Extending Phenomenological Crystal-Field Methods to C1 Point-Group Symmetry: Characterization of the Optically Excited Hyperfine Structure of Er 167 3+: Y2SiO5

We show that crystal-field calculations for C1 point-group symmetry are possible, and that such calculations can be performed with sufficient accuracy to have substantial utility for rare-earth based quantum information applications. In particular, we perform crystal-field fitting for a C1-symmetry site in Er1673+:Y2SiO5. The calculation simultaneously includes site-selective spectroscopic data up to 20 000 cm-1, rotational Zeeman data, and ground- and excited-state hyperfine structure determined from high-resolution Raman-heterodyne spectroscopy on the 1.5 μm telecom transition. We achieve an agreement of better than 50 MHz for assigned hyperfine transitions. The success of this analysis opens the possibility of systematically evaluating the coherence properties, as well as transition energies and intensities, of any rare-earth ion doped into Y2SiO5.