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 $\Omega_R$ is anisotropic. Here, we present a study of the variations of $\Omega_R(\vec{H}_{0})$ with the magnitude and direction of the static magnetic field $\vec{H_{0}}$ for the odd $^{167}$Er isotope in a single crystal CaWO$_4$:Er$^{3+}$. The hyperfine interactions split the $\Omega_R(\vec{H}_{0})$ 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.