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arXiv:2310.15344 · IEEE Transactions on Applied Superconductivity

Modeling and Testing Superconducting Artificial CPW Lines Suitable for Parametric Amplification

Fausto Patricio Mena, D. Valenzuela, C. Espinoza, Francisco Pizarro, Boon-Kok Tan, David Johannes Thoen, J. J. A. Baselmans, Ricardo Finger

Published May 1, 2024• 1 citation

Abstract

Achieving amplification with high gain and quantum-limited noise is a difficult problem to solve. Parametric amplification using a superconducting transmission line with high kinetic inductance is a promising technology not only to solve this problem but also adding several benefits. Compared to other technologies, they have the potential to improve power saturation, achieve larger fractional bandwidths, and operate at higher frequencies. In this type of amplifier, the selection of the proper transmission line is a key element in its design. Given current fabrication limitations, traditional lines such as coplanar waveguides (CPW), are not ideal for this purpose, since it is difficult to make them with the proper characteristic impedance for good matching and slow enough phase velocity for making them more compact. Capacitively loaded lines, also known as artificial lines, are a good solution to this problem. However, few design rules or models have been presented to guide their accurate design. This fact is even more crucial considering that they are usually fabricated in the form of Floquet lines that have to be designed carefully to suppress undesired harmonics appearing in the parametric process. In this article we present, first, a new modeling strategy, based on the use of electromagnetic-simulation software, and, second, a first-principles model that facilitate and speed the design of CPW artificial lines and of Floquet lines made out of them. Then, we present comparisons with experimental results that demonstrate their accuracy. Finally, the theoretical model allows one to predict the high-frequency behavior of the artificial lines, showing that they are good candidates for implementing parametric amplifiers above 100 GHz.

DOI: 10.1109/tasc.2024.3389652

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Achieving amplification with high gain and quantum-limited noise is a difficult problem to solve. Parametric amplification using a superconducting transmission line with high kinetic inductance is a promising technology not only to solve this problem but also adding several benefits. Compared to other technologies, they have the potential to improve power saturation, achieve larger fractional bandwidths, and operate at higher frequencies. In this type of amplifier, the selection of the proper transmission line is a key element in its design. Given current fabrication limitations, traditional lines such as coplanar waveguides (CPW), are not ideal for this purpose, since it is difficult to make them with the proper characteristic impedance for good matching and slow enough phase velocity for making them more compact. Capacitively loaded lines, also known as artificial lines, are a good solution to this problem. However, few design rules or models have been presented to guide their accurate design. This fact is even more crucial considering that they are usually fabricated in the form of Floquet lines that have to be designed carefully to suppress undesired harmonics appearing in the parametric process. In this article we present, first, a new modeling strategy, based on the use of electromagnetic-simulation software, and, second, a first-principles model that facilitate and speed the design of CPW artificial lines and of Floquet lines made out of them. Then, we present comparisons with experimental results that demonstrate their accuracy. Finally, the theoretical model allows one to predict the high-frequency behavior of the artificial lines, showing that they are good candidates for implementing parametric amplifiers above 100 GHz.

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Abstract We measured the microwave transmission characteristics of coplanar waveguides (CPWs) fabricated using YBa2Cu3O7−δ (YBCO) thin films with DC current biases. Kinetic inductances ( L K ) and nonlinear parameters ( I * ) were evaluated for CPWs with film thicknesses of 20, 50, and 200 nm. The results indicate that the experimental values closely follow the second-order nonlinearity exhibited by the L K . To operate as a superconducting parametric amplifier with a standard gain of 20 dB and a pump power of −10 dBm, we introduced a step-impedance structure into the transmission line. As a result, when using an MgO substrate, the required line length was estimated to be approximately 1.25 m, corresponding to approximately 29 times the wavelength of the CPW.

Broadband quantum-limited parametric amplifiers (PAs) are essential components in quantum information science and technology. Impedance-engineered resonator-based PAs and traveling-wave PAs are the primary approaches taken to overcome the gain-bandwidth constraint. While the former PAs are simpler to fabricate, the target characteristic impedance

{Z}_{\mathrm{NR}}

of the nonlinear resonator has been restricted to be below $10\phantom{\rule{0.2em}{0ex}}\mathrm{\ensuremath{\Omega}}$, requiring large capacitance. Moreover, these PAs have only been implemented with aluminum-based Josephson junctions (JJs), hindering their operation at high temperatures or strong magnetic fields. To address these issues, we propose a three-stage impedance-transformer scheme, showcased with a 20 nm thick, 250 nm wide, high-kinetic-inductance niobium-titanium-nitride (

\mathrm{Nb}\mathrm{Ti}\mathrm{N}

) film. Our scheme enables

{Z}_{\mathrm{NR}}

up to several tens of ohms---a tenfold improvement over conventional designs, achieved through an additional quarter-wavelength transmission line with a characteristic impedance of 180 $\mathrm{\ensuremath{\Omega}}$. Our kinetic-inductance impedance-engineered parametric amplifiers (KIMPAs), featuring a 330 fF shunt capacitor, demonstrate a phase-preserving amplification with a 450-MHz bandwidth at 17 dB gain, and added noise ranging from 0.5 to 1.3 quanta near the center frequency of 8.4 GHz. Owing to the high critical current of the

\mathrm{Nb}\mathrm{Ti}\mathrm{N}

nanowire, the KIMPA also achieves an output saturation power of up to $\ensuremath{-}51\ifmmode\pm\else\textpm\fi{}3$ dBm, approximately 25 dB higher than that of JJ-based PAs. This scheme also opens new possibilities for other three-wave-mixing building blocks.