High cooperativity between a phosphorus donor spin ensemble and a microwave resonator

  1. Christoph W. Zollitsch,
  2. Kai Mueller,
  3. David P. Franke,
  4. Sebastian T. B. Goennenwein,
  5. Martin S. Brandt,
  6. Rudolf Gross,
  7. and Hans Huebl
We investigate the coupling of an ensemble of phosphorus donors in an isotopically purified 28Si host lattice interacting with a superconducting coplanar waveguide resonator. The microwave transmission spectrum of the resonator shows a normal mode splitting characteristic for high cooperativity. The evaluated collective coupling strength geff is of the same order as the loss rate of the spin system γ, indicating the onset of strong coupling. We develop a statistical model to describe the influence of temperature on the coupling strength from 50mK to 3.5K and find a scaling of the coupling strength with the square root of the number of thermally polarized spins.
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