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Low-loss tunable metamaterials using superconducting thin-film circuits with Josephson junctions

S. Butz, P. Jung, Alexey Vladimirovich Ustinov

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

We report on experiments with superconducting Josephson metamaterials. In such a material, conventional split ring resonators are replaced by superconducting loops that are interrupted by Josephson junctions, so called rf-SQUIDs. Like the split ring resonators, they can be seen as LCresonators that couple to the magnetic component of the incoming wave. The advantage of superconducting thin-film metamaterials is that due to the tunable intrinsic inductance of the Josephson junction, the resonance frequency of the rf-SQUID can be changed by applying an external dc magnetic field. We present experimental results that show the tunability of the resonance frequency of these devices.

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We report on experiments with superconducting Josephson metamaterials. In such a material, conventional split ring resonators are replaced by superconducting loops that are interrupted by Josephson junctions, so called rf-SQUIDs. Like the split ring resonators, they can be seen as LCresonators that couple to the magnetic component of the incoming wave. The advantage of superconducting thin-film metamaterials is that due to the tunable intrinsic inductance of the Josephson junction, the resonance frequency of the rf-SQUID can be changed by applying an external dc magnetic field. We present experimental results that show the tunability of the resonance frequency of these devices.
We have prepared meta-atoms based on radio-frequency superconducting quantum-interference devices (rf SQUIDs) and examined their tunability with dc magnetic field, rf current, and temperature. rf SQUIDs are superconducting split-ring resonators in which the usual capacitance is supplemented with a Josephson junction, which introduces strong nonlinearity in the rf properties. We find excellent agreement between the data and a model that regards the Josephson junction as the resistively and capacitively shunted junction. A magnetic field tunability of 80 THz=G at 12 GHz is observed, a total tunability of 56% is achieved, and a unique electromagnetically induced transparency feature at intermediate excitation powers is demonstrated for the first time. An rf SQUID metamaterial is shown to have qualitatively the same behavior as a single rf SQUID with regard to dc flux and temperature tuning.
We propose tunable superconducting split-ring resonators (SRRs) employing nonlinear Josephson inductance. A fraction of SRR is replaced by Nb-AlOx-Nb Josephson tunnel junctions connected in parallel and forming a superconducting quantum interference device, whose inductance is sensitive to the external dc magnetic field. Due to the lumped nature of the Josephson inductance, the SRR can be made very compact, and its resonance frequency can be tuned by applying magnetic field. We present the model, results of extensive electromagnetic-simulation and experimental data for the SRR weakly coupled to a transmission line within frequency range of 11–13 GHz.
We investigate the ultrastrong tunable coupler for coupling of superconducting resonators. The obtained coupling constant exceeds 1 GHz, and the wide-range tunability is achieved for both antiferromagnetics and ferromagnetics from $\ensuremath{-}1086$ to 604 MHz. The ultrastrong coupler is composed of a rf superconducting quantum interference device (SQUID) and dc SQUID as tunable junctions, which connect to resonators via shared aluminum thin-film meander lines enabling such a huge coupling constant. The spectrum of the coupler obviously shows the breaking of the rotating-wave approximation, and our circuit model treating the Josephson junction as a tunable inductance reproduces the experimental results well. The ultrastrong coupler is expected to be utilized in quantum annealing circuits and/or noisy intermediate-scale quantum devices with dense connections between qubits.
Metamamterials are 1D, 2D or 3D arrays of articial atoms. The articial atoms, called "meta-atoms", can be any component with tailorable electromagnetic properties, such as resonators, LC circuits, nano particles, and so on. By designing the properties of individual meta-atoms and the interaction created by putting them in a lattice, one can create a metamaterial with intriguing properties not found in nature. My Ph. D. work examines the meta-atoms based on radio frequency superconducting quantum interference devices (rf-SQUIDs); their tunability with dc magnetic field, rf magnetic field, and temperature are studied. The rf-SQUIDs are superconducting split ring resonators in which the usual capacitance is supplemented with a Josephson junction, which introduces strong nonlinearity in the rf properties. At relatively low rf magnetic field, a magnetic field tunability of the resonant frequency of up to 80 THz/Gauss by dc magnetic field is observed, and a total frequency tunability of 100% is achieved. The macroscopic quantum superconducting metamaterial also shows manipulative self-induced broadband transparency due to a qualitatively novel nonlinear mechanism that is different from conventional electromagnetically induced transparency (EIT) or its classical analogs. A near complete disappearance of resonant absorption under a range of applied rf flux is observed experimentally and explained theoretically. The transparency comes from the intrinsic bi-stability and can be tuned on/ off easily by altering rf and dc magnetic fields, temperature and history. Hysteretic in situ 100% tunability of transparency paves the way for auto-cloaking metamaterials, intensity dependent filters, and fast-tunable power limiters. An rf-SQUID metamaterial is shown to have qualitatively the same behavior as a single rf-SQUID with regards to dc flux, rf flux and temperature tuning. The two-tone response of self-resonant rf-SQUID meta-atoms and metamaterials is then studied here via intermodulation (IM) measurement over a broad range of tone frequencies and tone powers. A sharp onset followed by a surprising strongly suppressed IM region near the resonance is observed. This behavior can be understood employing methods in nonlinear dynamics; the sharp onset, and the gap of IM, are due to sudden state jumps during a beat of the two-tone sum input signal. The theory predicts that the IM can be manipulated with tone power, center frequency, frequency difference between the two tones, and temperature. This quantitative understanding potentially allows for the design of rf-SQUID metamaterials with either very low or very high IM response.
Using superconducting quantum interference devices (SQUIDs) as the basic, low-loss elements of thin-film metamaterials has one main advantage: their resonance frequency is easily tunable by applying a weak magnetic field. The downside, however, is a strong sensitivity to stray and inhomogeneous magnetic fields. In this work, we demonstrate that even small magnetic fields from electronic components destroy the collective, resonant behaviour of the SQUID metamaterial. We also show how the effect of these fields can be minimized. As a first step, magnetic shielding decreases any initially present fields, including the earth's magnetic field. However, further measures such as improvements in the sample geometry have to be taken to avoid the trapping of Abrikosov vortices.
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.