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arXiv:2206.09047 · Optics and Spectroscopy

Zeeman-Hyperfine Measurements of a Pseudo-Degenerate Quadruplet in CaF2:Ho3+

Kieran M. Smith, Michael F. Reid, Jon‐Paul R. Wells

Published Jun 1, 2023• 2 citations
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Abstract

We report Zeeman infra-red spectroscopy of electronic-nuclear levels of 5I8 → 5I7 transitions of Ho3+ in the C4v(F–) centre in CaF2 with the magnetic field along the 〈111〉 direction of the crystal. Transitions to the lowest 5I7 state, an isolated electronic doublet, and the next group of states, a pseudo-quadruplet consisting of a doublet and two nearby singlets, exhibit strongly non-linear Zeeman splittings and intensity variations. Simulated spectra based upon a crystal-field analysis give an excellent approximation to the data, illustrating the strong predictive ability of the parametrized crystal-field approach. Anti-crossings in the hyperfine splittings, the basis of quantum information storage in rare-earth doped insulating dielectrics, are also predicted.

DOI
10.1134/s0030400x23020200

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We report Zeeman infra-red spectroscopy of electronic-nuclear levels of 5I8 →5I7 transitions of Ho3+ in the C4v(F−) centre in CaF2 with the magnetic field along the ⟨111⟩ direction of the crystal. Transitions to the lowest 5I7 state, an isolated electronic doublet, and the next group of states, a pseudo-quadruplet consisting of a doublet and two nearby singlets, exhibit strongly non-linear Zeeman splittings and intensity variations. Simulated spectra based upon a crystal-field analysis give an excellent approximation to the data, illustrating the strong predictive ability of the parametrised crystal-field approach. Anti-crossings in the hyperfine splittings, the basis of quantum information storage in rare-earth doped insulating dielectrics, are also predicted.

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We report Zeeman infra-red spectroscopy of electronic-nuclear levels of 5I8 →5I7 transitions of Ho3+ in the C4v(F−) centre in CaF2 with the magnetic field along the ⟨111⟩ direction of the crystal. Transitions to the lowest 5I7 state, an isolated electronic doublet, and the next group of states, a pseudo-quadruplet consisting of a doublet and two nearby singlets, exhibit strongly non-linear Zeeman splittings and intensity variations. Simulated spectra based upon a crystal-field analysis give an excellent approximation to the data, illustrating the strong predictive ability of the parametrised crystal-field approach. Anti-crossings in the hyperfine splittings, the basis of quantum information storage in rare-earth doped insulating dielectrics, are also predicted.

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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 → 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 → 4 I 15 / 2 and 4 I 13 / 2 → 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. • Detailed spectroscopic study of the C 3v (O 2 − ) Centre in CaF 2 :Er 3 + . • Crystal-field fit to 34 energy levels and ground-state magnetic splitting. • Transition intensity analysis for the technologically relevant infrared transitions.

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arXiv:2409.15622•Sep 23, 2024•0 citations
We report Zeeman infra-red spectroscopy of electronic-nuclear levels of 5I8 → 5I7 transitions of Ho3+ in the C4v(F–) centre in CaF2 with the magnetic field along the 〈111〉 direction of the crystal. Transitions to the lowest 5I7 state, an isolated electronic doublet, and the next group of states, a pseudo-quadruplet consisting of a doublet and two nearby singlets, exhibit strongly non-linear Zeeman splittings and intensity variations. Simulated spectra based upon a crystal-field analysis give an excellent approximation to the data, illustrating the strong predictive ability of the parametrized crystal-field approach. Anti-crossings in the hyperfine splittings, the basis of quantum information storage in rare-earth doped insulating dielectrics, are also predicted.
We report Zeeman infra-red spectroscopy of electronic-nuclear levels of 5I8 →5I7 transitions of Ho3+ in the C4v(F−) centre in CaF2 with the magnetic field along the ⟨111⟩ direction of the crystal. Transitions to the lowest 5I7 state, an isolated electronic doublet, and the next group of states, a pseudo-quadruplet consisting of a doublet and two nearby singlets, exhibit strongly non-linear Zeeman splittings and intensity variations. Simulated spectra based upon a crystal-field analysis give an excellent approximation to the data, illustrating the strong predictive ability of the parametrised crystal-field approach. Anti-crossings in the hyperfine splittings, the basis of quantum information storage in rare-earth doped insulating dielectrics, are also predicted.
We report Zeeman infra-red spectroscopy of electronic-nuclear levels of 5I8 →5I7 transitions of Ho3+ in the C4v(F−) centre in CaF2 with the magnetic field along the ⟨111⟩ direction of the crystal. Transitions to the lowest 5I7 state, an isolated electronic doublet, and the next group of states, a pseudo-quadruplet consisting of a doublet and two nearby singlets, exhibit strongly non-linear Zeeman splittings and intensity variations. Simulated spectra based upon a crystal-field analysis give an excellent approximation to the data, illustrating the strong predictive ability of the parametrised crystal-field approach. Anti-crossings in the hyperfine splittings, the basis of quantum information storage in rare-earth doped insulating dielectrics, are also predicted.
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 → 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 → 4 I 15 / 2 and 4 I 13 / 2 → 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. • Detailed spectroscopic study of the C 3v (O 2 − ) Centre in CaF 2 :Er 3 + . • Crystal-field fit to 34 energy levels and ground-state magnetic splitting. • Transition intensity analysis for the technologically relevant infrared transitions.
Rare-earth-doped crystals can be attractive materials for quantum information processing, because of the long coherence times that can be expected, in particular, from non-Kramers ions. In this paper, Ho3+-doped yttrium and lutetium vanadate single crystals have been investigated using linear and coherent optical spectroscopy. For Ho3+:YVO4, the crystal-field levels of the I-5(8), F-5, F-5(4) and S-5(2) multiplets have been determined and compared with crystal-field level calculations. This allowed us to unambiguously assign most of the observed transitions, although some results suggest that the site symmetry of the Ho3+ ion could deviate from D-2d. Similar conclusions were reached for Ho3+:LuVO4. Hole burning measurements indicate that the coherence time of the I-5(8)-F-5(5) optical transitions is rather short in both compounds (around 40 ns). Assuming that the coherence is limited by spin interactions, this is accounted for by the high nuclear moment of the nearby vanadium ions, since the large crystal-field level splittings of the I-5(8) and F-5(5) multiplets do not favour a large enhanced nuclear Zeeman effect.
Rare-earth doped insulators have been widely recognized as excellent candidate materials for optical quantum computing and information processing. This is principally due to a combination of optical coherence times of up to milliseconds and ground-state hyperfine coherence times of seconds exhibited by rare-earth 4𝑓 𝑁 states. A key contender among rare-earth doped materials is Er3+:Y2SiO5, for which homogeneous linewidths as narrow as 50 Hz have been reported, and for which transitions between the ground and first excited states fall within the 1.5 𝜇m telecommunications wavelength band. However, attempts to utilize this material for spin-wave storage have been hampered by the complexity of the excited-state hyperfine structure, which inhibits the necessary theoretical work required to predict the location of zero first-order zeeman transitions. To address this, a novel crystal-field fitting method was developed to allow an accurate analysis of the 𝐶1 point-group symmetry sites of Y2SiO5. This work was complemented with spectral hole-burning spectroscopy, which revealed ground-state hyperfine level storage with a lifetime of 1.6 ± 0.4 seconds for the 4I15/2𝑍1 → 4F9/2𝐷1 transition. This type of storage time is uncharacteristic for erbium without an external magnetic field, since spin-flips of the unpaired electron in nearby Er3+ ions are typically understood to lead to fast hole filling. The development process of the theoretical and experimental tools required to perform the above work enabled several additional investigations. In particular, the novel crystal-field fitting methods were applied to the 𝑆4 site of Ce3+:LiYF4 and to the 𝐶2𝑣 site of Sm3+:Na+/Li+:CaF2/SrF2. These studies consisted of excellent tests for the developed methods yet also amounted to interesting investigations in their own respect. Similarly, the experimental work afforded an opportunity to directly determine the hyperfine splittings of the 5I8𝑍1 → 5F5𝐷1 transition in Ho3+:KY3F10. This was achieved using high-resolution excitation spectroscopy. Furthermore, the experimentally determined hyperfine structure could be accurately reproduced using a crystal field model. Finally, a lifetime measurement of the 6H7/2 state of Sm3+:LiYF4 was conducted. By utilizing an infrared free-electron laser, pico-second pump-probe spectroscopy allowed for a direct measurements of one of the shortest lifetimes of an RE3+ doped insulator reported in the literature to date. This confirmed the previously suggested two-gradient modification required for the energy-gap law at very short time scales.
Spectroscopy, Crystal-Field, and Transition Intensity Analyses of the C3v_{\rm 3v}3v​(O2−^{2-}2−) Centre in Er3+^{3+}3+ Doped CaF2_{2}2​ Crystals
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 C3v_{\rm 3v}3v​(O2−^{2-}2−) centre in CaF2_22​:Er3+^{3+}3+ as an interesting erbium site case study. The 4^{4}4I15/2_{15/2}15/2​Z1→4_1 \rightarrow {^{4}}1​→4I13/2_{13/2}13/2​Y1_11​ transition has a low-temperature inhomogeneous linewidth of 1 GHz with hyperfine structure observable from the 167^{167}167Er 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^{4}4I11/2→4_{11/2}\rightarrow {^{4}}11/2​→4I15/2_{15/2}15/2​ and 4^{4}4I13/2→4_{13/2} \rightarrow {^{4}}13/2​→4I15/2_{15/2}15/2​ inter-multiplet transitions are in excellent agreement with the experimentally measured spectra. The 4^{4}4I13/2_{13/2}13/2​ excited state lifetime is 25.0\,ms and the intensity calculation is in excellent agreement with this value.