# Possible hundredfold enhancement in the direct magnetic coupling of a single atomic spin to a circuit resonator

## TL;DR

This paper proposes a novel superconducting resonator design with a nano-scale spiral inductor to significantly enhance the magnetic coupling rate between a single atomic spin and a circuit resonator, potentially enabling strong coupling in quantum systems.

## Contribution

It introduces a new resonator design with a nano-scale spiral inductor that increases the magnetic field focus and coupling rate by approximately two orders of magnitude compared to traditional coplanar resonators.

## Key findings

- Coupling rate g/2π=0.24 MHz with niobium resonator and phosphorus donor.
- Coupling rate g/2π=0.39 MHz with aluminum resonator and bismuth donor.
- Design achieves strong coupling regime for hybrid cavity QED systems.

## Abstract

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 $^{28}$Si. The resonator impedance is significantly smaller than the practically achievable limit using prevalent coplanar resonators. Furthermore, the resonator includes a nano-scale spiral inductor to spatially focus the magnetic field from the photons at the location of the implanted donor. 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 the magnetic field of 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 $g/2\pi$=0.24 MHz (0.39 MHz) 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.