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Journal of Alloys and Compounds

Calculations of rare earth hyperfine structures and application to quantum information

Philippe Goldner, O. Guillot-Noël

Published Apr 17, 2007• 6 citations
Publisher
DOI
10.1016/j.jallcom.2007.04.071

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Clock transitions play an important role in extending the coherence time of rare-earth (RE) ion-doped crystals. It is still a challenge to accurately obtain the hyperfine structure of these crystals to determine their clock transitions and establish a proper solid-state quantum memory system. In this work, a nonspin-Hamiltonian method combining density functional theory (DFT)-based geometric optimization and effective Hamiltonian is utilized to obtain the hyperfine sublevels and clock transitions under an external magnetic field for the Kramers RE ion in crystals. To show clearly, the 173 Yb 3+:Y 2 SiO 5 crystal is first investigated to demonstrate that the complicated hyperfine structure of the Kramers RE ion can be correctly calculated by the complete diagonalization (of energy) matrix (CDM) formalism. Second, optical and angular-dependent electron paramagnetic resonance (EPR) spectra of the 171 Yb 3+:Lu 2 Si 2 O 7 crystal are studied by fitting calculations based on the DFT-optimized geometric structure. By reliable fitting parameters, the external magnetic field at clock transitions is determined successfully. Such two case studies indicate that the hyperfine structure and clock transitions of the Kramers RE ion in the crystal can be accurately predicted by the present approach. This is very useful for designing and searching practical RE-based quantum memory materials with longer optical or spin coherence time.

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We show that crystal-field calculations for C_{1} 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 C_{1}-symmetry site in ^{167}Er^{3+}:Y_{2}SiO_{5}. 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 Y_{2}SiO_{5}.
Electron paramagnetic resonance (EPR) spectroscopy of rare earth ions in crystals is a powerful tool to analyze the hyperfine structure of the rare earth ground state. This can be useful for coherent spectroscopy and quantum information applications where the hyperfine structure of the electronic levels is used. In this work, we give a detailed analysis of the hyperfine structure of the ground state [4I15∕2(0)][^{4}I_{15∕2}(0)][4I15∕2​(0)] of Er3+{\mathrm{Er}}^{3+}Er3+ ions in Y2SiO5{\mathrm{Y}}_{2}\mathrm{Si}{\mathrm{O}}_{5}Y2​SiO5​. The electronic Zeeman, hyperfine, and quadrupole matrices are obtained from angular variations of the magnetic field in three orthogonal crystal planes. An excellent agreement is obtained between experimental and simulated magnetic field positions and relative intensities of EPR lines.
Clock transitions play an important role in extending the coherence time of rare-earth (RE) ion-doped crystals. It is still a challenge to accurately obtain the hyperfine structure of these crystals to determine their clock transitions and establish a proper solid-state quantum memory system. In this work, a nonspin-Hamiltonian method combining density functional theory (DFT)-based geometric optimization and effective Hamiltonian is utilized to obtain the hyperfine sublevels and clock transitions under an external magnetic field for the Kramers RE ion in crystals. To show clearly, the 173 Yb 3+:Y 2 SiO 5 crystal is first investigated to demonstrate that the complicated hyperfine structure of the Kramers RE ion can be correctly calculated by the complete diagonalization (of energy) matrix (CDM) formalism. Second, optical and angular-dependent electron paramagnetic resonance (EPR) spectra of the 171 Yb 3+:Lu 2 Si 2 O 7 crystal are studied by fitting calculations based on the DFT-optimized geometric structure. By reliable fitting parameters, the external magnetic field at clock transitions is determined successfully. Such two case studies indicate that the hyperfine structure and clock transitions of the Kramers RE ion in the crystal can be accurately predicted by the present approach. This is very useful for designing and searching practical RE-based quantum memory materials with longer optical or spin coherence time.