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arXiv:2306.12701 · Applied Physics Letters

High impedance Josephson junction resonators in the transmission line geometry

Antti Ranni, Harald Havir, Subhomoy Haldar, V. F. Maisi

Published Sep 11, 2023• 10 citations
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Abstract

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.

DOI
10.1063/5.0164323

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We present an experimental investigation of lumped-element superconducting LC resonators designed to provide different types of coupling to a transmission line. We have designed four resonator geometries including dipole and quadrupole configured inductors connected in parallel with low-lossSiNx{\rm SiN}_{\rm x}SiNx​dielectric parallel-plate capacitors. The design of the resonator allows a change in the symmetry of the inductor or grounding of the capacitor to create LC resonators with: 1) inductive coupling, 2) capacitive coupling, 3) both types of coupling, or 4) greatly reduced coupling. We measured all four designs at a temperature of 30 mK at different values of power. We compare the extracted data from the four resonator types and find that both capacitive and inductive coupling can be included and that when nominally turned off, the coupling is greatly reduced from only minor changes in the circuit design. We also find a variation in the measured loss tangent of less than a few percent between the designs over a large range of internal quality factors, which are created by usingSiNx{\rm SiN}_{\rm x}SiNx​as a nonlinear lossy element within the capacitor.
It has been recently demonstrated that a single Josephson junction with a properly engineered impedance environment can be used as a reflection amplifier approaching the quantum limit at microwave frequencies. In this article the authors describe an improved microwave setup for such a device. Voltage-tunable capacitors enable precise impedance matching across a wide range of operating points. Also, a branch-line coupler instead of a microwave circulator is used for the separation of the input and the output signals to make the system more compact and affordable. Furthermore, a custom-designed bias tee is introduced. The authors present characterization results of individual components as well as of the complete system. In particular, noise spectroscopy is used to study amplifier stability as a function of input matching.
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.
We report the efficient coupling of a 50 Ω microwave circuit to a high impedance conductor. We use an impedance transformer consisting of a λ/4 co-planar resonator whose inner conductor contains an array of superconducting quantum interference devices (SQUIDs), providing it with a tunable lineic inductance L∼80 μ0, resulting in a characteristic impedance ZC∼1 kΩ. The impedance matching efficiency is characterized by measuring the shot noise power emitted by a dc biased tunnel junction connected to the resonator. We demonstrate matching to impedances in the 15 to 35 kΩ range with bandwidths above 100 MHz around a resonant frequency tunable between 4 and 6 GHz.
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.
A high temperature superconducting YBa2Cu3Oy array of five Josephson junctions designed with additional coupling lines has been developed to demonstrate the effects of frequency locking and impedance matching for applications such as oscillators, mixers, and detectors. The Josephson self-radiation power was directly detected by a superheterodyne receiver, and Shapiro steps were also measured. The Josephson self-radiation properties reveal good quality of phase locking and microwave coupling with external circuits. The maximum self-radiation power of our array is about 50 pW which is several ten times higher than that of a single Josephson junction, and its peak point exactly satisfies the Josephson current-voltage relation. The Shapiro-step measurements show that the behavior of current-voltage curve depends on the effective inductance of coupling lines which affects the total impedance of Josephson junction array and microwave coupling. The Josephson oscillation frequency was obtained up to about 880 GHz which is 73% of the maximum available frequency calculated from the characteristic voltage of the Josephson junctions. Experimental results show that this type of Josephson junction array can improve the Josephson self-radiation power and increase the maximum detectable frequency.