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arXiv:2401.02943 · Superconductor Science and Technology

Temperature dependence of microwave losses in lumped-element resonators made from superconducting nanowires with high kinetic inductance

Ermes Scarano, Elisabet K. Arvidsson, August K. Roos, Erik Holmgren, David B. Haviland

Published May 19, 2024• 4 citations
arXivHTMLPDF

Abstract

Abstract We study the response of several microwave resonators made from superconducting NbTiN thin-film meandering nanowires with large kinetic inductance, having different circuit topology and coupling to the transmission line. Reflection measurements reveal the parameters of the circuit and analysis of their temperature dependence in the range 1.7–6 K extract the superconducting energy gap and critical temperature. The lumped-element LC resonator, valid in our frequency range of interest, allows us to predict the quasiparticle (QP) contribution to internal loss, independent of circuit topology and characteristic impedance. Our analysis shows that the internal quality factor is limited not by thermal-equilibrium QP, but an additional temperature-dependent source of internal microwave loss.

DOI
10.1088/1361-6668/ad4d5c

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Abstract We study the response of several microwave resonators made from superconducting NbTiN thin-film meandering nanowires with large kinetic inductance, having different circuit topology and coupling to the transmission line. Reflection measurements reveal the parameters of the circuit and analysis of their temperature dependence in the range 1.7–6 K extract the superconducting energy gap and critical temperature. The lumped-element LC resonator, valid in our frequency range of interest, allows us to predict the quasiparticle (QP) contribution to internal loss, independent of circuit topology and characteristic impedance. Our analysis shows that the internal quality factor is limited not by thermal-equilibrium QP, but an additional temperature-dependent source of internal microwave loss.
Abstract The overall, loaded quality factor Q L quantifies the loss of energy stored in a resonator. Here we discuss on general grounds how Q L of a planar microwave resonator made of a conventional superconductor should depend on temperature and frequency. We consider contributions to Q L due to dissipation by thermal quasiparticles ( Q QP ), due to residual dissipation ( Q Res ), and due to coupling ( Q C ). We present experimental data obtained with superconducting stripline resonators fabricated from lead (Pb), with different center conductor widths and different coupling gaps. We probe the resonators at various harmonics between 0.7 GHz and 6 GHz and at temperatures between 1.5 K and 7 K. We find a strongly frequency- and temperature-dependent Q L , which we can describe by a lumped-element model. For certain resonators at lowest temperatures we observe a maximum in the frequency-dependent Q L when Q Res and Q C match, and here the measured Q L can exceed 2 × 10 5 .
Superconducting high kinetic inductance elements constitute a valuable resource for quantum circuit design and millimeter-wave detection. Granular aluminum (grAl) in the superconducting regime is a particularly interesting material since it has already shown a kinetic inductance in the range of nH/□ and its deposition is compatible with conventional Al/AlOx/Al Josephson junction fabrication. We characterize microwave resonators fabricated from grAl with a room temperature resistivity of 4×10^{3} μΩ cm, which is a factor of 3 below the superconductor to insulator transition, showing a kinetic inductance fraction close to unity. The measured internal quality factors are on the order of Q_{i}=10^{5} in the single photon regime, and we demonstrate that nonequilibrium quasiparticles (QPs) constitute the dominant loss mechanism. We extract QP relaxation times in the range of 1 s and we observe QP bursts every ∼20 s. The current level of coherence of grAl resonators makes them attractive for integration in quantum devices, while it also evidences the need to reduce the density of nonequilibrium QPs.
We evaluate the performance of hybrid microwave resonators made by combining sputtered Nb thin films with Tungsten nanowires grown with a He-beam induced deposition technique. Depending on growth conditions, the nanowires have a typical width w∈[35−75] nm and thickness t∈[5−40] nm. We observe a high normal state resistance R◻∈[65−150] Ω/◻ which together with a critical temperature Tc∈[4−6] K ensures a high kinetic inductance making the resonator strongly nonlinear. Both lumped and coplanar waveguide resonators were fabricated and measured at low temperature exhibiting internal quality factors up to 3990 at 4.5 GHz in the few photon regime. Analyzing the wire length, temperature, and microwave power dependence, we extracted a kinetic inductance for the W nanowire of LK≈15 pH/◻, which is 250 times higher than the geometrical inductance, and a Kerr non-linearity as high as KW,He/2π=200±120 Hz/photon at 4.5 GHz. The nanowires made with the helium focused ion beam are thus versatile objects to engineer compact, high impedance, superconducting environments with a mask and resist free direct write process.
We report the design, fabrication, and characterization of parametric amplifiers based on nonlinearities arising from current-induced pair-breaking in high kinetic inductance superconducting nanowires. We call these devices microwave entangler circuits (MEC), as they are intended for use in cluster state generation. The MECs are implemented as high quality factor lumped-element LC resonators and designed to support three-wave mixing, targeting a resonance frequency of 4.5 GHz and total loss rates below 2 MHz. Fabrication involved sputtering of 14 nm NbTiN films followed by lithography and reactive ion etching to define the nanoscale circuits. Resonator properties were characterized in a rapid thermal cycle cryostat at temperatures down to 1.7 K to extract the resonant frequency, and both internal and external loss rates. Parametric amplification from three-wave mixing was demonstrated with the application of a combined DC bias and high-frequency pump. Both signal and idler gain were observed, with gain up to 18 dB. A theoretical framework was also developed to model the operation of the MECs. The models help explain the observed gain and nonlinear response. This work lays the groundwork for future cluster state generation experiments.
We evaluate the performance of hybrid microwave resonators made by combining sputtered Nb thin films with Tungsten nanowires grown with a He-beam induced deposition technique. Depending on growth conditions, the nanowires have a typical width w [35 - 75] nm and thickness t [5 - 40] nm. We observe a high normal state resistance R [65 - 150] Ω / which together with a critical temperature T c [4 - 6] K ensures a high kinetic inductance making the resonator strongly nonlinear. Both lumped and coplanar waveguide resonators were fabricated and measured at low temperature exhibiting internal quality factors up to 3990 at 4.5 GHz in the few photon regime. Analyzing the wire length, temperature, and microwave power dependence, we extracted a kinetic inductance for the W nanowire of L K 15 pH / which is 250 times higher than the geometrical inductance, and a Kerr non-linearity as high as K W, He / 2 π = 200 ± 120 Hz / photon at 4.5 GHz. The nanowires made with the helium focused ion beam are thus versatile objects to engineer compact, high impedance, superconducting environments with a mask and resist free direct write process.
We study the temperature-dependent microwave response of high-kinetic-inductance superconducting resonators fabricated in Albanova's Nanolab as a part of the LKIPA device project. The investigated devices are based on circuit layouts designed for kinetic-inductance parametric amplification but are characterized using single-tone microwave measurements. We first compare the resonance parameters of different circuit designs to discuss and evaluate the performance of some fabricated resonators. A selected device is then measured in a cryostat, between 1.7 K and 3.0 K, to investigate how the resonance frequency, internal and external loss rates, and Kerr nonlinearity depend on temperature. The results show that the temperature dependence of the resonance frequency and external loss rate can be well described using a Mattis-Bardeen approach for linear responses in the investigated temperature interval. The internal loss rate, however, requires additional resistive channels beyond quasiparticle losses. By investigating near-resonance nonlinearities, we also demonstrate that nonlinear effects are less prominent when the temperature is increased. Deviations between the scattering fit and measured data are also discussed to evaluate possible limitations of the scattering model.