🔬 mesoscale physics

High-quality and field resilient microwave resonators on Ge/SiGe quantum well heterostructures

This paper reports the fabrication of high-quality microwave resonators on Ge/SiGe quantum well heterostructures that achieve record-breaking internal quality factors at low power and demonstrate robust performance in high magnetic fields, overcoming previous limitations of photon losses in such hybrid quantum devices.

Original authors: Luigi Ruggiero, Carlo Ciacca, Pauline Drexler, Vera Jo Weibel, Christian Olsen, Christian Schönenberger, Dominique Bougeard, Andrea Hofmann

Published 2026-07-29

📖 3 min read☕ Coffee break read

CC BY 4.0

Original authors: Luigi Ruggiero, Carlo Ciacca, Pauline Drexler, Vera Jo Weibel, Christian Olsen, Christian Schönenberger, Dominique Bougeard, Andrea Hofmann

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the world of quantum computing as a high-stakes orchestra where tiny particles called qubits are the musicians. For the music to be perfect, these musicians need to play in a silent, vibration-free room. In the quantum world, that silence is provided by microwave resonators—special circuits that act like tuning forks, vibrating at precise frequencies to help read the qubits' notes or connect them to one another. However, just like a real tuning fork loses its ring if it's made of cheap metal or placed on a bumpy table, these quantum resonators often lose their energy (or "quality") due to tiny defects in the materials they are built on. For a long time, scientists have been trying to build these resonators on a specific type of material called Germanium (Ge) because it's great for making qubits, but the "tables" they were built on were too wobbly, causing the music to fade away too quickly. The big question has been: Can we build a resonator on a Germanium platform that is both high-quality and tough enough to survive in the presence of magnetic fields, which are necessary for controlling the qubits?

This paper tells the story of a team that finally built a much sturdier, higher-quality "tuning fork" for the quantum orchestra. Instead of building their resonator on a Germanium layer grown on top of a Silicon base (which creates a messy, defect-ridden interface), they grew their entire structure directly on a pure Germanium substrate. Think of it like building a house on a solid, single piece of granite rather than stacking mismatched bricks on top of a shaky foundation. They also grew a thin layer of superconducting aluminum directly onto this structure without ever breaking the vacuum seal, ensuring a super-clean connection. The result? They created microwave resonators that are incredibly efficient. At very low power levels (where only a single photon, or particle of light, is circulating), they achieved a quality factor of about 49,000, and even at lower power, they saw a plateau around 20,000. This is roughly ten times better than previous attempts on similar Germanium structures. Furthermore, they tested how these resonators behave in magnetic fields. They found that the resonators can withstand strong magnetic fields pushing from the side (in-plane) up to 850 mT without losing their shape. However, when the magnetic field pushes from the top (out-of-plane), the resonator shows a "hysteresis," meaning its behavior depends on the history of the field, like a magnet that remembers which way it was last pulled. This suggests a complex dance between tiny magnetic whirlpools (vortices) and energy-carrying particles (quasiparticles) inside the material. The authors suggest that while the resonators are now much better, the interplay between these particles and whirlpools is still a fascinating puzzle that needs more study, but the new design offers a promising path toward building better, more resilient quantum devices.

Technical Summary: High-quality and field resilient microwave resonators on Ge/SiGe quantum well heterostructures

Problem Statement
Superconducting resonators integrated with germanium (Ge) quantum wells (QWs) represent a promising platform for hybrid quantum devices, enabling fast, high-fidelity readout and long-range qubit coupling. However, achieving high-quality resonators within compact heterostructure architectures has been hindered by significant photon losses. Previous approaches utilizing Ge QWs grown on silicon (Si) substrates via virtual Ge substrates suffer from high dislocation densities at the Si-Ge interface, limiting internal quality factors ( $Q_i$ ) to approximately 1,000. Conversely, approaches yielding higher $Q_i$ values often require thick buffer layers and extended growth times. Furthermore, existing studies on Ge-based resonators have largely been limited to low magnetic fields, despite the necessity of field resilience for qubit applications.

Methodology
The authors present a hybrid superconductor/semiconductor heterostructure (HS) grown via molecular-beam epitaxy (MBE) on a commercial Ge substrate, rather than a Si substrate. The stack consists of a Ge/SiGe QW structure with a constant SiGe composition, topped by an 8 nm thin aluminum (Al) film deposited in-situ without breaking vacuum. This design aims to eliminate the lossy Si-Ge interface while maintaining a compact stack.

To characterize the platform, the researchers:

Fabricated microwave resonators by patterning the Al film using wet-etching and reactive ion etching (RIE), leaving the underlying Ge/SiGe QW intact.
Measured three samples in a dilution refrigerator (10 mK) using a vector network analyzer. Sample A contained eight $\lambda/4$ resonators of varying lengths to analyze statistical variability and extract kinetic inductance; Samples B and C contained single resonators for magnetic field characterization.
Systematically analyzed the internal quality factor ( $Q_i$ ) and resonance frequency ( $f_r$ ) as a function of input power (photon number), temperature, and magnetic field orientation (in-plane and out-of-plane).

Key Contributions and Results

High Internal Quality Factors: The study consistently achieved internal quality factors $Q_i > 1,000$ . Notably, at single-photon occupation, the team reached $Q_i \approx 49,000$ . At sub-one photon levels, a plateau of $Q_i \approx 20,000$ was observed. These values represent an order of magnitude improvement over previously reported resonators on Ge QW structures grown on Si substrates at low power.
Material Characterization:
- Kinetic Inductance: By analyzing the resonance frequency dependence on resonator length, the authors extracted a kinetic inductance of $L_{kin} = (36 \pm 2)$ pH/ $\square$ . This is four times larger than that of 10 nm ex-situ Al films, consistent with the expected increase for thinner films.
- Superconducting Gap: Temperature-dependent measurements following Bardeen–Cooper–Schrieffer (BCS) theory yielded a zero-temperature superconducting gap of $\Delta_0 = (298 \pm 4)$ $\mu$ eV, slightly higher than comparable ex-situ films.
- Kinetic Inductance Fraction: The kinetic inductance fraction was extracted as $\alpha = (0.75 \pm 0.08)$ .
Loss Mechanisms: The $Q_i$ dependence on photon number revealed that for most resonators, losses were dominated by two-level systems (TLS) at low powers, which saturated at higher powers. The best resonator exhibited a low-power plateau, indicating a regime where unsaturated TLS dominate. Variability in $Q_i$ across the sample was correlated with etching imperfections and ground plane inhomogeneities.
Magnetic Field Resilience:
- In-Plane Fields: The resonators demonstrated resilience up to in-plane magnetic fields of 850 mT. While the quality factor decreased by less than 75% at this field strength, the resonance remained well-defined.
- Out-of-Plane Fields: Measurements revealed a pronounced hysteresis in both resonance frequency and quality factor. The authors attribute this to an interplay between vortex dynamics and quasiparticle trapping. Specifically, they observed that vortex annihilation upon sweeping the field back to zero led to a sharp rise in frequency but a further drop in quality factor, suggesting that vortices in this system are effective at suppressing quasiparticle-induced loss.

Significance
The paper claims that this approach successfully delivers high-quality microwave resonators with large in-plane magnetic field resilience by utilizing a Ge-substrate-based hybrid HS with an in-situ grown Al film. By avoiding the dislocation-rich Si-Ge interface, the authors achieve internal quality factors that exceed the coherence times of many reported Ge-based qubits. The demonstrated resilience to in-plane fields corresponds to Zeeman energies suitable for typical Ge quantum dot qubits, and the characterization of out-of-plane hysteresis provides critical insight into loss mechanisms involving vortices and quasiparticles. These results suggest that the platform is suitable for integration into future hybrid quantum devices requiring high-fidelity readout and magnetic field operation.

More like this