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We report on electron spin resonance (ESR) measurements of phosphorus donorslocalized in a 200 square micron area below the inductive wire of a lumpedelement superconducting resonator. By combining quantum limited parametricamplification with a low impedance microwave resonator design we are able todetect around 20000 spins with a signal-to-noise ratio (SNR) of 1 in a singleshot. The 150 Hz coupling strength between the resonator field and individualspins is significantly larger than the 1 - 10 Hz coupling rates obtained withtypical coplanar waveguide resonator designs. Due to the larger coupling rate,we find that spin relaxation is dominated by radiative decay into the resonatorand dependent upon the spin-resonator detuning, as predicted by Purcell.

Electron Spin Resonance at the Level of 10000 Spins Using Low Impedance Superconducting Resonators