Coupling of Erbium-Implanted Silicon to a Superconducting Resonator

Erbium-implanted silicon is promising for both photonic and quantum-technology platforms, since it possesses both telecommunications and integrated-circuit processing compatibility. However, several different $\mathrm{Er}$ centers are generated during the implantation and annealing process, the presence of which could hinder the development of these applications. When $\mathrm{Si}$ is coimplanted with ${10}^{17}\phantom{\rule{0.1em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ $\mathrm{Er}$ and ${10}^{20}\phantom{\rule{0.1em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ $\mathrm{O}$ ions, and the appropriate annealing process is used, one of these centers, which is present at higher $\mathrm{Er}$ concentrations, can be eliminated. Characterization of samples with $\mathrm{Er}$ concentrations of ${10}^{17}\phantom{\rule{0.1em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ is limited by the sensitivity of standard electron paramagnetic resonance (EPR) instruments. The collective coupling strength between a superconducting (SC) $\mathrm{Nb}\mathrm{N}$ lumped-element resonator and a ${10}^{17}\phantom{\rule{0.1em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ $\mathrm{Er}$-implanted $\mathrm{Si}$ sample at 20 mK is measured to be about 1 MHz, which provides a basis for the characterization of low-concentration $\mathrm{Er}$-implanted $\mathrm{Si}$ and for future networks of hybrid quantum systems that exchange quantum information over the telecommunication network. Of six known $\mathrm{Er}$-related EPR centers, only one trigonal center couples to the SC resonator.