Possible Hundredfold Enhancement in the Direct Magnetic Coupling of a Single-Atom Electron Spin to a Circuit...

We report on the challenges and limitations of direct coupling of the magnetic field from a circuit resonator to an electron spin bound to a donor potential. We propose a device consisting of a trilayer lumped-element superconducting resonator and a single donor implanted in enriched ²⁸Si. The resonator impedance is significantly smaller than the practically achievable limit obtained with prevalent coplanar resonators. Furthermore, the resonator includes a nanoscale spiral inductor to spatially focus the magnetic field from the photons at the location of the implanted donor. The design promises an increase of approximately 2 orders of magnitude in the local magnetic field, and thus the spin-to-photon coupling rate $g$ , compared with the estimated rate of coupling to the magnetic field of coplanar transmission line resonators. We show that by use of niobium (aluminum) as the resonator's superconductor and a single phosphorous (bismuth) atom as the donor, a coupling rate of $g/2\pi =0.24\text{MHz}\left(0.39\text{MHz}\right)$ can be achieved in the single-photon regime. For this hybrid cavity-quantum-electrodynamic system, such enhancement in $g$ is sufficient to enter the strong-coupling regime.