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arXiv:2501.03211 · Physical Review Applied

Compact superconducting vacuum-gap capacitors with low microwave loss and high mechanical coherence for scalable quantum circuits

Amir Youssefi, Mahdi Chegnizadeh, Marco Scigliuzzo, Tobias J. Kippenberg

Published May 16, 2025• 1 citation
arXivHTMLPDF

Abstract

Vacuum-gap capacitors have recently attracted significant interest in superconducting circuit platforms due to their compact design and exceptionally low dielectric losses in the microwave regime. Their intrinsic ability to support mechanical vibrational modes makes them well-suited for circuit optomechanics. However, precise control over the gap size and the realization of high-coherence mechanical modes remain longstanding challenges. Here, we present a detailed and scalable fabrication process for vacuum-gap capacitors that support ultra-high-coherence mechanical motion, exhibit low microwave loss, and occupy a significantly smaller footprint compared to conventional planar geometries. By employing a planarized $\mathrm{SiO}_2$ sacrificial layer, we achieve vacuum gaps on the order of 150 nm. Using this platform, we have recently demonstrated ground-state cooling and motion squeezing of a mechanical oscillator with a quality factor of 40 million, a 100-fold improvement compared to prior works, as well as a single-photon optomechanical coupling rate of approximately 15Hz. Additional achievements include the realization of an optomechanical topological lattice with 24 sites and the observation of quantum collective dynamics in a mechanical hexamer. Collectively, these results underscore the potential of vacuum-gap capacitors as a platform for coupling superconducting qubits to mechanical systems, enabling quantum storage, and probing gravitational effects in quantum mechanics.

DOI
10.1103/q5bc-y54w

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Vacuum-gap capacitors have recently attracted significant interest in superconducting circuit platforms due to their compact design and exceptionally low dielectric losses in the microwave regime. Their intrinsic ability to support mechanical vibrational modes makes them well-suited for circuit optomechanics. However, precise control over the gap size and the realization of high-coherence mechanical modes remain longstanding challenges. Here, we present a detailed and scalable fabrication process for vacuum-gap capacitors that support ultra-high-coherence mechanical motion, exhibit low microwave loss, and occupy a significantly smaller footprint compared to conventional planar geometries. By employing a planarized SiO2\mathrm{SiO}_2SiO2​ sacrificial layer, we achieve vacuum gaps on the order of 150 nm. Using this platform, we have recently demonstrated ground-state cooling and motion squeezing of a mechanical oscillator with a quality factor of 40 million, a 100-fold improvement compared to prior works, as well as a single-photon optomechanical coupling rate of approximately 15Hz. Additional achievements include the realization of an optomechanical topological lattice with 24 sites and the observation of quantum collective dynamics in a mechanical hexamer. Collectively, these results underscore the potential of vacuum-gap capacitors as a platform for coupling superconducting qubits to mechanical systems, enabling quantum storage, and probing gravitational effects in quantum mechanics.
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We have produced high-quality complex microwave circuits, such as multiplexed resonators and superconducting phase qubits, using a “vacuum-gap” technology that eliminates lossy dielectric materials. We have improved our design and fabrication strategy beyond our earlier work, leading to increased yield, enabling the realization of these complex circuits. We incorporate both novel vacuum-gap wiring crossovers for gradiometric inductors and vacuum-gap capacitors (VGC) on chip to produce resonant circuits that have large internal quality factors (30 000<QI<165 000) at 50 mK, outperforming most dielectric-filled devices. Resonators with VGCs as large as 180 pF confirm single mode behavior of our lumped-element components.
State-of-the-art transmon qubits rely on large capacitors, which systematically improve their coherence due to reduced surface-loss participation. However, this approach increases both the footprint and the parasitic cross-coupling and is ultimately limited by radiation losses---a potential roadblock for scaling up quantum processors to millions of qubits. In this work we present transmon qubits with sizes as low as $36\phantom{\rule{0.2em}{0ex}}\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0.2em}{0ex}}39\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}{\mathrm{m}}^{2}$ with $\ensuremath{\gtrsim}100$-nm-wide vacuum-gap capacitors that are micromachined from commercial silicon-on-insulator wafers and shadow evaporated with aluminum. We achieve a vacuum participation ratio up to 99.6% in an in-plane design that is compatible with standard coplanar circuits. Qubit relaxation-time measurements for small gaps with high zero-point electric field variance of up to 22 V/m reveal a double exponential decay indicating comparably strong qubit interaction with long-lived two-level systems. The exceptionally high selectivity of up to 20 dB to the superconductor-vacuum interface allows us to precisely back out the sub-single-photon dielectric loss tangent of aluminum oxide previously exposed to ambient conditions. In terms of future scaling potential, we achieve a ratio of qubit quality factor to a footprint area equal to $20\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}{\mathrm{m}}^{\ensuremath{-}2}$, which is comparable with the highest T1{T}_{1}T1​ devices relying on larger geometries, a value that could improve substantially for lower surface-loss superconductors.
Quantum memories and networks for distributed quantum information processing require links between the microwave, mechanical, and optical domains. Coherent integration of long-lived superconducting qubits (SCQs) with optomechanical and photonic devices (OMPDs) remains an outstanding challenge. We present a step towards coherent integration using a suspended trace air-gap resonator (STAR): a superconducting resonator on a silicon-on-insulator (SOI) substrate with the signal trace suspended by silicon tethers above and between galvanically connected ground metal planes. As a result, the electric field energy is closely confined within the microwave structure, yielding lower crosstalk compared to conventional coplanar waveguides (CPW). An order of magnitude improvement in the quality factors for STAR over previous work on SOI is achieved, in a transverse cross-sectional area that is an order of magnitude more compact. Electric field participation in lossy bulk dielectrics, a dominant source of energy leakage in previous measurements of aluminum CPW resonators on SOI, is virtually eliminated in STAR. The loss from the metal-air interface now dominates, but can be reduced by several factors using superconductors with better surface properties. Most importantly, STAR fabrication is compatible with Josephson junction and air-bridge deposition for highly coherent integration of SCQs and OMPDs to realize proposals for quantum information storage and networking.
Cavity optomechanics enables controlling mechanical motion via radiation pressure interaction, and has contributed to the quantum control of engineered mechanical systems ranging from kg scale LIGO mirrors to nano-mechanical systems, enabling entanglement, squeezing of mechanical objects, to position measurements at the standard quantum limit, and quantum transduction. Yet, nearly all prior schemes have employed single- or few-mode optomechanical systems. In contrast, novel dynamics and applications are expected when utilizing optomechanical arrays and lattices, which enable to synthesize non-trivial band structures, and have been actively studied in the field of circuit QED. Superconducting microwave optomechanical circuits are a promising platform to implement such lattices, but have been compounded by strict scaling limitations. Here we overcome this challenge and realize superconducting circuit optomechanical lattices. We demonstrate non-trivial topological microwave modes in 1-D optomechanical chains as well as 2-D honeycomb lattices, realizing the canonical Su-Schrieffer-Heeger (SSH) model. Exploiting the embedded optomechanical interaction, we show that it is possible to directly measure the mode shapes, without using any local probe or inducing perturbation. This enables us to reconstruct the full underlying lattice Hamiltonian beyond tight-binding approximations, and directly measure the existing residual disorder. The latter is found to be sufficiently small to observe fully hybridized topological edge modes. Such optomechanical lattices, accompanied by the measurement techniques introduced, offers an avenue to explore out of equilibrium physics in optomechanical lattices such as quantum and quench dynamics, topological properties and more broadly, emergent nonlinear dynamics in complex optomechanical systems with a large number of degrees of freedoms.
Mechanical oscillators in the quantum regime hold promise for quantum sensing, frequency conversion and information processing. Because mechanical motion is linear, coupling to an external nonlinear system, such as a qubit, is essential for these applications. Recent advances in piezoelectric interfaces between mechanical oscillators and superconducting qubits have successfully demonstrated precise control of non-classical states of motion. However, challenges associated with heterogeneous integration of piezoelectric materials have limited mechanical quality factors in these systems to around one million, constraining their broader utility. In this thesis, we explore an alternative approach that harnesses the nonlinearity of electrostatic forces to engineer interactions between superconducting circuits and mechanical oscillators. This strategy allows us to employ mechanical oscillators made of silicon, a non-piezoelectric material with extremely low acoustic loss. We reach the strong coupling regime between a superconducting qubit and a long-lived mechanical oscillator with a quality-factor of around a billion. We employ this system to generate non-classical states of motion that exhibit clear signatures of quantum behavior. Furthermore, we explore the origins of acoustic decoherence and implement strategies to mitigate its impact. The mechanical lifetimes, which exceed those of best superconducting qubits, open new possibilities for storing and processing microwave quantum information in motional states. Furthermore, our material-agnostic approach is broadly applicable to a variety of material platforms that possess significance for quantum science but lack a piezoelectric response.