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arXiv:2607.29301

Diode Effect in Nonlinear High-Kinetic-Inductance Transmission Line Resonators

Niklas Gaiser, Ciprian Padurariu, Björn Kubala, Nadav Y. Katz, Joachim Ankerhold

Published Jul 31, 2026• 0 citations
arXivHTMLPDF

Abstract

High-kinetic-inductance (HKI) transmission lines provide a promising platform for compact nonlinear superconducting microwave devices. Existing theoretical descriptions are typically based on the slowly varying envelope approximation, which becomes inadequate for strongly nonlinear resonant structures with pronounced spatial field variations. Here, we develop a theoretical framework for single-frequency nonlinear wave propagation in HKI transmission lines by formulating the problem as a boundary value problem that retains the full spatial dependence of the electromagnetic fields. Applying the method to resonant transmission-line geometries, we demonstrate power-dependent resonance shifts, bistable transmission solutions, and strongly direction-dependent transport arising from asymmetric impedance barriers, yielding transmission contrasts of up to $93\%$ without magnetic bias fields. The framework is further extended to a three-port stub geometry, where nonlinear interference produces shifted anti-resonances and Duffing-like spectral distortions. Our approach provides a versatile tool for the analysis and design of strongly nonlinear superconducting microwave devices.

DOI
10.48550/arxiv.2607.29301

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High-kinetic-inductance (HKI) transmission lines provide a promising platform for compact nonlinear superconducting microwave devices. Existing theoretical descriptions are typically based on the slowly varying envelope approximation, which becomes inadequate for strongly nonlinear resonant structures with pronounced spatial field variations. Here, we develop a theoretical framework for single-frequency nonlinear wave propagation in HKI transmission lines by formulating the problem as a boundary value problem that retains the full spatial dependence of the electromagnetic fields. Applying the method to resonant transmission-line geometries, we demonstrate power-dependent resonance shifts, bistable transmission solutions, and strongly direction-dependent transport arising from asymmetric impedance barriers, yielding transmission contrasts of up to 93%93\%93% without magnetic bias fields. The framework is further extended to a three-port stub geometry, where nonlinear interference produces shifted anti-resonances and Duffing-like spectral distortions. Our approach provides a versatile tool for the analysis and design of strongly nonlinear superconducting microwave devices.
We describe a novel class of devices based on the nonlinearity of the kinetic inductance of a superconducting thin film. By placing a current-dependent inductance in a microwave resonator, small currents can be measured through their effect on the resonator’s frequency. By using a high-resistivity material for the film and nanowires as kinetic inductors, we can achieve a large coefficient of nonlinearity to improve device sensitivity. We demonstrate a current sensitivity of 8 pA/√Hz, making this device useful for transition-edge sensor (TES) readout and other cutting-edge applications. An advantage of these devices is their natural ability to be multiplexed in the frequency domain, enabling large detector arrays for TES-based instruments. A traveling-wave version of the device, consisting of a thin-film microwave transmission line, is also sensitive to small currents as they change the phase length of the line due to their effect on its inductance. We demonstrate a current sensitivity of 5 pA/√Hz for this version of the device, making it also suitable for TES readout as well as other current-detection applications. It has the advantage of multi-gigahertz bandwidth and greater dynamic range, offering a different approach to the resonator version of the device. Finally, we also demonstrate a transmission-line resonator version of the device that combines some of the advantages of the nanowire resonator and the traveling-wave device. This version of the device has high dynamic range but can also be easily multiplexed in the frequency domain. A lumped-element resonator similar to the first device can be placed in a loop configuration to make it sensitive to magnetic fields. We demonstrate an example of such a device whose sensitivity could ultimately reach levels similar to those of state-of-the-art DC SQUIDs, making it potentially useful for many magnetometry applications given its ease of multiplexing. Finally, a similar microwave resonator is shown to exhibit parametric gain of up to 29 dB in the presence of a strong pump tone. The noise performance of this parametric amplifier approaches the quantum limit, making it useful for applications in quantum information and metrology.
We study the microwave impedance of extremely high aspect ratio (length/width ≈ 5000) superconducting niobium nitride nanowires. The nanowires are fabricated in a compact meander geometry that is in series with the center conductor of a 50 Ω coplanar waveguide transmission line. The transmission coefficient of the sample is measured up to 20 GHz. At high frequency, a peak in the transmission coefficient is seen. Numerical simulations show that this is a half-wave resonance along the length of the nanowire, where the nanowire acts as a high impedance, slow wave transmission line. This resonance sets the upper frequency limit for these nanowires as inductive elements. Fitting simulations to the measured resonance enables a precise determination of the nanowire's complex sheet impedance at the resonance frequency. The real part is a measure of dissipation, while the imaginary part is dominated by kinetic inductance. We characterize the dependence of the sheet resistance and sheet inductance on both temperature and current and compare the results to recent theoretical predictions for disordered superconductors. These results can aid in the understanding of high frequency devices based on superconducting nanowires. They may also lead to the development of novel superconducting devices such as ultra-compact resonators and slow-wave structures.
We study the microwave impedance of extremely high aspect ratio (length/width ≈ 5000) superconducting niobium nitride nanowires. The nanowires are fabricated in a compact meander geometry that is in series with the center conductor of a 50 Ω coplanar waveguide transmission line. The transmission coefficient of the sample is measured up to 20 GHz. At high frequency, a peak in the transmission coefficient is seen. Numerical simulations show that this is a half-wave resonance along the length of the nanowire, where the nanowire acts as a high impedance, slow wave transmission line. This resonance sets the upper frequency limit for these nanowires as inductive elements. Fitting simulations to the measured resonance enables a precise determination of the nanowire's complex sheet impedance at the resonance frequency. The real part is a measure of dissipation, while the imaginary part is dominated by kinetic inductance. We characterize the dependence of the sheet resistance and sheet inductance on both temperature and current and compare the results to recent theoretical predictions for disordered superconductors. These results can aid in the understanding of high frequency devices based on superconducting nanowires. They may also lead to the development of novel superconducting devices such as ultra-compact resonators and slow-wave structures.
We examine the DC and radio frequency (RF) response of superconducting transmission line resonators comprised of very thin NbTiN films, <12 nm in thickness, in the high-temperature limit, where the photon energy is less than the thermal energy. The resonant frequencies of these superconducting resonators show a significant nonlinear response as a function of RF input power, which can approach a frequency shift of Δf=−0.15% in a −20 dB span in the thinnest film. The strong nonlinear response allows these very thin film resonators to serve as high kinetic inductance parametric amplifiers.
Superconducting boron-doped silicon is a promising material for integrated silicon quantum devices. In particular, its low electronic density and moderate disorder make it a suitable candidate for the fabrication of large inductances with low losses at microwave frequencies. We study experimentally the electrodynamics of superconducting silicon thin layers using coplanar waveguide resonators, focusing on the kinetic inductance, the internal losses, and the variation of these quantities with the resonator readout power. We report the observation in a doped semiconductor of microwave resonances with internal quality factors of a few thousand. As expected in the BCS framework, superconducting silicon presents a large sheet kinetic inductance in the 50--500-pH range, comparable to that of strongly disordered superconductors. The temperature dependence of the kinetic inductance is well described by the Mattis-Bardeen theory. However, we find an unexpectedly strong nonlinearity in the complex surface impedance that cannot be satisfactorily explained either by depairing or by quasiparticle heating.
Nonlinear superconducting devices, typically based on Josephson-junction (JJ) nonlinearities, are the basis for superconducting quantum electronics, enabling, e.g., the formation of isolated two-level superconducting qubits and amplifiers. While emerging spin, hybrid spin-superconducting (including Majorana), and nanomagneto-optical quantum systems could benefit tremendously from superconducting nonlinearities, the presence of strong magnetic fields in these systems is incompatible with conventional JJ devices, which are highly sensitive to applied magnetic fields. One potential solution is the use of kinetic inductance (KI) nonlinearity. To date, only linear KI devices have been shown to operate in high magnetic fields, while nonlinear KI device operation in high magnetic fields has received virtually no attention. Here, we study the nonlinearity of superconducting nanowire (NW) KI resonators and their performance as parametric amplifiers for in-plane magnetic fields. We study the Kerr coefficients of NW KI resonators made from 10-nm-thick $\mathrm{Nb}\text{\ensuremath{-}}\mathrm{Ti}\text{\ensuremath{-}}\mathrm{N}$ films with characteristic impedance up to 3 $\mathrm{k}\mathrm{\ensuremath{\Omega}}$, and demonstrate both nondegenerate and degenerate parametric amplification, at magnetic fields up to 2 T. We find that narrow KI resonators of width $0.1\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\mathrm{m}$ are robust, in terms of gain, dynamic range and noise, to magnetic fields up to approximately 2T2\phantom{\rule{0.2em}{0ex}}\mathrm{T}2T, for up to 12 dB (16 dB) of phase-insensitive (phase-sensitive) gain. In comparison, wider KI resonators of width $1\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\mathrm{m}$ suffer significant suppression in the gain at fields well below 222 T. Around 8-dB deamplification is also observed for coherent states for a 0.1-$\text{\ensuremath{\mu}}\mathrm{m}$ NW KI resonator, implying the capability of noise squeezing. These results open a pathway to developing nonlinear quantum devices that operate in or generate high magnetic fields such as spin, hybrid spin-superconducting, and magneto-optomechanical devices.