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Theory of Computing Systems

Microwave Photos in High Impedance Transmission line: Dispersion, Disorder and Localization

Mehta, Nitish Jitendrakumar

Published Jan 1, 2017• 0 citations
Publisher

Abstract

In this thesis we will describe the theoretical and experimental studies of a TEM on-chip superconducting transmission line with a wave impedance as high as 20 $\mathrm{k}\Omega$, phase and group velocity of waves simultaneously reduced by a factor of 100 in a broad range of frequencies from 0 to about 10 $\mathrm{GHz}$. A conventional microwave coaxial transmission line gets its inductance and capacitance from magnetic and electric fields stored in the space between its inner and outer conductors. This in turn limits its impedance to around 50 $\Omega$ and group velocity of waves very close to the speed of light in vacuum. In this work we are able to increase the impedance by over two orders of magnitude and reduce the group and phase velocity of waves by over two orders of magnitude as well, by constructing a coplanar transmission line out of a pair of long Al/AlOx/Al Josephson tunnel junction chains. A Josephson junction gets its inductance not from the magnetic energy but rather from the much larger kinetic energy of tunneling Cooper pairs, which is unrelated to the electromagnetic properties of vacuum. In this work we present a design of such a transmission line and low-temperature measurement of its dispersion relation. We then study and characterize the disorder present in the circuit parameters of our system and using this, we conclude that for frequencies up to 12 GHz, there is no evidence of Anderson localization of waves, even for chains exceeding 30,000 junctions. Low dissipation and absence of localization make this transmission line ideal for use in various experiments where high impedance can enable strong coupling between light and matter.

DOI
10.13016/m2x921k0x

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In this thesis we will describe the theoretical and experimental studies of a TEM on-chip superconducting transmission line with a wave impedance as high as 20 kΩ\mathrm{k}\OmegakΩ, phase and group velocity of waves simultaneously reduced by a factor of 100 in a broad range of frequencies from 0 to about 10 GHz\mathrm{GHz}GHz. A conventional microwave coaxial transmission line gets its inductance and capacitance from magnetic and electric fields stored in the space between its inner and outer conductors. This in turn limits its impedance to around 50 Ω\OmegaΩ and group velocity of waves very close to the speed of light in vacuum. In this work we are able to increase the impedance by over two orders of magnitude and reduce the group and phase velocity of waves by over two orders of magnitude as well, by constructing a coplanar transmission line out of a pair of long Al/AlOx/Al Josephson tunnel junction chains. A Josephson junction gets its inductance not from the magnetic energy but rather from the much larger kinetic energy of tunneling Cooper pairs, which is unrelated to the electromagnetic properties of vacuum. In this work we present a design of such a transmission line and low-temperature measurement of its dispersion relation. We then study and characterize the disorder present in the circuit parameters of our system and using this, we conclude that for frequencies up to 12 GHz, there is no evidence of Anderson localization of waves, even for chains exceeding 30,000 junctions. Low dissipation and absence of localization make this transmission line ideal for use in various experiments where high impedance can enable strong coupling between light and matter.
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.
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In this article, we present an experimental study of microwave resonators made out of Josephson junctions. The junctions are embedded in a transmission line geometry so that they increase the inductance per length for the line. By comparing two devices with different input/output coupling strengths, we show that the coupling capacitors, however, add a significant amount to the total capacitance of the resonator. This makes the resonators with high coupling capacitance to act rather as lumped element resonators with inductance from the junctions and capacitance from the end sections. Based on a circuit analysis, we show that the input and output couplings of the resonator are limited to a maximum value of ωrZ0/4Zr, where ωr is the resonance frequency and Z0 and Zr are the characteristic impedances of the input/output lines and the resonator, respectively.
Superconducting microwave transmission lines can be designed to have lower loss, lower dispersion, and lower phase velocity than conventional metal lines. These properties make superconducting transmission lines attractive for use in many devices and systems such as filters and analog to digital converters. The problem with designing microwave circuits which utilizes these lines is that accurate circuit models do not exist. This paper present models for the microwave transmission line parameters (phase velocity, attenuation, and characteristic impedance) of superconducting lines as a function of temperature and geometry. An experiment to verify these models is also presented.
Superinductances are superconducting circuit elements that combine a large inductance with a low parasitic capacitance to ground, resulting in a characteristic impedance exceeding the resistance quantum RQ=h/(2e)2≃6.45kΩR_Q = h/(2e)^2 \simeq 6.45 \mathrm{k}ΩRQ​=h/(2e)2≃6.45kΩ. In recent years, these components have become key enablers for emerging quantum circuit architectures. However, achieving high characteristic impedance while maintaining scalability and fabrication robustness remains a major challenge. In this work, we present two fabrication techniques for realizing superinductances based on vertically stacked Josephson junctions. Using a multi-angle Manhattan (MAM) process and a zero-angle (ZA) evaporation technique -- in which junction stacks are connected pairwise using airbridges -- we fabricate one-dimensional chains of stacks that act as high-impedance superconducting transmission lines. Two-tone microwave spectroscopy reveals the expected n\sqrt{n}n​ scaling of the impedance with the number of junctions per stack. The chain fabricated using the ZA process, with nine junctions per stack, achieves a characteristic impedance of ∼16kΩ\sim 16 \mathrm{k}Ω∼16kΩ, a total inductance of 5.9μH5.9 \mathrm{μH}5.9μH, and a maximum frequency-dependent impedance of 50kΩ50 \mathrm{k}Ω50kΩ at 1.4 GHz. Our results establish junction stacking as a scalable, robust, and flexible platform for next-generation quantum circuits requiring ultra-high impedance environments.