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Superconducting Parallel-Plate Resonators for the Detection of Single Electron Spins

André Pscherer, Jannes Liersch, Patrick Abgrall, Andrew D. Beyer, Fabien Defrance, Sunil R. Gowala, Hélène Le Sueur, James O'Sullivan, Emmanuel Flurin, Patrice Bertet

Abstract

We introduce a multilayer superconducting microwave resonator with sub-Ohm impedance optimized for high coupling strength to single electron spins. The design minimizes the magnetic far-field and therefore achieves a Purcell factor $F_P > 10^{15}$. We show several ways to fabricate this type of resonator and present resonators with an intrinsic $Q$-factor exceeding $2 \cdot 10^4$ at the single-photon level. We further characterize these resonators in magnetic fields up to $500 \, \text{mT}$. Finally, we evaluate the impact of the achievable Purcell factor on single-spin detection through photon counting and dispersive readout.

Superconducting Parallel-Plate Resonators for the Detection of Single Electron Spins

Abstract

We introduce a multilayer superconducting microwave resonator with sub-Ohm impedance optimized for high coupling strength to single electron spins. The design minimizes the magnetic far-field and therefore achieves a Purcell factor . We show several ways to fabricate this type of resonator and present resonators with an intrinsic -factor exceeding at the single-photon level. We further characterize these resonators in magnetic fields up to . Finally, we evaluate the impact of the achievable Purcell factor on single-spin detection through photon counting and dispersive readout.

Paper Structure

This paper contains 23 sections, 12 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. Simulation
  3. Working principle
  4. Coupling to the transmission line
  5. 3D cavity
  6. Coplanar waveguide
  7. Fabrication
  8. Architectures
  9. Additive fabrication
  10. Silicon membrane
  11. Trilayer etching
  12. Processes
  13. Nb deposition
  14. a-Si:H deposition
  15. Al hard mask
  16. ...and 8 more sections

Figures (7)

  • Figure 1: (a) Exploded view of the resonator (not to scale) and equivalent lumped-element circuit. (b) Current density in the nanowire region (bottom) and the counter-electrode. (c) Cross-section through the nanowire showing the magnetic field ZPF $|\delta B|$ and the coupling strength between the resonator and a free electron spin $g_0$.
  • Figure 2: (a) A parallel-plate resonator couples via an antenna to a 3D box mode, which couples to a coaxial cable via the cable pin. (b) Coupling $Q$-factor of the parallel-plate resonator to the transmission line as a function of the cable pin penetration depth. (c) Superconducting layers of a waveguide-coupled parallel-plate resonator with a close-up (d) of the nanowire region. (e) The coupling to the coplanar waveguide is controlled through the width of the constriction in the counter-electrode layer.
  • Figure 3: Fabrication of a waveguide-coupled parallel-plate resonator from a Nb-Si-Nb trilayer. See the text for an explanation of the steps. The features of the resonator are not to scale.
  • Figure 4: Dependence of $Q_i$ of the resonators listed in Table \ref{['tab:samples']} with the photon number $\bar{n}$ in the resonator. At low power, two-level systems cause additional losses.
  • Figure 5: (a) Relative change of the resonance frequency and (b) $Q_i$ as a function of the in-plane magnetic field strength $| \vec{B} |$. Sample 4 was tested in fields at 0°, 45° and 90° with respect to the nanowire.
  • ...and 2 more figures