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AIP Advances

Nonlinear response of superconducting (YBCO) fractal microstrip resonators: Distributed current ABCD-matrix model

A. A. Kalenyuk, S. I. Futimsky, Andrii P. Shapovalov

Published Feb 1, 2025• 2 citations
Publisher

Abstract

In this work, we experimentally investigated the nonlinear microwave response of YBa2Cu3O7–x Hilbert fractal superconducting microstrip resonators with sharp and rounded corners. We developed a resonator model that incorporates a distributed current-dependent nonlinear propagation parameter, γ(I), and used the ABCD matrix method for numerical simulations. Our findings demonstrated that the nonlinear response of the resonators can be effectively modeled with a current-proportional propagation parameter, γ∼I. In addition, we observed a significant reduction in the nonlinear response when transitioning from sharp to rounded corners in the resonator design. This work provides valuable insights into improving the design of superconducting resonators by minimizing their nonlinearities, which is crucial for advancing applications in microwave and quantum technologies.

DOI
10.1063/5.0242194

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In this work, we experimentally investigated the nonlinear microwave response of YBa2Cu3O7–x Hilbert fractal superconducting microstrip resonators with sharp and rounded corners. We developed a resonator model that incorporates a distributed current-dependent nonlinear propagation parameter, γ(I), and used the ABCD matrix method for numerical simulations. Our findings demonstrated that the nonlinear response of the resonators can be effectively modeled with a current-proportional propagation parameter, γ∼I. In addition, we observed a significant reduction in the nonlinear response when transitioning from sharp to rounded corners in the resonator design. This work provides valuable insights into improving the design of superconducting resonators by minimizing their nonlinearities, which is crucial for advancing applications in microwave and quantum technologies.
The simplest model of nonlinear response of a superconducting thin film is used for modeling the nonlinear phenomena in a superconducting transmission line and a microstrip resonator. The specified characteristic power of the transmission line is suggested to use as a fitting parameter for numerical description of the microstrip line nonlinearity at microwaves. Quantitative agreement of simulated and experimental data has been obtained for the incident power dependent transmission coefficient of a microstrip line section and a high quality microstrip resonator. Numerical results have also been obtained for the power of the third harmonic radiated from the nonlinear resonator.
Micro-channels of nanosized columnar tracks were planted by heavy-ion irradiation into superconducting microwave microstrip resonators that were patterned from YBa2Cu3O7-x thin films on LaAlO3 substrates. Three different ion fluences were used, producing different column densities, with each fluence having a successively greater impact on the nonlinearity of the device, as compared to a control sample. Photoresponse images made with a 638 nm rastered laser beam revealed that the channel is a location of enhanced photoresponse and a hot spot for the generation of intermodulation distortion. The microwave photoresponse technique was also advanced in this work by investigating the role of coupling strength on the distribution of photoresponse between inductive and resistive components.
This paper presents a comprehensive study of microwave nonlinearities in superconductors, with an emphasis on intermodulation distortion and third-harmonic generation. It contains the analysis of various resonant and nonresonant test devices and its validation using numerical simulations based on harmonic balance (HB). The HB simulations made on test devices show that the closed-form equations for intermodulation and third-harmonic generation are only valid at low power levels. The paper also contains examples of application of HB to illustrate that this technique is useful to simulate superconductive devices other than simple test devices, and that the validity of the simulations is not restricted to low drive power levels. Most of the analyses and simulations of this paper are based on electrical parameters that describe the nonlinearities in the superconducting material. These parameters are compatible with many existing models of microwave nonlinearities in superconductors. We discuss the particulars on how to relate these electrical parameters with one of the existing models that postulates that the nonlinear effects are due to a dependence of the penetration depth on the current density in the superconductor.
In the field of circuit quantum electrodynamics (c-QED), the coherent interaction of two-level systems (TLSs) with photons, confined in a superconducting microwave\nresonator, opens up new possibilities for quantum computing experiments.\nThis thesis contributes to the expansion of c-QED tool-box with slow propagation line-based solutions for ubiquitous techniques, such as cryogenic Near Field Scanning Microwave Microscopy (NSMM), Electron Spin Resonance (ESR) spectroscopy and Traveling Wave Parametric Amplifier (TWPA). For NSMM, novel compact superconducting fractal resonators have been developed to be directly integrated on a scanning probe. We report NSMM operation based on a microwave high-Q resonator populated with less than 10^3 photons and demonstrate a capacitive sensitivity of 0.38 aF/rtHz.\nThe unique properties and the design flexibility of fractal resonators also boost their resiliency to strong magnetic fields for ESR studies. The reported high Q-factors above 10^5 in a magnetic field up to 0.4 T translate into ESR sensitivity of 5 10^5 spins/rtHz.\nFurthermore, we demonstrate the operation of a practical TWPA based on a slow propagation fractal line. We achieve per unit length gain of > 0.5 dB/cm and total gain of ~6 dB for a 10 cm long line. Due to a radically shortened line, the amplifier is less vulnerable to fabrication defects. Moreover, due to a successful impedance matching\nbetween the amplifier line and in/out terminals, the obtained gain vs frequency characteristic has only moderate ripples. To mitigate a common TWPA problem of\ncoupling to parasitic ground plane resonances, we deploy a novel multilayer fabrication technology, which combines high and low kinetic inductance (KI) elements.\nFinally, we present an alternative implementation of a slow propagation line: a microstrip line with a thin film Atomic Layer Deposition (ALD) Al2O3 oxide. The resonator, based on a segment of a microstrip line, has a Q-factor on the order of 10^4 at single photon powers, reaching up to 10^5 at higher powers. As an additional functionality,\nwe incorporate dc current control over KI so that the resonance frequency is tuned by 62 MHz range, which corresponds to a KI-related nonlinearity of 3%.
We have investigated numerically a system consisting of a long Josephson junction embedded into a microstrip resonator. For such a configuration the Josephson vortex dynamics in the junction is driven by the oscillating currents in the resonator. We have calculated the complex impedance of the junction at the resonant frequency. The Q factor of the resonator and the change of the resonant frequency of the whole system can then be easily calculated knowing the parameters of the resonator without Josephson junction. The fluxon dynamics and the complex impedance of the junction are simulated for different values of the junction length, damping, dc bias current, and dc magnetic field. This allows us to explain the behavior of the impedance of the junction and different loss mechanisms. In particular, we predict a nonmonotonic dependence of the both real and imaginary parts of the impedance on the amplitude of the oscillating current in the resonator for some range of parameters. Our results show that such a combination of active and passive superconducting elements forms a rather interesting nonlinear physical system which might be useful for development of tunable/switchable superconducting resonators and suggests an experimental technique for detecting trapped vortices in long junctions.
Some results of an investigation of nonlinear behavior of NbN and YBa2Cu3O7-x films at microwaves are presented. Nonlinear microwave properties of superconducting films are analyzed on the basis of dynamic Current Voltage Characteristics (CVC) measured from the film response to the short duration video pulse. Conversion loss of the microwave signal into the intermediate frequency signal under various local oscillator power has been obtained from this analysis. The experimental data for the mixing of two microwave signals are described. Mixing effect was observed on superconducting NbN and YBa2Cu3O7-x film elements in microbridge and coplanar line forms. Conversion loss of about 20 dB was obtained in the running-wave regime.