Coupling erbium spins to a three-dimensional superconducting cavity at zero magnetic field

We experimentally demonstrate the coupling at zero magnetic field of an isotopically pure erbium doped yttrium orthosilicate crystal ($^{167}$Er:YSO) to a three-dimensional superconducting cavity with a $Q$ factor of $10^5$. A tunable loop-gap resonator is used, and its resonance frequency is tuned to observe the hyperfine transitions of the erbium sample. The observed spectrum differs from what is predicted by the published spin Hamiltonian parameters. The narrow cavity linewidth also enables the observation of asymmetric line shapes for these hyperfine transitions. Such a broadly tunable superconducting cavity (from 1.6 GHz to 4.0 GHz in the current design) is a promising device for building hybrid quantum systems.