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

TL;DR

This paper provides a detailed spectroscopic analysis of the Er$^{3+}$ doped CaF$_2$ crystal, including energy level fitting, transition intensity analysis, and comparison with experimental spectra, advancing understanding of erbium's optical properties for quantum tech.

Contribution

It introduces a comprehensive crystal-field and transition intensity analysis of the Er$^{3+}$ site in CaF$_2$, including fitting a Hamiltonian to energy levels and simulating spectra.

Findings

Low-temperature inhomogeneous linewidth of 1 GHz

Excellent agreement between simulated and measured spectra

Excited state lifetime of 25.0 ms

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$_{\rm 3v}$(O$^{2-}$) centre in CaF$_2$:Er$^{3+}$ as an interesting erbium site case study. The $^{4}$I$_{15/2}$Z$_1 \rightarrow {^{4}}$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$_{11/2}\rightarrow {^{4}}$I$_{15/2}$ and $^{4}$I$_{13/2} \rightarrow {^{4}}$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.