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

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