Extending Phenomenological Crystal-Field Methods to $C_1$ Point-Group Symmetry: Characterization of the Optically-Excited Hyperfine Structure of ${}^{167}$Er${}^{3+}$:Y${}_2$SiO${}_5$

Abstract

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 $\mu$m 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${}_5$ .

arXiv comment6 pages, plus 5 pages in supplementary information, 4 figures total

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Cited by in corpus (21)

• Long spin coherence times in the ground state and an optically excited state of ${}^{167}$Er${}^{3+}$:Y${}_2$SiO${}_5$ at zero magnetic field
• Coherent optical and spin spectroscopy of nanoscale Pr3+:Y2O3
• Electron Spin Resonance with up to 20 Spin Sensitivity Measured using a Superconducting Flux Qubit
• Superhyperfine induced photon-echo collapse of erbium in Y${}_2$SiO${}_5$
• Electron-Nuclear Interactions as a Test of Crystal-Field Parameters for Low Symmetry Systems: Zeeman-Hyperfine Spectroscopy of Ho${}^{3+}$ Doped Y${}_2$SiO${}_5$
• The Zeeman and hyperfine interactions of a single ${}^{167}E{r}^{3+}$ ion in Si
• Prediction of the Optical Polarization and High Field Hyperfine Structure Via a Parametrized Crystal-Field Model for the Low Symmetry Centers in Er${}^{3+}$ Doped Y${}_2$SiO${}_5$
• Spectral Multiplexing of Rare-earth Emitters in a Co-doped Crystalline Membrane
• Proposal for transduction between microwave and optical photons using ${}^{167}\mathrm{Er}$-doped yttrium orthosilicate
• Extending the spin coherence lifetimes of ${}^{167}$Er${}^{3+}$$:$Y${}_2$SiO${}_5$ at subkelvin temperatures
• Demonstration of site-selective angular-resolved absorption spectroscopy of the ${}^4{I}_{15/2}\to$${}^4{I}_{13/2}$ erbium transition in the monoclinic crystal Y${}_2$SiO${}_5$
• Growth and Spectroscopy of Lanthanide Doped Y${}_2$SiO${}_5$ Microcrystals for Quantum Information Processing
• Complete crystal field calculation of Zeeman-hyperfine splittings in europium
• A Raman heterodyne determination of the magnetic anisotropy for the ground and optically excited states of Y${}_2$SiO${}_5$ doped with Sm${}^{3+}$
• Laser Site-Selective Spectroscopy and Magnetic Hyperfine Splittings of Ho${}^{3+}$ doped Y${}_2$SiO${}_5$
• Reproduction of the electronic and magnetic structure of the low symmetry sites of Y${}_2$SiO${}_5$ doped with Sm${}^{3+}$ via a parameterized crystal-field model
• Zeeman-Hyperfine Measurements of a Pseudo-Degenerate Quadruplet in CaF${}_2$:Ho${}^{3+}$
• Infrared Absorption and Laser Spectroscopy of Ho${}^{3+}$ Doped K${}_2$YF${}_5$ Microparticles
• Spectroscopy and Crystal-Field Analysis of Low -Symmetry Er${}^{3+}$ Centres in K${}_2$YF${}_5$ Microparticles
• Exploration of optimal hyperfine transitions for spin-wave storage in ${}^{167}$Er${}^{3+}$:Y${}_2$SiO${}_5$
• Spectroscopy of Sm${}^{3+}$ Ions in the C${}_{\mathrm{s}}$ Symmetry Centres of Hydrothermally Prepared K${}_2$YF${}_5$ Microcrystals