High-resolution magneto-optical spectroscopy of ${}^7\mathrm{LiYF}_4:{}^{167}\mathrm{Er}^{3+},{}^{166}\mathrm{Er}^{3+}$ and analysis of hyperfine structure of ultranarrow optical transitions

We performed high-resolution magneto-optical spectroscopy of the hyperfine transitions from ${}^{4}I_{15/2}$ to the ${}^{4}I_{13/2}$ and ${}^{4}I_{9/2}$ multiplets of ${}^{167}\mathrm{Er}^{3+}$ and ${}^{166}\mathrm{Er}^{3+}$ in an isotopically purified ${}^7\mathrm{LiYF}_4$ crystal in various external magnetic fields up to 0.7 T. The obtained experimental results are interpreted in the framework of the generalized theoretical approach. The derived model successfully explains all the experimentally observed optical hyperfine transitions by using a single set of basic parameters found for the crystal-field interaction, magnetic dipole and electric quadrupole hyperfine interactions, together with Zeeman interactions at different orientations of the external magnetic field. A number of the studied quantum transitions appears to be promising for use in Raman quantum storage at optical telecommunication wavelengths.

Figure 1

${}^7\mathrm{LiYF}_4$:${}^{167}\mathrm{Er}^{3+}$ (0.005 at. $\%$) single-crystal absorption spectra corresponding to the ${}^{4}I_{15/2}\left({\mathrm{\Gamma }}_{56}\right)\to {}^4{I}_{9/2}\left({\mathrm{\Gamma }}_{78}\right)$ transition at $B_0=0$ and $B_0=589$ G and two orientations of the crystal sample. Experimental data and the results of calculations are represented by solid black and red dotted lines, respectively. Frequency origin at $B_0=0$ corresponds to 370.574 THz transition. $T=4$ K, $c$ is the crystal's $C_4$ axis, $\mathbf{E}$ and $\mathbf{k}$ denote the electric field and the wave vector of the incident radiation, respectively.

Figure 2

${}^7\mathrm{LiYF}_4$:${}^{167}\mathrm{Er}^{3+}$ (0.005 at. $\%$) single-crystal absorption spectra corresponding to the ${}^{4}I_{15/2}\left({\mathrm{\Gamma }}_{56}\right)\to {}^4{I}_{13/2}\left({\mathrm{\Gamma }}_{56}\right)$ transition at $B_0=0$ and two orientations of the crystal sample. Experimental data and the simulated spectra are represented by solid black and red dotted lines, respectively. Frequency origin at $B_0=0$ corresponds to 196.013 THz transition. $T=4$ K.

Figure 3

${}^7\mathrm{LiYF}_4$:${}^{167}\mathrm{Er}^{3+}$ (0.005 at. $\%$) single-crystal absorption spectra corresponding to the ${}^{4}I_{15/2}\left({\mathrm{\Gamma }}_{56}\right)\to {}^4{I}_{13/2}\left({\mathrm{\Gamma }}_{78}\right)$ transition at $B_0=0$ and $B_0=589$ G and two orientations of the crystal sample. Experimental data and the results of calculations are represented by solid black and red dotted lines, respectively. Frequency origin at $B_0=0$ corresponds to 195.893 THz transition. $T=4$ K.

Figure 4

Demonstration of the mixed nature of the ${}^{4}I_{15/2}\left({\mathrm{\Gamma }}_{56}\right)\to {}^{4}I_{13/2}\left({\mathrm{\Gamma }}_{78}\right)$ transition. The upper (black) and the second (red) curves represent the experimental and calculated ${}^7\mathrm{LiYF}_4$:${}^{167}\mathrm{Er}^{3+}$ (0.005 at. $\%$) single-crystal absorption spectra at $B_0=0$ and $T=4$ K. The two bottom (blue and green) curves are the calculated contributions of the magnetic and electric dipole transitions, respectively.

Figure 5

The calculated hyperfine structure schemes of Kramers levels of ${}^{167}\mathrm{Er}^{3+}$ in ${}^7\mathrm{LiYF}_4$ involved in narrow optical transitions. $B_0=0$. Singlet hyperfine levels ${\mathrm{\Gamma }}_1$ and ${\mathrm{\Gamma }}_2$ are represented by dashed and dashed-dotted black lines, respectively. Doublet hyperfine levels ${\mathrm{\Gamma }}_{34}$ are represented by solid black lines. Quasidoublet levels ${\mathrm{\Gamma }}_1,{\mathrm{\Gamma }}_1$ and ${\mathrm{\Gamma }}_2,{\mathrm{\Gamma }}_2$ are marked by dotted and dashed-dotted-dotted red lines, respectively. Energy distances between the levels are shown in MHz.

Figure 6

Calculated energies of the ground-state hyperfine levels vs magnetic field. Crossing and anticrossing points with gaps of 0.3 and 0.8 MHz are shown as red crosses and circles, respectively.