Figure 1

(a) The structure of the energy levels of Er${}^{3+}$ ions. (b) A picture of the rare-earth ion chip. The Er:YSO crystal of $1\times 1.5\times 3$ mm${}^3$ size is placed on the $\lambda /2$ resonator. The width of the central transmission line of the resonator is 20 $\mu$m; gaps are 9 $\mu$m. The magnetic field is applied along the chip surface. Several interference fringes are visible due to improper placement of the crystal (see text). (c) The sketch of the crystal orientation marked with its optical extinction axes $b$ and $D$${}_1$ with respect to the directions of the bias magnetic field $B$ and microwave field $B\left(t\right)$.Reuse & Permissions

Figure 2

Transmission spectroscopy of the rare-earth ion chip. (a) The amplitude of the transmitted signal $|S_{21}|$. The energy spectrum of different magnetic transitions is shown with dashed lines. The spin tuning rate ${\gamma }_S/2\pi$ $=$ 162.9 GHz/T and values for the hyperfine splitting are taken from the fit of the frequency shift (see text). (b) The calculated energy spectrum of Er:YSO in the magnetic field. Allowed and forbidden transitions are shown with arrows.Reuse & Permissions

Figure 3

Frequency shift of the resonator ${\omega }_0^{\prime }/2\pi -8.9$ GHz and its quality factor $Q$ vs. the applied magnetic field for (a) the transition 7/2 [Gray dots are experimental data. The dashed line is fit to Eq. (1)], and (b) the transition S [Light gray and dark gray dots are experimental data taken at the excitation level of 10${}^2$ and 10${}^5$ photons, respectively. The dashed line is a fit of the low-excitation data to Eq. (1)]. (c) Gray dots are experimental data points. The solid line is the fit of experimental data. Clearly observed dips correspond to different magnetic transitions. Inset: The temperature dependence of the collective coupling $v_s$ vs. temperature. Circles present measured data. The solid line is a fit to the data (see text).Reuse & Permissions