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arXiv:2407.03079

Strong Charge-Photon Coupling in Planar Germanium Enabled by Granular Aluminium Superinductors

Marián Janík, Kévin Roux, Carla Borja, Olivér Sági, Abdulhamid Baghdadi, Thomas Adletzberger, Stefano Calcaterra, Marc Botifoll, Alba Garzón Manjón, Jordi Arbiol, Daniel Chrastina, Giovanni Isella, Ioan M. Pop, Georgios Katsaros

Published Jul 3, 2024• 1 citation
arXivHTMLPDF

Abstract

High kinetic inductance superconductors are gaining increasing interest for the realisation of qubits, amplifiers and detectors. Moreover, thanks to their high impedance, quantum buses made of such materials enable large zero-point fluctuations of the voltage, boosting the coupling rates to spin and charge qubits. However, fully exploiting the potential of disordered or granular superconductors is challenging, as their inductance and, therefore, impedance at high values are difficult to control. Here we have integrated a granular aluminium resonator, having a characteristic impedance exceeding the resistance quantum, with a germanium double quantum dot and demonstrate strong charge-photon coupling with a rate of $g_\text{c}/2π= (566 \pm 2)$ MHz. This was achieved due to the realisation of a wireless ohmmeter, which allows \emph{in situ} measurements during film deposition and, therefore, control of the kinetic inductance of granular aluminium films. Reproducible fabrication of circuits with impedances (inductances) exceeding 13 k$Ω$ (1 nH per square) is now possible. This broadly applicable method opens the path for novel qubits and high-fidelity, long-distance two-qubit gates.

DOI
10.48550/arxiv.2407.03079

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High kinetic inductance superconductors are gaining increasing interest for the realisation of qubits, amplifiers and detectors. Moreover, thanks to their high impedance, quantum buses made of such materials enable large zero-point fluctuations of the voltage, boosting the coupling rates to spin and charge qubits. However, fully exploiting the potential of disordered or granular superconductors is challenging, as their inductance and, therefore, impedance at high values are difficult to control. Here we have integrated a granular aluminium resonator, having a characteristic impedance exceeding the resistance quantum, with a germanium double quantum dot and demonstrate strong charge-photon coupling with a rate of gc/2π=(566±2)g_\text{c}/2π= (566 \pm 2)gc​/2π=(566±2) MHz. This was achieved due to the realisation of a wireless ohmmeter, which allows \emph{in situ} measurements during film deposition and, therefore, control of the kinetic inductance of granular aluminium films. Reproducible fabrication of circuits with impedances (inductances) exceeding 13 kΩΩΩ (1 nH per square) is now possible. This broadly applicable method opens the path for novel qubits and high-fidelity, long-distance two-qubit gates.
Abstract High kinetic inductance superconductors are gaining increasing interest for the realisation of qubits, amplifiers and detectors. Moreover, thanks to their high impedance, quantum buses made of such materials enable large zero-point fluctuations of the voltage, boosting the coupling rates to spin and charge qubits. However, fully exploiting the potential of disordered or granular superconductors is challenging, as their inductance and, therefore, impedance at high values are difficult to control. Here, we report a reproducible fabrication of granular aluminium resonators by developing a wireless ohmmeter, which allows in situ measurements during film deposition and, therefore, control of the kinetic inductance of granular aluminium films. Reproducible fabrication of circuits with impedances (inductances) exceeding 13 kΩ (1 nH per square) is now possible. By integrating a 7.9 kΩ resonator with a germanium double quantum dot, we demonstrate strong charge-photon coupling with a rate of g c/2π = 566 ± 2 MHz. This broadly applicable method opens the path for novel qubits and high-fidelity, long-distance two-qubit gates.
Superconducting circuits based on high kinetic inductance materials are promising candidates for future quantum technologies, owing to their magnetic field resilience, low microwave losses, and lithographic scalability. In this thesis, we explore the properties of granular aluminum (grAl) resonators in two distinct geometries, using the nonlinear kinetic inductance of grAl for applications in superconducting quantum circuits. In the first part, we present compact meandered ring resonators fabricated using a single-step electron-beam lithography and lift-off process. By optimizing film resistivity and geometry, we achieve superinductors with characteristic impedances exceeding 100 kΩ100~\mathrm{k}\Omega100 kΩ, corresponding to total inductances of several microhenries, while maintaining internal quality factors on the order of 10510^{5}105 in the single-photon regime. In the second part, we investigate DC-tunable resonators based on a 3λ/43\lambda/43λ/4 fractal geometry that allows direct current injection for in-situ tuning of the resonance frequency. We achieve frequency tunability up to 4.5%4.5\%4.5% and analyze the nonlinear kinetic inductance using models based on Ginzburg-Landau, Mattis-Bardeen-BCS, and an effective Josephson-junction-array model. This work establishes granular aluminum as a material for realizing high-impedance and frequency-tunable superconducting circuits, offering new opportunities for advanced applications in protected qubits, hybrid quantum systems, broadband phase shifters, and three-wave mixing parametric amplifiers.
Spin-photon coupling presents an enticing opportunity for the long-range coupling of spin qubits. The spin-photon coupling rate, gs{g}_{s}gs​, is proportional to the charge-photon coupling rate, gc{g}_{c}gc​. To move deeper into the strong-coupling regime, gc{g}_{c}gc​ can be enhanced by fabricating high-impedance cavities using high-kinetic-inductance films. Here, we report dc transport and microwave response investigations of niobium nitride (NbN\mathrm{Nb}\mathrm{N}NbN) films of different thicknesses. The kinetic inductance increases rapidly as the film thickness is reduced below 50 nm and for 15-nm NbN\mathrm{Nb}\mathrm{N}NbN films we measure a sheet kinetic inductance Lk,S=41.2pH/◻{L}_{k,S}=41.2\phantom{\rule{0.2em}{0ex}}\text{pH}/◻Lk,S​=41.2pH/◻. As an application of the high-kinetic-inductance films, we fabricate compact LCLCLC filters that are commonly used to reduce microwave leakage in circuit quantum electrodynamics (cQED) devices. These filters feature up to 60 dB of attenuation near typical cavity resonance frequencies of fc=8{f}_{c}=8fc​=8 GHz.
We design superinductors made of strongly disordered superconductors for implementation in ``hybrid'' superconducting quantum circuits. The superinductors are fabricated as meandered nanowires made from granular aluminum films. Optimization of the device geometry enables the realization of superinductors with an inductance of approximately 1 $\ensuremath{\mu}\mathrm{H}$ and a self-resonance frequency of over 3 GHz. These compact superinductors are attractive for a wide range of applications, from superconducting circuits for quantum computing to microwave elements of cryogenic parametric amplifiers and kinetic inductance photon detectors.
Superconducting inductors with impedance surpassing the resistance quantum, i.e., superinductors, are important for quantum technologies because they enable the development of protected qubits, enhance coupling to systems with small electric dipole moments, and facilitate the study of phase-slip physics. We demonstrate superinductors with densely packed meandered traces of granular aluminum ( grAl ) with inductances up to 4 µH, achieving impedances exceeding 100 k in the 4–8 GHz range. Ring resonators made with grAl meandered superinductors exhibit quality factors on the order of 10 5 in the single-photon regime, and low nonlinearity on the order of tens of hertz. Depending on the grAl resistivity, at 10 Hz, we measure frequency-noise spectral densities in the range of 10 2 – 10 3 Hz / Hz . In some devices, in the single-photon regime, we observe a positive Kerr coefficient of unknown origin. Using more complex fabrication, the devices could be released from the substrate, either freestanding or suspended on a membrane, thereby further improving their impedance by a factor of 3.
Granular aluminum is a promising material for high kinetic inductance devices such as qubit circuits. It has the advantage over atomically disordered materials such as NbNx, to maintain a high kinetic inductance concomitantly with a high quality factor. We show that high quality nano-scale granular aluminum films having a sharp superconducting transition with normal state resistivity values on the order of 1×105 μΩ cm and kinetic inductance values on the order of 10 nH/◻ can be obtained, surpassing the state-of-the-art values. We argue that this is a result of the different nature of the metal-to-insulator transition, being electronic correlations driven (Mott type) in the former and disorder driven (Anderson type) in the latter.