Prospective two orders of magnitude enhancement in direct magnetic coupling of a single-atom spin to a circuit resonator

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 lumped-element superconducting resonator and a single donor implanted in enriched 28Si. The resonator, in contrast to coplanar waveguide resonators, includes a nano-scale spiral inductor to spatially focus the magnetic field from the photons within. The design promises approximately two orders of magnitude increase in the local magnetic field, and thus the spin to photon coupling rate g, compared to the estimated coupling rate to coplanar transmission-line resonators. We show that by using niobium (aluminum) as the resonator’s superconductor and a single phosphorous (bismuth) atom as the donor, a coupling rate of g/2π=0.24 MHz (0.39 MHz) can be achieved in the small photon limit. For this truly linear cavity quantum electrodynamic system, such enhancement in g is sufficient to enter the strong coupling regime.