Publisher’s Note: Spin-Orbit Qubits of Rare-Earth-Metal Ions in Axially Symmetric Crystal Fields [Phys. Rev. Lett. 103, 226402 (2009)]

Figure 1

Energy spectrum of ${{}^{167}\mathrm{E}\mathrm{r}}^{3+}$ with $I=7/2$ calculated numerically in the rotating frame. The detuning field is, by definition, the difference between the applied field $H_0$ and the resonant field of the $I=0$ isotope. The Rabi frequencies are equal to the splittings at avoided level crossings (dressed states). Allowed EPR transitions ($\mathrm{\Delta }{m}_I=0$) are gapped and their anisotropy for different directions of the microwave polarization is shown in the inset.

Figure 2

Rabi oscillation recorded on the nuclear-spin free ${\mathrm{Er}}^{3+}$ isotope in ${\mathrm{CaWO}}_4$ ($H_0=325.1\mathrm{mT}$, $h_{\mathrm{m}\mathrm{w}}=0.26\mathrm{mT}$) and (b) its Fourier transform. (c) Contour plot of the Rabi frequency distribution measured in the $I=7/2$ isotope while $H_0$ tilted by $12°$ from the $c$ axis is swept from 220 to 440 mT (colored isomagnetization scale increases from blue to red). The eight Rabi frequencies with smaller intensity correspond to the transitions $(1/2,m_I)\to (-1/2,m_I)$ of the $I=7/2$ isotope ($\mathrm{\Delta }{m}_I=0$) and the single one with larger intensity to the $I=0$ isotope. Calculated ${\mathrm{\Omega }}_R$ are represented by symbols going from black square ($m_I=-7/2$) to green circle ($m_I=7/2$).

Figure 3

Evolution of ${\mathrm{\Omega }}_R$ with ${\mathrm{\Omega }}_R$ vs $\parallel {\overrightarrow{H}}_0\parallel$ while the resonant field is rotated. The symbols represent the same data and the lines are calculated numerically and analytically as in Fig. 3. The dotted line represents the conventional equation ${\mathrm{\Omega }}_R=g^{\alpha }{\mu }_B{h}_{\mathrm{m}\mathrm{w}}^{\alpha }/2h$ [21].