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Applied Physics Letters

Controllable coupling between fundamental modes in an asymmetric superconducting coplanar waveguide resonator

E. Mutsenik, A. Sh. Sultanov, S. Linzen, Matthias Schmelz, Daria A. Kalacheva, O. V. Astafiev, G. Oelsner, Mario Ziegler, Uwe Hübner, Ronny Stolz, Evgeni V. Il’ichev

Published Jul 22, 2024• 0 citations
Publisher

Abstract

Controllable coupling between the odd and even fundamental modes of an asymmetric half-wavelength superconducting coplanar waveguide resonator is demonstrated. The resonant frequency of the even mode Ωe could be tuned by an external magnetic field, while the resonant frequency of the odd mode Ωo is field independent. To realize the tunability of Ωe, the central conductor of the NbN-based resonator was galvanically coupled to an array of Al-based rf-SQUIDs (radio frequency superconducting quantum interferometer device). These rf-SQUIDs are placed in only one resonator gap, ensuring its strong asymmetry. By adjusting the appropriate external magnetic flux Φ, equal frequencies of both modes were obtained. At this resonant point Ωo(Φ)=Ωe(Φ) an avoided level crossing of the eigenfrequencies was observed, demonstrating the coupling between the odd and even fundamental modes.

DOI
10.1063/5.0206959

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Controllable coupling between the odd and even fundamental modes of an asymmetric half-wavelength superconducting coplanar waveguide resonator is demonstrated. The resonant frequency of the even mode Ωe could be tuned by an external magnetic field, while the resonant frequency of the odd mode Ωo is field independent. To realize the tunability of Ωe, the central conductor of the NbN-based resonator was galvanically coupled to an array of Al-based rf-SQUIDs (radio frequency superconducting quantum interferometer device). These rf-SQUIDs are placed in only one resonator gap, ensuring its strong asymmetry. By adjusting the appropriate external magnetic flux Φ, equal frequencies of both modes were obtained. At this resonant point Ωo(Φ)=Ωe(Φ) an avoided level crossing of the eigenfrequencies was observed, demonstrating the coupling between the odd and even fundamental modes.
We have created a doubly tunable resonator, with the intention to simulate relativistic motion of the resonator boundaries in real space. Our device is a superconducting coplanar-waveguide microwave resonator, with fundamental resonant frequency ω 1 / (2 π ) ~ 5 GHz. Both of its ends are terminated to ground via dc-SQUIDs, which serve as magnetic-flux-controlled inductances. Applying a flux to either SQUID allows the tuning of ω 1 / (2 π ) by approximately 700 MHz. Using two separate on-chip magnetic-flux lines, we modulate the SQUIDs with two tones of equal frequency, close to 2 ω 1 . We observe photon generation, at ω 1 , above a certain pump amplitude threshold. By varying the relative phase of the two pumps we are able to control this threshold, in good agreement with a theoretical model. At the same time, some of our observations deviate from the theoretical predictions, which we attribute to parasitic couplings resulting in current driving of the SQUIDs.
Abstract We investigated both theoretically and experimentally open-ended coplanar waveguide resonators with rf SQUIDs embedded in the central conductor at different positions. These rf SQUIDs can be tuned by an external magnetic field and thus may exhibit the non-centrosymmetric nonlinearity of χ(2) type with suppressed Kerr nonlinearity. We demonstrated that this nonlinearity allows for efficient mixing of λ/2 andλmodes in the cavity and thus enables various parametric effects with three wave mixing. These effects are the second harmonic generation, the halftone generation, the parametric amplification in both degenerate and non-degenerate regimes and deamplification in degenerate regime.
In this work, we study a series of tunable flux qubits inductively coupled to a coplanar waveguide resonator fabricated on a sapphire substrate. Each qubit includes an asymmetric superconducting quantum interference device, which is controlled by the application of an external magnetic field and acts as a tunable Josephson junction. The tunability of the qubits is typically $\ifmmode\pm\else\textpm\fi{}3.5\phantom{\rule{0.2em}{0ex}}\mathrm{GHz}$ around their central gap frequency. The measured relaxation times are limited by dielectric losses in the substrate and can attain ${T}_{1}\ensuremath{\sim}8\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\mathrm{s}$. The echo dephasing times are limited by flux noise even at optimal points and reach ${T}_{2E}\ensuremath{\sim}4\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\mathrm{s}$, almost an order of magnitude longer than state of the art.
Voltage-tunable superconductor-semiconductor devices offer a unique platform to realize dynamic tunability in superconducting quantum circuits. By galvanically connecting a gated InAs\mathrm{In}\mathrm{As}InAs-Al\mathrm{Al}Al Josephson junction to a coplanar waveguide resonator, we demonstrate the use of a superconducting element with wideband gate tunability. We show that the resonant frequency is controlled via a gate-tunable Josephson inductance and that the nonlinearity of the InAs\mathrm{In}\mathrm{As}InAs-Al\mathrm{Al}Al junction is nondissipative as is the case with conventional AlOx-Al{\mathrm{Al}\mathrm{O}}_{\mathrm{x}}\text{-Al}AlOx​-Al junctions. As the gate voltage is decreased, the inductive participation of the junction increases up to $44\mathrm{%}$, resulting in the resonant frequency being tuned by over 2GHz2\phantom{\rule{0.2em}{0ex}}\mathrm{GHz}2GHz. Utilizing the wide tunability of the device, we demonstrate that two resonant modes can be adjusted such that they strongly hybridize, exhibiting an avoided-level crossing with a coupling strength of 51MHz51\phantom{\rule{0.2em}{0ex}}\mathrm{MHz}51MHz. Implementing such voltage-tunable resonators is the first step toward realizing wafer-scale continuous voltage control in superconducting circuits for qubit-qubit coupling, quantum limited amplifiers, and quantum memory platforms.
Frequency combs are useful in a wide range of applications, such as optical metrology and high-precision spectroscopy. We experimentally study a controllable frequency comb generated in a tunable superconducting coplanar-waveguide resonator in the microwave regime. A two-tone drive is applied on one of the resonance modes of the resonator and comb generation is observed around the resonance frequency of the resonator. Both central frequency and teeth density of the comb are precisely controllable, and the teeth spacing can be adjusted from Hz to MHz. Moreover, we show that a few hundreds of sidebands can be generated using a sufficiently strong drive power and the weakest drive power needed to generate the comb can be reduced to approach the quantum limit. These experimental results can be qualitatively explained via theoretical analysis.
We performed transmission spectroscopy experiments on coplanar half-wavelength niobium resonators at temperature T=4.2T=4.2\phantom{\rule{0.16em}{0ex}}T=4.2K. We observe not only a strong dependence of the quality factor QQQ and the resonance frequency fres{f}_{\mathrm{res}}fres​ on an externally applied magnetic field but also on the magnetic history of our resonators, i.e., on the spatial distribution of trapped Abrikosov vortices in the device. This is valid for a broad range of frequencies and angles between the resonator plane and the magnetic field direction and holds for resonators with and without antidots near the edges of the center conductor and the ground planes. In a detailed analysis, we show that characteristic features of the experimental data can only be reproduced by calculations if we assume a highly inhomogeneous rf current density and a flux density gradient with maxima at the edges of the superconductor. We furthermore demonstrate that the hysteretic behavior of the resonator properties can be used to considerably reduce the vortex-induced losses and to fine-tune the resonance frequency by the proper way of cycling to a desired magnetic field value.