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Applied Physics Letters

High kinetic inductance NbTiN superconducting transmission line resonators in the very thin film limit

Terence Bretz-Sullivan, Rupert Lewis, Ana L. Lima-Sharma, David Lidsky, Christopher M. Smyth, Charles Thomas Harris, M. B. Venuti, Serena Eley, Tzu‐Ming Lu

Published Aug 1, 2022• 19 citations
Publisher

Abstract

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.

DOI
10.1063/5.0100961

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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.
Nonlinear resonators of superconducting thin-film kinetic inductance have attracted considerable research interest in the fields of detectors, qubits, parametric amplifiers, and more. By tuning the deposition parameters, niobium titanium nitride (NbTiN) films (∼12 nm in thickness) present high resistivity(∼2000 μΩ cm) and large sheet kinetic inductance (∼0.7 nH/□). We designed resonators with NbTiN micronwire as the inductor and aluminum as the capacitor, which result in a high internal quality factor and a Kerr nonlinearity of a few hertz. The radio frequency response of the resonators demonstrates nonlinear behavior similar to that of the cubic Duffing oscillator, including frequency shift and hysteresis region. The kinetic inductance resonator is a promising candidate for high saturation power parametric amplifiers.
We present broadband parametric amplifiers based on the kinetic inductance of superconducting NbTiN thin films in an artificial (lumped-element) transmission line architecture. We demonstrate two amplifier designs implementing different phase matching techniques: periodic impedance loading and resonator phase shifters placed periodically along the transmission line. Our design offers several advantages over previous CPW-based amplifiers, including intrinsic 50 Ω characteristic impedance, natural suppression of higher pump harmonics, lower required pump power, and shorter total trace length. Experimental realizations of both versions of the amplifiers are demonstrated. With a transmission line length of 20 cm, we have achieved gains of 15 dB over several GHz of bandwidth.
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.
Abstract Ultra-thin superconducting aluminum films of 3-nm grown on sapphire by molecule-beam epitaxy show excellent superconductivity and large kinetic inductance. This results in a record high Kerr non-linearity of 33 kHz and 3.62 MHz per photon in notch-type and transmission-type resonators, respectively. 4-wave mixing leverages this non-linearity to achieve 12 dB parametric amplification in transmission type resonator, making the ultra-thin film ideal for photon detection and amplification applications.
A quantum-limited amplification chain is a fundamental advantage for any application that may benefit from the detection of very faint signals. Reading out arrays of superconducting detectors (TESs or MKIDs), resonant cavities, or qubits, calls for large bandwidth amplifiers in addition to having the lowest possible noise. At millikelvin temperatures, Kinetic Inductance Traveling-Wave Parametric Amplifiers (KI-TWPAs) working in 3-wave-mixing (3WM) and fabricated from a 20 nm thick NbTiN film have shown promising noise performances, as they can operate close to the quantum limit (Malnou et al., 2021). However, they still require fairly high pump power. Devices that would require lower pump power would be easier to implement in readout chains, could reach the quantum limit and they would be compatible with qubit readout. A possible solution for obtaining this optimal configuration is to use a thinner superconducting film. In this work we explore the properties of NbTiN films with a thickness less than 20 nm and we report the obtained experimental characterizations in terms of critical temperature, normal resistivity, and kinetic inductance. A new design for a 3WM KI-TWPA amplifier, based on these developed superconducting films, is introduced and discussed.
We present a design and implementation of a frequency-tunable superconducting resonator. The resonance frequency tunability is achieved by flux-coupling a superconducting LC loop to a current-biased feedline; the resulting screening current leads to a change of the kinetic inductance and shift in the resonance frequency. The thin-film aluminum resonator consists of an interdigitated capacitor and thin line inductors forming a closed superconducting loop. The magnetic flux from the nearby niobium current feedline induces Meissner shielding currents in the resonator loop leading to a change in the kinetic part of the total inductance of the resonator. We demonstrate continuous frequency tuning within 160 MHz around the resonant frequency of 2.7 GHz. We show that: (1) frequency up-conversion is achieved when a kilohertz ac modulation signal is superimposed onto the dc bias resulting in sidebands to the resonator tone; (2) three-wave mixing is attained by parametrically pumping the nonlinear kinetic inductance using a strong rf pump signal in the feedline. The simple architecture is amenable to large-array multiplexing and on-chip integration with other circuit components. The concept could be applied in flux magnetometers, up-converters, and parametric amplifiers operating above 4 K when alternative high-critical-temperature material with high kinetic inductance is used.