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Superconductor Science and Technology

Coplanar superconducting resonators with nonlinear kinetic inductance bridge

Daria A. Kalacheva, Gleb Fedorov, Ivan Khrapach, O. V. Astafiev

Published Feb 15, 2023• 4 citations
Publisher

Abstract

Abstract We present a model and experimental realization of coplanar superconducting resonators terminated by a shunting kinetic inductance bridge made of ultra-thin Al films. The fabrication process that we propose allows us to create very homogeneous films, which makes them suitable for many applications in quantum devices. Due to the specific properties of the films, the resonators exhibit a Duffing oscillator behavior resulting in bifurcations and interactions between different power sources, which was previously observed in similar systems. Moreover, since the nonlinearity of such a system is concentrated at the bridge, while the wave propagates in a linear environment, it is possible to propose a simple model that accurately describes its behavior. We show that, when resonators are operated within a notch-port architecture, our model has a closed-form solution for the transmission coefficient and allows one to accurately extract parameters of the system, including the kinetic inductance of the bridge and its depairing current. Potential applications of such systems include tunable resonators, photon detectors, bifurcation and parametric amplifiers, as well as a measurement device for studying the properties of thin films.

DOI
10.1088/1361-6668/acbc53

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Abstract We present a model and experimental realization of coplanar superconducting resonators terminated by a shunting kinetic inductance bridge made of ultra-thin Al films. The fabrication process that we propose allows us to create very homogeneous films, which makes them suitable for many applications in quantum devices. Due to the specific properties of the films, the resonators exhibit a Duffing oscillator behavior resulting in bifurcations and interactions between different power sources, which was previously observed in similar systems. Moreover, since the nonlinearity of such a system is concentrated at the bridge, while the wave propagates in a linear environment, it is possible to propose a simple model that accurately describes its behavior. We show that, when resonators are operated within a notch-port architecture, our model has a closed-form solution for the transmission coefficient and allows one to accurately extract parameters of the system, including the kinetic inductance of the bridge and its depairing current. Potential applications of such systems include tunable resonators, photon detectors, bifurcation and parametric amplifiers, as well as a measurement device for studying the properties of thin films.
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 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.
The objective of this thesis is to evaluate a generic process for fabrication and characterization of the Superconductive coplanar waveguide (CPW) resonators. Superconductive CPW resonators with various lengths and shapes are designed to investigate their electrical and magnetic properties as well as resonance properties and sensitivities. In the first part of thesis, two different models are introduced in order to estimate the nonlinear kinetic inductance of a superconducting CPW resonator. The first model is based on Bean critical-state model and the second one is based on current dependence of London penetration depth. The existence of a shift in resonant frequency of Superconductive CPW resonator caused by a non-linear kinetic inductance is also shown experimentally. Simulations were carried out to estimate the nonlinear kinetic inductance due to the self- induced magnetic field penetration. The rest of the thesis is concerned with development of very smooth Aluminum (Al) thin films with RMS (Root Mean Square) roughness 1~nm and CAD (Computer Aid Design) of superconductive CPW resonators. Experimental investigation of a generic fabrication technique for superconductive CPW resonator is carried out. Many resonators are fabricated with different design parameters, such as centerline or gap width, film thickness and gap capacitors length. The fabrication process is described in detail. Electron Beam Lithography is used to fabricate Nb and Al CPW resonators which are coupled to outer conductors via gap capacitors. We have fabricated GHz frequency CPW resonators with quality factors, Q up 5X10^5.
The objective of this thesis is to evaluate a generic process for fabrication and characterization of the Superconductive coplanar waveguide (CPW) resonators. Superconductive CPW resonators with various lengths and shapes are designed to investigate their electrical and magnetic properties as well as resonance properties and sensitivities. In the first part of thesis, two different models are introduced in order to estimate the nonlinear kinetic inductance of a superconducting CPW resonator. The first model is based on Bean criticalstate model and the second one is based on current dependence of London penetration depth, λL(I). The existence of a shift in resonant frequency, f0, of Superconductive CPW resonator caused by a non-linear kinetic inductance is also shown experimentally. Simulations were carried out to estimate the nonlinear kinetic inductance due to the selfinduced magnetic field penetration. The rest of the thesis is concerned with development of very smooth Aluminum (Al) thin films with RMS (Root Mean Square) roughness ∼ 1 nm and CAD (Computer Aid Design) of superconductive CPW resonators. Experimental investigation of a generic fabrication technique for superconductive CPW resonator is carried out. Many resonators are fabricated with different design parameters, such as centerline or gap width, film thickness and gap capacitors length. The fabrication process is described in detail. Electron Beam Lithography is used to fabricate Nb and Al CPW resonators which are coupled to outer conductors via gap capacitors. We have fabricated GHz frequency CPW resonators with quality factors, Q up to 5× 10.
This work focuses on the development and demonstration of tunable superconducting on-chip resonator, leveraging the intrinsic current-dependent non-linear kinetic inductance of superconducting aluminium, and investigating the effect of oxygen content. Thin films are deposited using standard metal evaporation. We present results from a comprehensive study based on a series of evaporated Al thin films. This research aims to inform and constrain optimisation strategies for the design of mm-wave on-chip spectrometers, particularly regarding yield, resolution, and efficiency. By systematically varying film stoichiometry, we use a series of DC measurements to extract fundamental film properties such as resistivity, critical current and critical temperature. Furthermore, we employ low-loss DC-coupled microwave resonators to characterise both their microwave properties and the non-linear kinetic inductance, comparing these findings to a determined non-linear kinetic model. Finally, we discuss the possibility of usage in a parametric amplifier.