Circuit Quantum Electrodynamics of Granular Aluminum Resonators

  1. N. Maleeva,
  2. L. Grünhaupt,
  3. T. Klein,
  4. F. Levy-Bertrand,
  5. O. Dupré,
  6. M. Calvo,
  7. F. Valenti,
  8. P. Winkel,
  9. F. Friedrich,
  10. W. Wernsdorfer,
  11. A. V. Ustinov,
  12. H. Rotzinger,
  13. A. Monfardini,
  14. M. V. Fistul,
  15. and I. M. Pop
The introduction of crystalline defects or dopants can give rise to so-called „dirty superconductors“, characterized by reduced coherence length and quasiparticle mean free
path. In particular, granular superconductors such as Granular Aluminum (GrAl), consisting of remarkably uniform grains connected by Josephson contacts have attracted interest since the sixties thanks to their rich phase diagram and practical advantages, like increased critical temperature, critical field, and kinetic inductance. Here we report the measurement and modeling of circuit quantum electrodynamics properties of GrAl microwave resonators in a wide frequency range, up to the spectral superconducting gap. Interestingly, we observe self-Kerr coefficients ranging from 10−2 Hz to 105 Hz, within an order of magnitude from analytic calculations based on GrAl microstructure. This amenable nonlinearity, combined with the relatively high quality factors in the 105 range, open new avenues for applications in quantum information processing and kinetic inductance detectors.

Microwave multimode memory with an Er3+:Y2SiO5 spin ensemble

  1. S. Probst,
  2. H. Rotzinger,
  3. A. V. Ustinov,
  4. and P. A. Bushev
Interfacing photonic and solid-state qubits within a hybrid quantum architecture offers a promising route towards large scale distributed quantum computing. In that respect, hybrid
quantum systems combining circuit QED with ions doped into solids are an attractive platform. There, the ions serve as coherent memory elements and reversible conversion elements of microwave to optical qubits. Among many possible spin-doped solids, erbium ions offer the unique opportunity of a coherent conversion of microwave photons into the telecom C-band at 1.54μm employed for long distance communication. In our work, we perform a time-resolved electron spin resonance study of an Er3+:Y2SiO5 spin ensemble at milli-Kelvin temperatures and demonstrate multimode storage and retrieval of up to 16 coherent microwave pulses. The memory efficiency is measured to be 10−4 at the coherence time of T2=5.6μs.

Nonreciprocal transmission of microwaves through a long Josephson junction

  1. A.L. Pankratov,
  2. K. G. Fedorov,
  3. M. Salerno,
  4. S. V. Shitov,
  5. and A. V. Ustinov
Nonreciprocal microwave transmission through a long Josephson junction in the flux-flow regime is studied analytically and numerically within the framework of the perturbed sine-Gordon
model. We demonstrate that the maximum attenuation of the transmitted power occurs when the direction of the flux flow is opposite to the direction of the microwave propagation. This attenuation is nonreciprocal with respect to the flux-flow direction and can be enhanced by increasing the system length and proper impedance matching of the junction ends to external transmission line.

Design and experimental study of superconducting left-handed transmission lines with tunable dispersion and improved impedance match

  1. E. A. Ovchinnikova,
  2. S. Butz,
  3. P. Jung,
  4. V. P. Koshelets,
  5. L. V. Filippenko,
  6. A.S. Averkin,
  7. S. V. Shitov,
  8. and A. V. Ustinov
We continue detailed study of microwave properties of a superconducting left-handed tunable CPW transmission line (LHTL). The line consists of a central conductor, loaded with series
of Josephson junctions as fixed inductors; the line is shunted with SQUIDs as tunable inductors. The inductance of the SQUIDs is varied in the range of 0.08-0.5 nH by applying an external dc magnetic field. The circuit is designed to have left- and right-handed transmission bands separated by a variable rejection band. At zero magnetic field, we observed only one pass-band between 8 and 10 GHz within the frequency range of 8-12 GHz. The rejection band is anticipated to appear between 10 GHz and 11 GHz by design, and it has been detected in our previous work. To solve the problem of standing waves and RF leak in measurements of our experimental 20-cell LHTL, we have designed a high-ratio (5-50 Ohm) wideband (8-11 GHz) impedance transformer integrated at the chip, along with improved sample holder. The experimental data are compared with numerical simulations.

Efficient and robust analysis of complex scattering data under noise in microwave resonators

  1. S. Probst,
  2. F. B. Song,
  3. P. A. Bushev,
  4. A. V. Ustinov,
  5. and M. Weides
Superconducting microwave resonators are reliable circuits widely used for detection and as test devices for material research. A reliable determination of their external and internal
quality factors is crucial for many modern applications, which either require fast measurements or operate in the single photon regime with small signal to noise ratios. Here, we use the circle fit technique with diameter correction and provide a step by step guide for implementing an algorithm for robust fitting and calibration of complex resonator scattering data in the presence of noise. The speedup and robustness of the analysis are achieved by employing an algebraic rather than an iterative fit technique for the resonance circle.

Hybrid quantum circuit with implanted erbium ions

  1. S. Probst,
  2. N. Kukharchyk,
  3. H. Rotzinger,
  4. A. Tkalcec,
  5. S. Wünsch,
  6. A. D. Wieck,
  7. M. Siegel,
  8. A. V. Ustinov,
  9. and P. A. Bushev
We report on hybrid circuit QED experiments with focused ion beam implanted Er3+ ions in Y2SiO5 coupled to an array of superconducting lumped element microwave resonators. The Y2SiO5
crystal is divided into several areas with distinct erbium doping concentrations, each coupled to a separate resonator. The coupling strength is varied from 5 MHz to 18.7 MHz, while the linewidth ranges between 50 MHz and 130 MHz. We confirm the paramagnetic properties of the implanted spin ensemble by evaluating the temperature dependence of the coupling. The efficiency of the implantation process is analyzed and the results are compared to a bulk doped Er:Y2SiO5 sample. We demonstrate the successful integration of these engineered erbium spin ensembles with superconducting circuits.

Broadband Sample Holder for Microwave Spectroscopy of Superconducting Qubits

  1. A.S. Averkin,
  2. A. Karpov,
  3. K. Shulga,
  4. E. Glushkov,
  5. N. Abramov,
  6. U. Huebner,
  7. E. Il'ichev,
  8. and A. V. Ustinov
We present a practical design and implementation of a broadband sample holder suitable for microwave experiments with superconducting integrated circuits at millikelvin temperatures.
Proposed design can be easily integrated in standard dilution cryostats, has flat pass band response in a frequency range from 0 to 32 GHz, allowing the RF testing of the samples with substrate size up to 4×4 mm. The parasitic higher modes interference in the holder structure is analyzed and prevented via design considerations. The developed setup can be used for characterization of superconducting parametric amplifiers, bolometers and qubits. We tested the designed sample holder by characterizing of a superconducting flux qubit at 20 mK temperature.

Probing the TLS Density of States in SiO Films using Superconducting Lumped Element Resonators

  1. S. T. Skacel,
  2. Ch. Kaiser,
  3. S. Wuensch,
  4. H. Rotzinger,
  5. A. Lukashenko,
  6. M. Jerger,
  7. G. Weiss,
  8. M. Siegel,
  9. and A. V. Ustinov
We have investigated dielectric losses in amorphous SiO thin films under operating conditions of superconducting qubits (mK temperatures and low microwave powers). For this purpose,
we have developed a broadband measurement setup employing multiplexed lumped element resonators using a broadband power combiner and a low-noise amplifier. The measured temperature and power dependences of the dielectric losses are in good agreement with those predicted for atomic two-level tunneling systems (TLS). By measuring the losses at different frequencies, we found that the TLS density of states is energy dependent. This had not been seen previously in loss measurements. These results contribute to a better understanding of decoherence effects in superconducting qubits and suggest a possibility to minimize TLS-related decoherence by reducing the qubit operation frequency.

Fabrication and measurements of hybrid Nb/Al Josephson junctions and flux qubits with pi-shifters

  1. A. V. Shcherbakova,
  2. K. G. Fedorov,
  3. K. V. Shulga,
  4. V. V. Ryazanov,
  5. V. V. Bolginov,
  6. V. A Oboznov,
  7. S. V. Egorov,
  8. V. O. Shkolnikov,
  9. M. J. Wolf,
  10. D. Beckmann,
  11. and A. V. Ustinov
We describe fabrication and testing of composite flux qubits combining Nb- and Al-based superconducting circuit technology. This hybrid approach to making qubits allows for employing
pi-phase shifters fabricated using well-established Nb-based technology of superconductor-ferromagnet-superconductor Josephson junctions. The important feature here is to obtain high interface transparency between Nb and Al layers without degrading sub-micron shadow mask. We achieve this by in-situ Ar etching using e-beam gun. Shadow-evaporated Al/AlOx/Al Josephson junctions with Nb bias pads show the expected current-voltage characteristics with reproducible critical currents. Using this technique, we fabricated composite Nb/Al flux qubits with Nb/CuNi/Nb pi-shifters and measured their magnetic field response. The observed offset between the field responses of the qubits with and without pi-junction is attributed to the pi phase shift. The reported approach can be used for implementing a variety of hybrid Nb/Al superconducting quantum circuits.

Ultra-compact tunable split-ring resonators

  1. A. Vidiborskiy,
  2. V. P. Koshelets,
  3. L. V. Filippenko,
  4. S. V. Shitov,
  5. and A. V. Ustinov
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 (SQUID), 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 EM-simulation and experimental data for the SRR weakly coupled to a transmission line within frequency range 11-13 GHz.