Fano Interference in Microwave Resonator Measurements

  1. D. Rieger,
  2. S. Günzler,
  3. M. Spiecker,
  4. A. Nambisan,
  5. W. Wernsdorfer,
  6. and I.M. Pop
Resonator measurements are a simple but powerful tool to characterize a material’s microwave response. The losses of a resonant mode are quantified by its internal quality factor
Qi, which can be extracted from the scattering coefficient in a microwave reflection or transmission measurement. Here we show that a systematic error on Qi arises from Fano interference of the signal with a background path. Limited knowledge of the interfering paths in a given setup translates into a range of uncertainty for Qi, which increases with the coupling coefficient. We experimentally illustrate the relevance of Fano interference in typical microwave resonator measurements and the associated pitfalls encountered in extracting Qi. On the other hand, we also show how to characterize and utilize the Fano interference to eliminate the systematic error.

Gralmonium: Granular Aluminum Nano-Junction Fluxonium Qubit

  1. D. Rieger,
  2. S. Günzler,
  3. M. Spiecker,
  4. P. Paluch,
  5. P. Winkel,
  6. L. Hahn,
  7. J. K. Hohmann,
  8. A. Bacher,
  9. W. Wernsdorfer,
  10. and I. M. Pop
Mesoscopic Josephson junctions (JJs), consisting of overlapping superconducting electrodes separated by a nanometer thin oxide layer, provide a precious source of nonlinearity for superconducting
quantum circuits and are at the heart of state-of-the-art qubits, such as the transmon and fluxonium. Here, we show that in a fluxonium qubit the role of the JJ can also be played by a lithographically defined, self-structured granular aluminum (grAl) nano-junction: a superconductor-insulator-superconductor (SIS) JJ obtained in a single layer, zero-angle evaporation. The measured spectrum of the resulting qubit, which we nickname gralmonium, is indistinguishable from the one of a standard fluxonium qubit. Remarkably, the lack of a mesoscopic parallel plate capacitor gives rise to an intrinsically large grAl nano-junction charging energy in the range of 10−100GHz, comparable to its Josephson energy EJ. We measure average energy relaxation times of T1=10μs and Hahn echo coherence times of Techo2=9μs. The exponential sensitivity of the gralmonium to the EJ of the grAl nano-junction provides a highly susceptible detector. Indeed, we observe spontaneous jumps of the value of EJ on timescales from milliseconds to days, which offer a powerful diagnostics tool for microscopic defects in superconducting materials.

Superconducting granular aluminum resonators resilient to magnetic fields up to 1 Tesla

  1. K. Borisov,
  2. D. Rieger,
  3. P. Winkel,
  4. F. Hernandez,
  5. F. Valenti,
  6. A. Ionita,
  7. M. Wessbecher,
  8. M. Spiecker,
  9. D. Gusenkova,
  10. I. M. Pop,
  11. and W. Wernsdorfer
High kinetic inductance materials constitute a valuable resource for superconducting quantum circuits and hybrid architectures. Superconducting granular aluminum (grAl) reaches kinetic
sheet inductances in the nH/□ range, with proven applicability in superconducting quantum bits and microwave detectors. Here we show that the single photon internal quality factor Qi of grAl microwave resonators exceeds 105 in magnetic fields up to 1T, aligned in-plane to the grAl films. Small perpendicular magnetic fields, in the range of 0.5mT, enhance Qi by approximately 15%, possibly due to the introduction of quasiparticle traps in the form of fluxons. Further increasing the perpendicular field deteriorates the resonators‘ quality factor. These results open the door for the use of high kinetic inductance grAl structures in circuit quantum electrodynamics and hybrid architectures with magnetic field requirements.

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.