Spectroscopy, Crystal-Field, and Transition Intensity Analyses of the C${}_{3v}$(O${}^{2-}$) Centre in Er${}^{3+}$ Doped CaF${}_2$ Crystals

Abstract

Erbium ions in crystals show considerable promise for the technologies that will form the backbone of future networked quantum information technology. Despite advances in leveraging erbium's fibre-compatible infrared transition for classical and quantum applications, the transitions are, in general, not well understood. We present detailed absorption and laser site-selective spectroscopy of the C${}_{3v}$(O${}^{2-}$) centre in CaF${}_2$:Er${}^{3+}$ as an interesting erbium site case study. The ${}^4$I${}_{15/2}$Z${}_1\to {}^4$I${}_{13/2}$Y${}_1$ transition has a low-temperature inhomogeneous linewidth of 1 GHz with hyperfine structure observable from the ${}^{167}$Er isotope. A parametrized crystal-field Hamiltonian is fitted to 34 energy levels and the two ground state magnetic splitting factors. The wavefunctions are used to perform a transition intensity analysis and electric-dipole parameters are fitted to absorption oscillator strengths. Simulated spectra for the ${}^4$I${}_{11/2}\to {}^4$I${}_{15/2}$ and ${}^4$I${}_{13/2}\to {}^4$I${}_{15/2}$ inter-multiplet transitions are in excellent agreement with the experimentally measured spectra. The ${}^4$I${}_{13/2}$ excited state lifetime is 25.0\,ms and the intensity calculation is in excellent agreement with this value.