Hyperfine spectroscopy in a quantum-limited spectrometer

We report measurements of electron-spin-echo envelope modulation (ESEEM) performed at millikelvin temperatures in a custom-built high-sensitivity spectrometer based on superconducting micro-resonators. The high quality factor and small mode volume (down to 0.2 pL) of the resonator allow us to probe a small number of spins, down to $$. We measure two-pulse ESEEM on two systems: erbium ions coupled to $$ nuclei in a natural-abundance $$ crystal and bismuth donors coupled to residual $$ nuclei in a silicon substrate that was isotopically enriched in the $$ isotope. We also measure three- and five-pulse ESEEM for the bismuth donors in silicon. Quantitative agreement is obtained for both the hyperfine coupling strength of proximal nuclei and the nuclear-spin concentration.