Erbium-doped solid-state crystals present an attractive platform for quantum communication, combining the telecom C-band spin–photon interface and long coherence times of erbium (Er3+) with the versatility of solid-state hosts. However, across commonly investigated materials, Er3+ is a “dim” ion, with low optical emission rates of kilohertz at most. This makes implementing quantum information transfer protocols (e.g., quantum teleportation) at usable rates a major challenge. One route to increasing Er3+ radiative rates is by careful selection of crystal hosts: the crystal field around an Er3+ ion may hybridize states of different parity, potentially increasing the radiative rate of its telecom transition. Here, using high-throughput computational methods, the radiative rates of Er3+ embedded in 9215 materials are estimated. The computation shows that careful host selection could increase Er3+ radiative rates by an order of magnitude compared to commonly studied hosts. Calculated results are compared with experimental radiative rates in a subset of materials, finding notable clustering but weak correlation. Nevertheless, the “brightest” candidates combined with suitable nanophotonics engineering could push Er3+-based quantum memories into the megahertz bandwidth regime.
This paper describes a scheme for the numerical calculation of crystal field (CF) energy levels and at the same time wave functions of the trivalent erbium ion in cubic symmetry. The 16-fold degenerate term 4I15=2 of the trivalent erbium ion splits into three Stark quartets Γ8 and two different doublets Γ6 and Γ7 (irreducible representations). The CF energy matrix of the Er3+ ion has been constructed and calculated from the complete diagonalization method, and the corresponding wave functions were used to calculate the ground state g-values. This method is outlined and illustrated by the examples of the Si:Er for comparison. The calculated g-factors are g = 6:8 and g = 6:0 for Γ6 and Γ7, respectively
We present a first-principles study of the defect formation and electronic structure of erbium (Er)--doped yttria
(Y2O3). This is an emerging material for spin-photon interfaces in quantum information science due to the narrow-linewidth optical emission from Er dopants at standard telecommunication wavelengths and their potential for quantum memories and transducers. We calculate formation energies of neutral and negatively and positively charged Er dopants and find the charge-neutral configuration to be the most stable, consistent with experiment. Of the two substitutional sites of Er for Y, the
C2 (more relevant for quantum memories) and
C3i (more relevant for quantum transduction), we identify the former as possessing the lowest formation energy. The electronic properties are calculated using the Perdew-Burke-Ernzerhof functional along with the Hubbard
U parameter and spin-orbit coupling, which yields a $\ensuremath{\sim}6\phantom{\rule{0.28em}{0ex}}{\ensuremath{\mu}}_{B}$ orbital and a $\ensuremath{\sim}3\phantom{\rule{0.28em}{0ex}}{\ensuremath{\mu}}_{B}$ spin magnetic moment, and 11 electrons in the Er
4f shell, confirming the formation of charge-neutral
Er3+. This standard density functional theory approach underestimates the band gap of the host and lacks a first-principles justification for
U. To overcome these issues we performed screened hybrid functional calculations, including a negative
U for the
4f orbitals, with mixing $(\ensuremath{\alpha})$ and screening
(w) parameters. These produced robust electronic features with slight modifications in the band gap and the
4f splittings depending on the choice of tuning parameters. We also computed the many-particle electronic excitation energies and compared them with experimental values from photoluminescence.
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.
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
4I
15/2Z
1→4I
13/2Y
1 transition has a low-temperature inhomogeneous linewidth of 1 GHz with hyperfine structure observable from the
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
4I
11/2→4I
15/2 and
4I
13/2→4I
15/2 inter-multiplet transitions are in excellent agreement with the experimentally measured spectra. The
4I
13/2 excited state lifetime is 25.0\,ms and the intensity calculation is in excellent agreement with this value.
Photoluminescence (PL) spectra of Er3+ in an Er-doped silicon film were recorded at 2 and 77 K over the wavelength range from 1.52 to 1.68 μm, which includes optical transitions between the Er3+ I13/24 and I15/24 manifolds. These spectra were then analyzed to determine the nature of the electrostatic field at the site of the Er ion that governs the ion’s optical behavior. The PL spectra were analyzed three different ways: by considering the Er3+ ions to be occupying sites of Td, C3, or D2d point group symmetry. Transition energies and magnetic dipole transition probabilities were calculated for each case by diagonalizing a Hamiltonian representing the free-ion and crystal-field interactions in a Russell–Saunders basis of states spanning the lowest 15 J multiplets of the 4f11 electronic configuration of Er3+. Crystal-field parameters were varied in each case to find the best agreement with the experiment. Our results showed that the site symmetry of the Er3+ ions most consistent with the data is D2d. For this case, the rms deviation between the experimental and calculated energy levels is 3.3 cm−1 with the calculated magnetic dipole transition probabilities in qualitative agreement with the experiment.