Hyperfine spectroscopy in a quantum-limited spectrometer

Abstract

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 $5\times {10}^2$. We measure two-pulse ESEEM on two systems: erbium ions coupled to ${}^{183}W$ nuclei in a natural-abundance ${\mathrm{CaWO}}_4$ crystal and bismuth donors coupled to residual ${}^{29}\mathrm{Si}$ nuclei in a silicon substrate that was isotopically enriched in the ${}^{28}\mathrm{Si}$ 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.