Spin-Orbit Qubits of Rare-Earth-Metal Ions in Axially Symmetric Crystal Fields

Contrary to the well known spin qubits, rare-earth qubits are characterized by a strong influence of crystal field due to large spin-orbit coupling. At low temperature and in the presence of resonance microwaves, it is the magnetic moment of the crystal-field ground-state which nutates (for several $\mu$s) and the Rabi frequency ${\mathrm{\Omega }}_R$ is anisotropic. Here, we present a study of the variations of ${\mathrm{\Omega }}_R({\vec{H}}_0)$ with the magnitude and direction of the static magnetic field $\overrightarrow{H_0}$ for the odd ${}^{167}$Er isotope in a single crystal CaWO${}_4$:Er${}^{3+}$. The hyperfine interactions split the ${\mathrm{\Omega }}_R({\vec{H}}_0)$ curve into eight different curves which are fitted numerically and described analytically. These “spin-orbit qubits” should allow detailed studies of decoherence mechanisms which become relevant at high temperature and open new ways for qubit addressing using properly oriented magnetic fields.