Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                

Hydrogen crystals reduce dissipation in superconducting resonators

Francesco Valenti, Andrew N. Kanagin, Andreas Angerer, Luiza Buimaga-Iarinca, Cristian Morari, Jörg Schmiedmayer, and Ioan M. Pop
Phys. Rev. B 109, 054503 – Published 6 February 2024
PDFHTMLExport Citation
Abstract
Authors
Article Text
  • INTRODUCTION
  • SETUP
  • SAMPLES
  • CRYSTALS
  • MODEL
  • CONCLUSIONS
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    We show that the internal quality factors of high-impedance superconducting resonators made of granular aluminum can be improved by coating them with micrometric films of solid parahydrogen molecular crystals. We attribute the average measured ≈8% reduction in dissipation to the absorption of stray terahertz radiation at the crystal-resonator interface and the subsequent dissipation of its energy in the form of phonons below the pair-breaking gap. Our results prove that contrary to expectations, replacing the vacuum dielectric atop a superconducting resonator can be beneficial, thanks to the added protection against Cooper pair-braking terahertz radiation. Moreover, at the level of internal quality factors in the 105 range, the hydrogen crystal does not introduce additional losses, which is promising for embedding impurities to couple to superconducting thin-film devices in hybrid quantum architectures.

    • Figure
    • Figure
    • Figure
    • Figure
    • Figure
    • Figure
    • Figure
    1 More
    • Received 16 August 2023
    • Revised 15 December 2023
    • Accepted 19 December 2023

    DOI:https://doi.org/10.1103/PhysRevB.109.054503

    ©2024 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Superconductors
    1. Physical Systems
    Molecular solids
    1. Techniques
    Microwave techniques
    Condensed Matter, Materials & Applied PhysicsQuantum Information, Science & Technology

    Authors & Affiliations

    Francesco Valenti1,*,†, Andrew N. Kanagin2,*, Andreas Angerer2, Luiza Buimaga-Iarinca3, Cristian Morari3, Jörg Schmiedmayer2, and Ioan M. Pop1,4,5,‡

    • 1Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology, 76344 Eggenstein-Leopoldshafen, Germany
    • 2Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, 1020 Vienna, Austria
    • 3National Institute for Research and Development of Isotopic and Molecular Technologies, 400293 Cluj-Napoca, Romania
    • 4Physikalisches Institut, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany
    • 5Physics Institute 1, Stuttgart University, 70569 Stuttgart, Germany

    • *These authors contributed equally to this work.
    • †Current address: IBM Quantum, IBM T. J. Watson Research Center, Yorktown Heights, 10598 NY, USA.
    • ‡ioan.pop@kit.edu

    Article Text (Subscription Required)

    Click to Expand

    References (Subscription Required)

    Click to Expand
    Issue

    Vol. 109, Iss. 5 — 1 February 2024

    Reuse & Permissions
    Access Options
    Author publication services for translation and copyediting assistance advertisement

    Authorization Required

    Log In
    Other Options
    ×

    Images

    • Figure 1
      Figure 1

      Cryogenic, microwave, and gas handling setup. (a) Schematics of the adiabatic demagnetization refrigerator together with microwave (blue) and gas (red) lines. A pulse tube cryocooler and liquid helium are used to cool down successive thermal stages at 50 and 4 K, respectively. The latter is connected via a thermal switch to two separate copper rods filled with two different paramagnetic salts: Gallium gadolinium garnet (GGG) and ferric ammonium alum (FAA), with magnetic ordering temperatures of about 1 K and 50 mK, respectively. The sample holder is mounted on the FAA-filled rod. A vector network analyzer (VNA) is used to perform transmission microwave spectroscopy on the sample. The signal towards the colder stages is progressively attenuated in order to reduce its thermal noise; after transmission through the sample, it is routed by an isolator and amplified both at cryogenic and room temperature stages. The first needle valve (v1) is used to regulate the incoming gas pressure from a room temperature tank. The line is connected via a four-way joint to a digital barometer and to a pump, regulated with an additional needle valve (v2), used to extract gaseous residues between successive crystal growths. The gas entering the cryostat is fed through copper tubes thermalized at 50 and 4 K and filled with an iron oxide for conversion to the para spin isomer of H2 (see main text for discussion). During deposition the second tube is heated from 4 to 14 K by feeding a PID-controlled current to a 100 Ω load in order to promote gas flow. (b) Photograph of the solid aluminum transmission sample holder showing the two SMA ports and printed circuit boards used to implement impedance-matched connections to the on-chip feedline (cf. Fig. 8 in Ref. [45] for details). (c) Schematic half-section of the sample holder and its lid. Note the 1.5×1.5cm2 opening on the backside of the sapphire chip (sealed with aluminum tape) and the circular hole in the lid, 1 cm in diameter. This is either left as is (d) or covered with two layers of aluminum tape with a 1 mm hole poked through (e). The stainless steel gas-carrying tube visible in both (d) and (e) is highlighted in red [cf. (a)]. (f) Schematics of the circuit, consis- ting of a coplanar waveguide (CPW) feedline capacitively loading 22 resonators (cf. Fig. 2 for details on feedline and resonator geometry).

      Reuse & Permissions
    • Figure 2
      Figure 2

      Terahertz loading and quasiparticles. (a) False-colored micrographs of the granular aluminum (grAl) resonator types used in the two measured samples, dubbed “S” and “L” for small and large coupling to vacuum impedance, respectively. The grAl resonators (pink/violet), patterned on sapphire (sage) and loaded by a CPW feedline with aluminum pin and ground plane (gray), share the same interdigitated capacitor design (pink), with variable finger length covering the 40–60 fF range. The grAl inductors (violet) are Hilbert curves of degree 2 and 3 respectively (see main text for discussion), having different widths to guarantee a comparable total inductance despite the factor 40 difference in resistivity. The resulting coupling to vacuum [cf. Eq. (2)] gives absorptivities A=11% and 97% for sample S and L, respectively. (b) Internal quality factor Qi as a function of the average number of drive photons in the resonator. The plotted traces are averaged over all visible resonators—error bars along both axes cover one standard deviation. Progressively increasing the optical loading on the sample, by increasing both the aperture and the coupling to vacuum, decreases the internal quality factor due to terahertz radiation breaking Cooper pairs: The largest Qi is attained when the sample holder cap [cf. Fig. 1] is solid aluminum instead of having a hole and the sample is placed into a terahertz shield, which we dub “dark” measurement, as reported in Ref. [45]. The Qi measurements taken with the front-facing hole covered with two layers of aluminum tape (orange) are denoted as “Tape,” and the Qi measurements based on the diameter of the front-facing hole, 1 mm (green) and 1 cm (red)—cf. Figs. 1 and 1—are plotted as well. Note that due to the relatively high coupling quality factor, systematic uncertainties introduced by Fano interference [46] are below the fitting uncertainty—whereas such uncertainties are likely playing a significant role for the data from Ref. [45] at higher powers.

      Reuse & Permissions
    • Figure 3
      Figure 3

      Effect of crystal thickness on dissipation. (a) Internal quality factors Qi for all visible resonances in sample S, measured with the 1 cm aperture over three separate cooldowns, in which crystals with different thickness t were grown. The reported values are averaged over 10 successive measurements each taken 5 minutes apart; error bars are comparable to marker size and thus omitted. Shaded and full colors represent measurements before and after crystal deposition, respectively. The full dataset is plotted. (b) Relative Qi variation as a function of the frequency shift induced by the dielectric change. For clarity, the value (colored markers) is averaged over all values (full gray markers) by dropping the largest and smallest (empty gray markers, when visible). y axis is bounded by two standard deviations calculated on all values for the deposited three crystals. (c) Distribution of the relative Qi shifts, with x axis bounded by two standard deviations calculated on all values.

      Reuse & Permissions
    • Figure 4
      Figure 4

      Terahertz absorption model. (a) Snapshot of the supercell used in the density functional theory (DFT) simulations (see main text for discussion), made of aluminum (red) and oxygen (yellow). Eight initially charge-neutral hydrogen molecules (purple) adhere via a site-dependent physisorption mechanism resulting in either charging or discharging (cf. isosurface representing charge density) and horizontal or vertical configurations, respectively. The H2 molecules in each supercell settle into one of two configurations: Almost perpendicular to the surface at a ≈80∘ angle, and almost parallel to the surface at a ≈15∘ angle. The grey double sided arrow indicates that hydrogen molecules can switch between the parallel and perpendicular configurations, resulting in a change of dipole moment. Black dashed arrows indicate the H-O coordination partners (the bottom H for the perpendicular configuration has two oxygen coordination partners). (b) Time traces of the total dipole of the supercell with both N=4 and N=5 adsorbed molecules (cf. Appendix pp5). (c) Spectral content of the above time traces (green) together with the blackbody radiance of the gas deposition tube, estimated to be between 3 and 4 K (purple, second y axis). The latter constitutes the dominant electromagnetic background seen by the samples, and is maximum close to the superconducting spectral gap at 160 GHz (gold). The hydrogen molecule dynamics result in an increased mode density around this region, leading to absorption.

      Reuse & Permissions
    • Figure 5
      Figure 5

      Scattering data (markers) and fit (solid lines) to the circle fit model used to extract microwave parameters, shown for a resonator in sample S with the 1 cm aperture before (blue) and after (green) deposition of a thick (saturating) crystal. Note that the transmission data is normalized to the sample holder response, and the frequency response in the right-hand side panels is horizontally offset by a line width κ=f0/Q∼25 kHz about the resonance for clarity, where 1/Q=1/Qi+1/Qc and Qc=1.66×105.

      Reuse & Permissions
    • Figure 6
      Figure 6

      Crystal thickness calibration. (a) Drawing of the niobium short-ended λ/2 “calibrator” resonator. The pitch to ground of the stripline (8µm) is comparable to that between fingers of the interdigitated capacitors of samples S and L [12µm; cf. Fig. 2]. (b) Real-time evolution of the resonant frequency of the Nb stripline during hydrogen deposition. (c) Simulated (solid lines) and (d) measured (histograms) resonant frequency shift for the grAl resonators in sample S. Measured values refer to the setup with a 1 cm hole (cf. Fig. 3); the shaded regions spanning both panels cover one standard deviation about the mean of measured values. By using the “thick” parameter set as a calibration for a crystal fully saturating the dielectric shift we obtain a permittivity for the parahydrogen crystal of 1.38±0.04, and we calibrate two other parameters sets, “thin” and “very thin,” to result in a crystal thickness of order of magnitude 10 and 1µm, respectively.

      Reuse & Permissions
    • Figure 7
      Figure 7

      Results of Sonnet simulation of a single resonator from sample S. The microwave response is shown in amplitude and phase (top) and as a circle in the complex plane (bottom). Open circles show the simulation data. The solid black line is the fit to the data. The inset shows the computed amplitude of surface current density on resonance, with overlayed geometry in white lines.

      Reuse & Permissions
    • Figure 8
      Figure 8

      Examples of time traces and relative spectra for increasing amounts of hydrogen molecules (top to bottom). (Left) Time series of the supercell dipole moment evolution. (Middle) Spectral content of the dipole moment dynamics. (Right) Comparison between the (zoomed in) spectral content from the central panel (green), the blackbody radiation from the gas tube estimated to be between 3 and 4 K (purple), and the superconducting spectral gap (gold). Visible fluctuations were observed only for N=5 and 6 for purely statistical reasons—the number of molecules does not influence the supercell dynamics.

      Reuse & Permissions
    ×

    Sign up to receive regular email alerts from Physical Review B

    Log In

    Cancel
    ×

    Search

    Article Lookup

    Paste a citation or DOI
    Enter a citation
    ×