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.
@article{arxiv.1507.03739,
title = {High cooperativity coupling between a phosphorus donor spin ensemble and a superconducting microwave resonator},
author = {Christoph W. Zollitsch and Kai Mueller and David P. Franke and Sebastian T. B. Goennenwein and Martin S. Brandt and Rudolf Gross and Hans Huebl},
journal= {arXiv preprint arXiv:1507.03739},
year = {2015}
}