LAUSR

We report on electron spin resonance measurements of phosphorus donors localized in a 200  μm^{2} area below the inductive wire of a lumped element superconducting resonator. By combining quantum limited parametric amplification with a low impedance microwave resonator design, we are able to detect around 2×10^{4} spins with a signal-to-noise ratio of 1 in a single shot. The 150 Hz coupling strength between the resonator field and individual spins is significantly larger than the 1-10 Hz coupling rates obtained with typical coplanar waveguide resonator designs. Because of the larger coupling rate, we find that spin relaxation is dominated by radiative decay into the resonator and dependent upon the spin-resonator detuning, as predicted by Purcell.