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arXiv:2403.00503 · Journal of Experimental and Theoretical Physics Letters

Granular Aluminum Kinetic Inductance Nonlinearity

M. Zhdanova, I. Pologov, G. Svyatsky, Vladimir I. Chichkov, Nataliya Maleeva

Published Mar 1, 2024• 1 citation
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Abstract

Granular Aluminum is a superconductor known for more than eighty years, which recently found its ap-plication in qubits, microwave detectors and compact resonators, due to its high kinetic inductance, critical magnetic field and critical current. Here we report on the nonlinear dependence of granular Aluminum inductance on current, which hints towards parametric amplification of the microwave signal in granular Aluminum films. The phase shift of the microwave signal reached 4 rad at a frequency of 7 GHz, which makes it possible to estimate the nonlinearity of the system as $$\Delta \phi {\text{/}}\phi = 1.4{\kern 1pt} \% $$ and the potential gain of the order of 17 dB.

DOI
10.1134/s002136402460037x

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Granular Aluminum is a superconductor known for more than eighty years, which recently found its ap-plication in qubits, microwave detectors and compact resonators, due to its high kinetic inductance, critical magnetic field and critical current. Here we report on the nonlinear dependence of granular Aluminum inductance on current, which hints towards parametric amplification of the microwave signal in granular Aluminum films. The phase shift of the microwave signal reached 4 rad at a frequency of 7 GHz, which makes it possible to estimate the nonlinearity of the system as Δϕ/ϕ=1.4%\Delta \phi {\text{/}}\phi = 1.4{\kern 1pt} \% Δϕ/ϕ=1.4% and the potential gain of the order of 17 dB.
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.
Granular aluminum (grAl) is a promising high kinetic inductance material for detectors, amplifiers, and qubits. Here we model the grAl structure, consisting of pure aluminum grains separated by thin aluminum oxide barriers, as a network of Josephson junctions, and we calculate the dispersion relation and nonlinearity (self-Kerr and cross-Kerr coefficients). To experimentally study the electrodynamics of grAl thin films, we measure microwave resonators with open-boundary conditions and test the theoretical predictions in two limits. For low frequencies, we use standard microwave reflection measurements in a low-loss environment. The measured low-frequency modes are in agreement with our dispersion relation model, and we observe self-Kerr coefficients within an order of magnitude from our calculation starting from the grAl microstructure. Using a high-frequency setup, we measure the plasma frequency of the film around 70 GHz, in agreement with the analytical prediction.
Superconducting high kinetic inductance elements constitute a valuable resource for quantum circuit design and millimeter-wave detection. Granular aluminum (grAl) in the superconducting regime is a particularly interesting material since it has already shown a kinetic inductance in the range of nH/□ and its deposition is compatible with conventional Al/AlOx/Al Josephson junction fabrication. We characterize microwave resonators fabricated from grAl with a room temperature resistivity of 4×10^{3} μΩ cm, which is a factor of 3 below the superconductor to insulator transition, showing a kinetic inductance fraction close to unity. The measured internal quality factors are on the order of Q_{i}=10^{5} in the single photon regime, and we demonstrate that nonequilibrium quasiparticles (QPs) constitute the dominant loss mechanism. We extract QP relaxation times in the range of 1 s and we observe QP bursts every ∼20 s. The current level of coherence of grAl resonators makes them attractive for integration in quantum devices, while it also evidences the need to reduce the density of nonequilibrium QPs.
Josephson junction parametric amplifiers have become essential tools for microwave quantum circuit readout with minimal added noise. Even after improving at an impressive rate in the past decade, they remain vulnerable to magnetic fields, which limits their use in many applications such as spin qubits, Andreev and molecular magnet devices, dark matter searches, etc. Kinetic inductance materials, such as granular aluminum (grAl), offer an alternative source of nonlinearity with innate magnetic field resilience. We present a nondegenerate amplifier made of two coupled grAl resonators resilient to in-plane magnetic fields up to 1T. It offers 20 dB of gain close to the quantum limit of added noise, with a gain-bandwidth product of 28 MHz and -110 dBm input saturation power.
High kinetic inductance materials constitute a valuable resource for superconducting quantum circuits and hybrid architectures. Superconducting granular aluminum (grAl) reaches kinetic sheet inductances in the nH/□ range, with proven applicability in superconducting quantum bits and microwave detectors. Here, we show that the single photon internal quality factor Qi of grAl microwave resonators exceeds 105 in magnetic fields up to 1 T, aligned in-plane to the grAl films. Small perpendicular magnetic fields, in the range of 0.5 mT, enhance Qi by approximately 15%, possibly due to the introduction of quasiparticle traps in the form of fluxons. Further increasing the perpendicular field deteriorates the resonators' quality factor. These results open the door for the use of high kinetic inductance grAl structures in circuit quantum electrodynamics and hybrid architectures with magnetic field requirements.
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.