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Bulletin of the American Physical Society

High quality factor superconducting resonators on Si/SiGe semiconductor heterostructures

Jeffrey V. Cady, Xiao Mi, J. R. Petta

Published Mar 4, 2015• 0 citations
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Ge/SiGe heterostructures represent a promising platform for hosting various quantum devices such as hole spin qubits and Andreev spin qubits. However, the compatibility of such heterostructures with high-quality-factor microwave superconducting cavities remains a challenge due to defects in the material stack. In this work, we present an approach to enhance the coherence of cavity modes on a reverse-graded Ge/SiGe heterostructure, which consists of etching the full $\sim 1.6~\mathrm{μm}$-thick Ge/SiGe stack down to its starting high-resistivity Si substrate, in order to pattern superconducting cavities directly on it. We engineer the mesa step to be tapered, so that it can be easily climbed by the superconducting cavities to reach the quantum devices potentially hosted in the Ge quantum well. Using this approach, we observe internal quality factors of $Q_\mathrm{i} \approx 10000-20000$ for high-impedance frequency-tunable Josephson junction array resonators, limited by the junctions' fabrication, and $Q_\mathrm{i} \approx 100000$ for $50~\mathrmΩ$ coplanar waveguide Nb lift-off resonators. These $Q_\mathrm{i}$ are preserved despite the overlap with the mesa structure in the climbing region, and are comparable to the ones obtained for identical resonators fabricated on a high-resistivity Si wafer reference. Thereby, this work paves a practical path toward superconductor-semiconductor hybrid devices, immediately applicable to emerging technologies on planar Ge.

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Abstract One major challenge to scaling quantum dot qubits is the dense wiring requirements, making it difficult to envision fabricating large 2D arrays of nearest-neighbor-coupled qubits necessary for error correction. We describe a method to ameliorate this issue by spacing out the qubits using superconducting resonators facilitated by 3D integration. To prove the viability of this approach, we use integration to couple an off-chip high-impedance TiN resonator to a double quantum dot in a Si/SiGe heterostructure. Using the resonator as a dispersive gate sensor, we tune the device down to the single electron regime with an SNR = 5.36. Characterizing the individual systems shows 3D integration can be done while maintaining low-charge noise for the quantum dots and high-quality factors for the superconducting resonator (single photon QL = 2.14 × 104 with Qi ≈ 3 × 105), necessary for readout and high-fidelity two-qubit gates.

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Spin qubits in semiconductor quantum dots constitute one of the leading platforms for quantum information processing, combining long coherence times, high-fidelity gate operations, and compatibility with semiconductor industry technologies. In particular, holes confined in planar Ge/SiGe heterostructures have recently emerged as promising qubit candidates owing to their low effective mass, high mobility, low percolation density, absence of valley states, and strong spin-orbit interaction, which enables fast all-electrical spin control. At the same time, spin-orbit interaction also gives rise to a highly anisotropic and electrically tunable gyromagnetic response. Understanding and controlling this response is therefore essential for high-fidelity single- and multi-qubit operations. The realization of scalable quantum processors also requires efficient qubit readout and long-range connectivity. Circuit quantum electrodynamics (cQED), based on the coupling between artificial atoms and microwave photons confined in superconducting resonators, provides a natural framework to address these challenges. However, the implementation of hybrid semiconductor-superconductor devices in planar Ge has so far been hindered by large microwave losses originating from the heterostructure. In this thesis, we demonstrate, for the first time in planar Ge, strong coupling between a hole charge qubit in a double quantum dot and a high-impedance microwave resonator, reaching a cooperativity of C â 100. In addition, we leverage the frequency tunability of the resonator to perform detailed spectroscopy of a multi-level energy spectrum of low-lying states arising from strong Coulomb-correlation effects. To further improve the quality of the hole-photon interface, we investigate the source of microwave losses in different Ge/SiGe heterostructures, identifying defects at the lattice-mismatched Si/Ge interface as the dominant source of resonator losses in reverse-graded heterostructures. To mitigate this limitation, a deep tapered-etching approach is introduced, enabling the fabrication of superconducting resonators directly on etched heterostructures. This method yields internal quality factors exceeding Qint > 10 000 for high-impedance Josephson junction array resonators and Qint > 100 000 for 50 â Nb resonators. Finally, this thesis explores the spin properties of multi-hole quantum dots beyond the conventional single-orbital picture. By reconstructing and electrically tuning the g tensors of holes confined in different orbital states, we show that confinement can substantially modify both their magnitude and orientation. These results open new opportunities for engineering qubit properties through orbital occupation. Furthermore, highly coherent singlet-triplet oscillations are demonstrated in the seven-hole regime, yielding a quality factor of approximately 330 at in-plane magnetic fields as low as 2.5 mT. Together, these results establish a foundation for high-fidelity hole-spin-qubit operation based on g-tensor engineering and for the integration of planar Ge quantum dots with superconducting quantum circuits.

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Ge/SiGe heterostructures represent a promising platform for hosting various quantum devices such as hole spin qubits and Andreev spin qubits. However, the compatibility of such heterostructures with high-quality-factor microwave superconducting cavities remains a challenge due to defects in the material stack. In this work, we present an approach to enhance the coherence of cavity modes on a reverse-graded Ge/SiGe heterostructure, which consists of etching the full ∼1.6 μm\sim 1.6~\mathrm{μm}∼1.6 μm-thick Ge/SiGe stack down to its starting high-resistivity Si substrate, in order to pattern superconducting cavities directly on it. We engineer the mesa step to be tapered, so that it can be easily climbed by the superconducting cavities to reach the quantum devices potentially hosted in the Ge quantum well. Using this approach, we observe internal quality factors of Qi≈10000−20000Q_\mathrm{i} \approx 10000-20000Qi​≈10000−20000 for high-impedance frequency-tunable Josephson junction array resonators, limited by the junctions' fabrication, and Qi≈100000Q_\mathrm{i} \approx 100000Qi​≈100000 for 50 Ω50~\mathrmΩ50 Ω coplanar waveguide Nb lift-off resonators. These QiQ_\mathrm{i}Qi​ are preserved despite the overlap with the mesa structure in the climbing region, and are comparable to the ones obtained for identical resonators fabricated on a high-resistivity Si wafer reference. Thereby, this work paves a practical path toward superconductor-semiconductor hybrid devices, immediately applicable to emerging technologies on planar Ge.
Abstract One major challenge to scaling quantum dot qubits is the dense wiring requirements, making it difficult to envision fabricating large 2D arrays of nearest-neighbor-coupled qubits necessary for error correction. We describe a method to ameliorate this issue by spacing out the qubits using superconducting resonators facilitated by 3D integration. To prove the viability of this approach, we use integration to couple an off-chip high-impedance TiN resonator to a double quantum dot in a Si/SiGe heterostructure. Using the resonator as a dispersive gate sensor, we tune the device down to the single electron regime with an SNR = 5.36. Characterizing the individual systems shows 3D integration can be done while maintaining low-charge noise for the quantum dots and high-quality factors for the superconducting resonator (single photon QL = 2.14 × 104 with Qi ≈ 3 × 105), necessary for readout and high-fidelity two-qubit gates.
Spin qubits in semiconductor quantum dots constitute one of the leading platforms for quantum information processing, combining long coherence times, high-fidelity gate operations, and compatibility with semiconductor industry technologies. In particular, holes confined in planar Ge/SiGe heterostructures have recently emerged as promising qubit candidates owing to their low effective mass, high mobility, low percolation density, absence of valley states, and strong spin-orbit interaction, which enables fast all-electrical spin control. At the same time, spin-orbit interaction also gives rise to a highly anisotropic and electrically tunable gyromagnetic response. Understanding and controlling this response is therefore essential for high-fidelity single- and multi-qubit operations. The realization of scalable quantum processors also requires efficient qubit readout and long-range connectivity. Circuit quantum electrodynamics (cQED), based on the coupling between artificial atoms and microwave photons confined in superconducting resonators, provides a natural framework to address these challenges. However, the implementation of hybrid semiconductor-superconductor devices in planar Ge has so far been hindered by large microwave losses originating from the heterostructure. In this thesis, we demonstrate, for the first time in planar Ge, strong coupling between a hole charge qubit in a double quantum dot and a high-impedance microwave resonator, reaching a cooperativity of C â 100. In addition, we leverage the frequency tunability of the resonator to perform detailed spectroscopy of a multi-level energy spectrum of low-lying states arising from strong Coulomb-correlation effects. To further improve the quality of the hole-photon interface, we investigate the source of microwave losses in different Ge/SiGe heterostructures, identifying defects at the lattice-mismatched Si/Ge interface as the dominant source of resonator losses in reverse-graded heterostructures. To mitigate this limitation, a deep tapered-etching approach is introduced, enabling the fabrication of superconducting resonators directly on etched heterostructures. This method yields internal quality factors exceeding Qint > 10 000 for high-impedance Josephson junction array resonators and Qint > 100 000 for 50 â Nb resonators. Finally, this thesis explores the spin properties of multi-hole quantum dots beyond the conventional single-orbital picture. By reconstructing and electrically tuning the g tensors of holes confined in different orbital states, we show that confinement can substantially modify both their magnitude and orientation. These results open new opportunities for engineering qubit properties through orbital occupation. Furthermore, highly coherent singlet-triplet oscillations are demonstrated in the seven-hole regime, yielding a quality factor of approximately 330 at in-plane magnetic fields as low as 2.5 mT. Together, these results establish a foundation for high-fidelity hole-spin-qubit operation based on g-tensor engineering and for the integration of planar Ge quantum dots with superconducting quantum circuits.