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Lanthanide-doped Y$_{2}$SiO$_{5}$ microcrystals were prepared using the solution combustion, solid state and sol-gel synthesis techniques. Of these, the sol-gel method yields the most reliable and high-quality X2 phase Y$_{2}$SiO$_{5}$ microcrystals. Absorption and laser site-selective fluorescence measurements of Nd$^{3+}$, Eu$^{3+}$ and Er$^{3+}$ doped material, performed at cryogenic temperatures, indicate that the as-grown microcrystals are of high optical quality with inhomogeneously broadened optical linewidths that are comparable to bulk crystals at similar dopant concentrations.

K$_2$YF$_5$ crystals doped with lanthanide ions have a variety of possible optical applications. Owing to the low symmetry of the system, the crystal structure cannot be unambiguously determined by x-ray diffraction. However, electron-paramagnetic resonance studies have demonstrated that lanthanide ions substitute for yttrium in sites of C$_{\rm s}$ local symmetry. In this work, we use high-resolution absorption and laser spectroscopy to determine electronic energy levels for Er$^{3+}$ ions in K$_2$YF$_5$ microparticles. A total of 39 crystal-field energy levels, distributed among 7 multiplets of the Er$^{3+}$ ion, have been assigned. This optical data is used for crystal-field modelling of the electronic structure of Er$^{3+}$ in K$_2$YF$_5$. Our model is fitted not only to the electronic energy levels, but also to the ground-state g-tensor. This magnetic-splitting data defines the axis system of the calculation, avoiding ambiguities associated with low-symmetry crystal-field fits.

Laser site-selective spectroscopy and high-resolution absorption measurements have been used to determine 51 crystal-field energy levels for one of the Ho$^{3+}$ centres in Y$_{2}$SiO$_{5}$. This centre is denoted as Site 2 and has been tentatively assigned as the seven-fold coordinated centre. High resolution absorption measurements reveal complex hyperfine patterns that obey and approximate selection rule. The application of a magnetic field along the three optical axes reveals the presence of avoided crossings below 0.5 Tesla, in both the ground and excited states.

We report Zeeman infra-red spectroscopy of electronic-nuclear levels of $^5$I$_8 \rightarrow ^5$I$_7$ transitions of Ho$^{3+}$ in the C$_{\rm 4v}$(F$^-$) centre in CaF$_2$ with the magnetic field along the $\langle 111\rangle$ direction of the crystal. Transitions to the lowest $^5$I$_7$ 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.

Computational crystal-field models have provided consistent models of both electronic and Zeeman-hyperfine structure for several rare earth ions. These techniques have not yet been applied to the Zeeman-hyperfine structure of Eu$^{3+}$ because modeling the structure of the $J=0$ singlet levels in Eu$^{3+}$ requires inclusion of the commonly omitted lattice electric quadrupole and nuclear Zeeman interactions. Here, we include these terms in a computational model to fit the crystal field levels and the Zeeman-hyperfine structure of the $^7F_0$ and $^5D_0$ states in three Eu$^{3+}$ sites: the C$_{4v}$ and C$_{3v}$ sites in CaF$_2$ and the C$_2$ site in EuCl$_3$.6H$_2$O. Close fits are obtained for all three sites which are used to resolve ambiguities in previously published parameters, including quantifying the anomalously large crystal-field-induced state mixing in the C$_{3v}$ site and determining the signs of Zeeman-hyperfine parameters in all three sites. We show that this model allows accurate prediction of properties for Eu$^{3+}$ important for quantum information applications of these ions, such as relative transition strengths. The model could be used to improve crystal field calculations for other non-Kramers singlet states. We also present a spin Hamiltonian formalism without the normal assumption of no $J$ mixing, suitable for other rare earth ion energy levels where this effect is important.

High-resolution Zeeman spectroscopy of electronic-nuclear hyperfine levels of ${^5\mathrm{I}_8}\rightarrow{^5\mathrm{I}_7}$ transitions in Ho$^{3+}$:Y$_2$SiO$_5$ is reported. Crystal-field parameters determined for the two $C_1$ symmetry sites in Er$^{3+}$:Y$_2$SiO$_5$ are successfully used to model the Zeeman-hyperfine data, including the prediction of avoided crossings between hyperfine levels under the influence of an external magnetic field. The two six- and seven-coordinate substitutional sites may be distinguished by comparing the spectra with crystal-field calculations.

We report studies of the Yb$^{3+}$ site distribution in Er$^{3+}$ co-doped upconverting alkaline earth fluoride nanoparticles using high-resolution absorption measurements. Similar to bulk crystals, Yb$^{3+}$ single ion cubic (O$_h$), and preferentially formed clusters are the dominant centres for moderate dopant concentrations. At higher concentrations, and for larger particle sizes, a minority C$_{4v}$(F$^-$) centre is also observed. Furthermore, the behaviour of Yb$^{3+}$ cluster centres, whose primary absorption band is located around 10205 cm$^{-1}$ (in near resonance with 980 nm laser diodes) was studied by tuning the metal cation in the host lattice from Ca$^{2+}{\rightarrow}$Sr$^{2+}{\rightarrow}$Ba$^{2+}$. For co-doped materials, with heterogeneous cluster centres, Er$^{3+}$ upconversion fluorescence was observed upon selective excitation of Yb$^{3+}$, resulting in strong visible emission from $^4$H$_{11/2}$, $^4$S$_{3/2}$ and $^4$F$_{9/2}$ multiplets. By monitoring the Er$^{3+}$ $^4$S$_{3/2}{\rightarrow}^4$I$_{15/2}$ (540 nm) fluorescence, whilst scanning a laser through the wavelength dependent Yb3+ absorption, we obtain an excitation spectrum for these heterogeneous cluster centres. It is demonstrated that the group of Yb$^{3+}$ ions residing near an Er$^{3+}$ ion represent a small subset of the overall Yb$^{3+}$ ensemble and therefore a linear absorption measurement is not necessarily a good indication of the optimum laser pump wavelength.

Zeeman spectroscopy is used to demonstrate that phenomenological crystal-field parameters determined for the two $C_1$ point-group sites in Er$^{3+}$:Y$_2$SiO$_5$ may be transferred to other ions. The two crystallographic six- and seven-coordinate substitutional sites may be distinguished by comparing the spectra with crystal-field calculations.

We present a comprehensive spectroscopic study of C$_{2v}$ point-group symmetry sites in Sm$^{3+}$:CaF$_2$/SrF$_2$ codoped with either NaF or LiF. Data includes electron paramagnetic resonance measurements of Zeeman and hyperfine interactions for the ground state, as well as site-selective excitation and fluorescence spectroscopy up to the $^{4}$G$_{5/2}$ multiplet. Inclusion of the EPR data allowed us to determine unique crystal-field parameters. The parameters provide information about the geometry of the sites and the nature of the interactions between the Sm$^{3+}$ dopant and the alkaline earth co-dopant.

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$_5$ ., Comment: 6 pages, plus 5 pages in supplementary information, 4 figures total

We demonstrate a direct measurement of the energy levels of impurity-trapped excitons in CaF$_2$:Yb$^{2+}$. The radically different radiative decay rates of the lowest exciton state and higher excited states enable the generation of a transient photoluminescence enhancement measured via a two-step excitation process. We observe sharp transitions arising from changes of state of localized electrons, broad bands associated with changes of state of delocalized electrons, and broad bands arising from trap liberation., Comment: Minor corrections. arXiv admin note: text overlap with arXiv:1107.4888v2

We discuss recent progress and future prospects for the analysis of the 4f${N-1}$5d excited states of lanthanide ions in host materials. Ab-initio calculations for Ce$^{3+}$ in LiYF$_4$ are used to estimate crystal-field and spin-orbit parameters for the 4f$^1$ and 5d$^1$ configurations. We discuss the possibility of using excited-state absorption to probe the electronic and geometric structure of the 4f$^{N-1}$5d excited states in more detail and we illustrate these ideas with calculations for Yb$^{2+}$ ions in SrCl$_2$.

For a quantum many-body problem, effective Hamiltonians that give exact eigenvalues in reduced model space usually have different expressions, diagrams and evaluation rules from effective transition operators that give exact transition matrix elements between effective eigenvectors in reduced model space. By modifying these diagrams slightly and considering the linked diagrams for all the terms of the same order, we find that the evaluation rules can be made the same for both effective Hamiltonian and effective transition operator diagrams, and in many cases it is possible to combine many diagrams into one modified diagram. We give the rules to evaluate these modified diagrams and show their validity., Comment: 5 journal pages, 4 figures

Perturbative contributions to single-beam two-photon transition rates may be divided into two types. The first, involving low-energy intermediate states, require a high-order perturbation treatment, or an exact diagonalization. The other, involving high energy intermediate states, only require a low-order perturbation treatment. We show how to partition the effective transition operator into two terms, corresponding to these two types, in such a way that a many-body perturbation expansion may be generated that obeys the linked cluster theorem and has a simple diagrammatic representation., Comment: 11 preprint pages

Effective interaction operators usually act on a restricted model space and give the same energies (for Hamiltonian) and matrix elements (for transition operators etc.) as those of the original operators between the corresponding true eigenstates. Various types of effective operators are possible. Those well defined effective operators have been shown being related to each other by similarity transformation. Some of the effective operators have been shown to have connected-diagram expansions. It is shown in this paper that under a class of very general similarity transformations, the connectivity is conserved. The similarity transformation between hermitian and non-hermitian Rayleigh-Schr\"{o}dinger perturbative effective operators is one of such transformation and hence the connectivity can be deducted from each other., Comment: 12 preprint pages

The $f\to d$ transition model by Duan and co-workers [Phys. Rev. B {\bf 66}, 155108 (2002); J. Solid State Chem. {\bf 171}, 299 (2003)] has been very useful in interpreting the $f\to d$ absorption, emission and nonradiative relaxation of light lanthanide ions in crystals. However, based on the assumption that the $f^{N-1}$ core spin-orbit interaction is weak compared to $f\to d$ exchange interaction, this model, in the original form, is not applicable to interpretation of the $f\to d$ transitions of heavy lanthanide ions or actinide ions in crystals. In this work the model is extended to cover the cases of heavy lanthanides and actinides, where the spin-orbit interaction of $f$ orbitals may be stronger than the $f-d$ exchange nteraction. Keywords: lanthanide; f-d transition; model; spectrum; actinide; VUV, Comment: Presented on AMN-2, Queenstown, New Zealand Feb 6-11, 2005; Will appear on Current Applied Physics

For emitters embedded in media of various refractive indices, different macroscopic or microscopic theoretical models predict different dependencies of the spontaneous emission lifetime on refractive index. Among those models are the two most promising models: the virtual-cavity model and the real-cavity model. It is a priori not clear which model is more relevant for a given situation. By close analysis of the available experimental results and examining the assumptions underlying the two models, we reach a consistent interpretation of the experimental results and give the criteria which model should apply for a given situation., Comment: 12 pages with 4 figures

The $4f-5d$ transition rates for rare-earth ions in crystals can be calculated with an effective transition operator acting between model $4f^N$ and $4f^{N-1}5d$ states calculated with effective Hamiltonian, such as semi-empirical crystal Hamiltonian. The difference of the effective transition operator from the original transition operator is the corrections due to mixing in transition initial and final states of excited configurations from both the center ion and the ligand ions. These corrections are calculated using many-body perturbation theory. For free ions, there are important one-body and two-body corrections. The one-body correction is proportional to the original electric dipole operator with magnitude of approximately 40% of the uncorrected electric dipole moment. Its effect is equivalent to scaling down the radial integral $\ME {5d} r {4f}$, to about 60% of the uncorrected HF value. The two-body correction has magnitude of approximately 25% relative to the uncorrected electric dipole moment. For ions in crystals, there is an additional one-body correction due to ligand polarization, whose magnitude is shown to be about 10% of the uncorrected electric dipole moment., Comment: 10 pages, 1 figure

For emitters embedded in media of various refractive indices, different theoretical models predicted substantially different dependencies of the spontaneous emission lifetime on refractive index. It has been claimed that various measurements on $4f\to 4f$ radiative transition of Eu$^{3+}$ in hosts with variable refractive index appear to favor the real-cavity model [J. Fluoresc. 13, 201 (2003) and references therein, Phys. Rev. Lett. 91, 203903 (2003)]. We notice that $5d\to 4f$ radiative transition of rare-earth ions, dominated by allowed electric-dipole transitions with line strengths less perturbed by the ligands, serves as a better test of different models. We analyze the lifetimes of $5d\to 4f$ transition of Ce$^{3+}$ in hosts of refractive indices varying from 1.4 to 2.2. The results favor the macroscopic virtual-cavity model based on Lorentz local field [J. Fluoresc. 13, 201 (2003)]., Comment: 9pages, 1 figures, presented on AMN-2 and to appear on Current Applied Physics

For emitters in a medium, different macroscopic or microscopic theoretical models predict substantially different dependencies of the spontaneous emission lifetime on refractive index. Various measurements have been carried out on Eu$^{3+}$, Ce$^{3+}$ and Nd$^{3+}$ ions, and quantum dots in different surrounding medial. The dependence of the spontaneous emission rates on refractive index has been interpreted with different models. By closely examining some of the experimental results, we notice that some interpretations are based on implicit assumptions which are hard to justify, and some measurements contain too big uncertainties to discriminate among different models. In this work we reanalyse the avilable measured results and give a consistent interpretation., Comment: 9 pages, 2 figures, to be presented on RERC2005, Keystone Colorado, Jun 26-30 2005

Effective operators needed in single-beam two-photon transition calculations have been represented with modified Goldstone diagrams similar to the type suggested by Duan and co-workers [J. Chem. Phys. 121, 5071 (2004) ]. The rules to evaluate these diagrams are different from those for effective Hamiltonian and one-photon transition operators. It is verified that the perturbation terms considered contain only connected diagrams and the evaluation rules are simplified and given explicitly., Comment: 10 preprint pages, to appear in Journal of Alloys and Compounds