation time of $T_1 = 17.7$ µs, suggesting a correlation between relaxation time, coupling strength, and the local environment (e.g., film thickness).
• Spin Qubit Feasibility: Based on the charge qubit parameters and the inferred electron position, the authors estimate that a spin qubit realized via EDSR with integrated ferromagnets could achieve single-qubit gate fidelities up to 99.5% (conservative estimate) or 99.994% (using improved post-annealing $T_1$ values and lower spin relaxation rates).

Significance and Claims
The paper establishes that NbTiN nanowire resonators on solid neon constitute a promising platform for realizing spin qubits, even in the absence of deterministic electron trapping at the optimal position. The authors claim that despite the challenges of surface roughness and the resulting non-optimal electron positioning, the demonstrated charge qubit performance (specifically the high Rabi frequencies and coherent control) provides a viable pathway toward spin-qubit demonstrations. They conclude that while controlling the neon film thickness and electron environment is essential for enhancing performance, the platform remains feasible for high-fidelity spin qubit operations without requiring perfect deterministic trapping. The work represents a critical step toward integrating solid-neon electron qubits with magnetic-field-compatible circuit QED architectures.