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Physical Review

Optical Linewidth and Line-Shape Studies of Energy Transfer Mechanisms between Rare-Earth Impurity Ions

William M. Yen, R. L. Greene, W. C. Scott, David L. Huber

Published Nov 15, 1965• 18 citations
Publisher

Abstract

We present optical linewidth and line-shape studies of transitions of $4f$ impurity ions in doubly doped systems and show that interactions which involve excitation transfer between the impurity systems produce homogeneous broadening and line-shape changes in the optical transitions. In particular, we have studied the behavior of the 5985-\AA{} line of ${\mathrm{Pr}}^{3+}$ in doubly doped La${\mathrm{F}}_{3}$: ${\mathrm{Pr}}^{3+}$, ${\mathrm{Nd}}^{3+}$ as a function of ${\mathrm{Nd}}^{3+}$ concentration. The 5985-\AA{} ${\mathrm{Pr}}^{3+}$ transition at 4.2\ifmmode^\circ\else\textdegree\fi{}K involves two long-lived electronic states of the ${\mathrm{Pr}}^{3+}$ ion; it follows that in the singly doped La${\mathrm{F}}_{3}$: ${\mathrm{Pr}}^{3+}$ the transition shows a Gaussian shape which is characteristic of inhomogeneous strain and imperfection broadening. As ${\mathrm{Nd}}^{3+}$ is added to the system, a broader Lorentzian component begins to appear in the 5985-\AA{} ${\mathrm{Pr}}^{3+}$ transition and eventually (at ${\mathrm{Nd}}^{3+}$ concentrations of \ensuremath{\sim}1% or above) completely dominates the width and shape of the transition. The Lorentzian component of the transition line shape was successfully separated using a Fourier-transform technique and the width of this component was studied as a function of the ${\mathrm{Nd}}^{3+}$ concentration. The width is found to increase linearly with increasing ${\mathrm{Nd}}^{3+}$ concentration up to concentrations of 2%; at higher concentrations, the linewidth saturates and approaches an asymptotic value of \ensuremath{\sim}2 ${\mathrm{cm}}^{\ensuremath{-}1}$. We construe this homogeneous component to be evidence of a rapid short-range energy transfer mechanism between the ${\mathrm{Pr}}^{3+}$ and ${\mathrm{Nd}}^{3+}$ systems at the terminating ${(^{3}H_{6})}_{1}$ level of the 5985-\AA{} ${\mathrm{Pr}}^{3+}$ transition. Various mechanisms are investigated as causes of the energy transfer process; it is concluded that the spin-exchange interaction is the most probable cause for the transfer. Results of other spectroscopic measurements on the doubly doped La${\mathrm{F}}_{3}$: ${\mathrm{Pr}}^{3+}$, ${\mathrm{Nd}}^{3+}$ system are also presented.

DOI
10.1103/physrev.140.a1188

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We present optical linewidth and line-shape studies of transitions of 4f4f4f impurity ions in doubly doped systems and show that interactions which involve excitation transfer between the impurity systems produce homogeneous broadening and line-shape changes in the optical transitions. In particular, we have studied the behavior of the 5985-\AA{} line of Pr3+{\mathrm{Pr}}^{3+}Pr3+ in doubly doped LaF3{\mathrm{F}}_{3}F3​: Pr3+{\mathrm{Pr}}^{3+}Pr3+, Nd3+{\mathrm{Nd}}^{3+}Nd3+ as a function of Nd3+{\mathrm{Nd}}^{3+}Nd3+ concentration. The 5985-\AA{} Pr3+{\mathrm{Pr}}^{3+}Pr3+ transition at 4.2\ifmmode^\circ\else\textdegree\fi{}K involves two long-lived electronic states of the Pr3+{\mathrm{Pr}}^{3+}Pr3+ ion; it follows that in the singly doped LaF3{\mathrm{F}}_{3}F3​: Pr3+{\mathrm{Pr}}^{3+}Pr3+ the transition shows a Gaussian shape which is characteristic of inhomogeneous strain and imperfection broadening. As Nd3+{\mathrm{Nd}}^{3+}Nd3+ is added to the system, a broader Lorentzian component begins to appear in the 5985-\AA{} Pr3+{\mathrm{Pr}}^{3+}Pr3+ transition and eventually (at Nd3+{\mathrm{Nd}}^{3+}Nd3+ concentrations of \ensuremath{\sim}1% or above) completely dominates the width and shape of the transition. The Lorentzian component of the transition line shape was successfully separated using a Fourier-transform technique and the width of this component was studied as a function of the Nd3+{\mathrm{Nd}}^{3+}Nd3+ concentration. The width is found to increase linearly with increasing Nd3+{\mathrm{Nd}}^{3+}Nd3+ concentration up to concentrations of 2%; at higher concentrations, the linewidth saturates and approaches an asymptotic value of \ensuremath{\sim}2 cm\ensuremath−1{\mathrm{cm}}^{\ensuremath{-}1}cm\ensuremath−1. We construe this homogeneous component to be evidence of a rapid short-range energy transfer mechanism between the Pr3+{\mathrm{Pr}}^{3+}Pr3+ and Nd3+{\mathrm{Nd}}^{3+}Nd3+ systems at the terminating (3H6)1{(^{3}H_{6})}_{1}(3H6​)1​ level of the 5985-\AA{} Pr3+{\mathrm{Pr}}^{3+}Pr3+ transition. Various mechanisms are investigated as causes of the energy transfer process; it is concluded that the spin-exchange interaction is the most probable cause for the transfer. Results of other spectroscopic measurements on the doubly doped LaF3{\mathrm{F}}_{3}F3​: Pr3+{\mathrm{Pr}}^{3+}Pr3+, Nd3+{\mathrm{Nd}}^{3+}Nd3+ system are also presented.
The nature of inhomogeneous broadening in rare earth systems plays an important role in the dynamical optical properties of ions in crystals. For this reason much of the work on the nature of the inhomogeneous broadening in rare earth doped systems has concentrated on the investigation of ion-ion interactions such as spectral transfer and up conversion processes.1,3 Variations in homogeneous optical dephasing times across the inhomogeneous optical line have also been reported.4 These studies concentrate on the variations of collective effects of ion- ion interactions at different positions in the inhomogeneous optical line in relatively heavily doped rare earth systems. We report variations in optically detected NQR (ODNQR) linewidths and shifts of Pr3+ hyperfme transitions in the optical ground state as a function of position in the inhomogeneous optical line and for satellite transitions of the 1D2-3H4 transition in lightly doped (0.5 at. %) Pr3+:LaF3.
Recent optical free-induction-decay (FID) measurements of the impurity ion Pr3+{\mathrm{Pr}}^{3+}Pr3+ in LaF3{\mathrm{F}}_{3}F3​ at 2 \ifmmode^\circ\else\textdegree\fi{}K reveal optical homogeneous linewidths of only a few kilohertz, considerably narrower than the inhomogeneous broadening due to crystalline strains (5 GHz) or the static local magnetic fields of the 19F^{19}\mathrm{F}19F nuclei (100 kHz). In this regime, the homogeneous broadening arises from local field fluctuations, as in NMR, and is due to the 19F^{19}\mathrm{F}19F nuclei which undergo resonant flip-flops and modulate the Pr3+{\mathrm{Pr}}^{3+}Pr3+ optical transition frequency. We treat the optical response of a two-level quantum system to an intense coherent field and to fluctuating perturbations using a Monte Carlo computer routine that assumes (1) the LaF3{\mathrm{F}}_{3}F3​ crystal structure and (2) a sudden fluorine spin-flip model. This procedure avoids many of the approximations of previous analytic theories of spectral diffusion in magnetic resonance and extends the calculation specifically to optical FID. The decay behavior is obtained by sampling statistically the Pr3+{\mathrm{Pr}}^{3+}Pr3+ phase history as subgroups of 19F^{19}\mathrm{F}19F spins flip randomly in space and time. These fluctuations modify the Bloch equations where the solutions for the preparative and post-preparative periods are obtained by numerical integration. In spite of the large lattice size assumed (2250 fluorines), only a few 19F^{19}\mathrm{F}19F spins contribute substantially to the homogeneous width, a result which shows for the first time that spin-flip correlations are not significant. Furthermore, a Pr3+{\mathrm{Pr}}^{3+}Pr3+ ion polarizes and detunes the nearest fluorines forming a frozen core that is incapable of resonant spin flipping with the bulk fluorines. We demonstrate that the core grows radially as the 141Pr(I=52)^{141}\mathrm{Pr}(I=\frac{5}{2})141Pr(I=25​) magnetic moment increases with Iz{I}_{z}Iz​, but the Pr optical linewidth changes little, producing essentially one rather than three linewidths. Our calculations utilize no free parameters and predict a Lorentzian line shape of 8.4 kHz half-width at half maximum which compares to the optical FID observation of a 10.1-kHz Lorentzian. The Monte Carlo algorithm is verified further by the static local magnetic broadening of a Pr quadrupole transition which is found to be Gaussian, 82 kHz full width at half maximum, in agreement with a second-moment calculation and current observations.
The temporal dependence of the fluorescence line shape of Pr ion diluted in LaF3{\mathrm{F}}_{3}F3​ has been studied in detail. The line-shape study is based on the assumption that the cross relaxation between Pr ions dominates the nonradiative process. The ion-ion interaction has been directly probed by the two-ion cooperative absorption process under which a 3P0^{3}P_{0}3P0​ level lifetime dilation has been observed. The dilation effect can be suppressed when the spectral energy transfer is switched on by raising the temperature of the host crystal. The temporal behavior of the fluorescence line shape of the 1D2^{1}D_{2}1D2​ level has been systematically investigated. The "inhomogeneous" linewidth is found to be composed of a main central peak and a series of ion-pair satellites. The shorter decay lifetime of the ion-pair states results in the narrowing of the emission line shape at later times. The energy positions of the ion-pair states have been measured from the 1D2^{1}D_{2}1D2​ ion pairs up-conversion fluorescence process. The lifetime of the ion-pair states is determined by the coupling strength of the cross relaxation from an excited ion to its partner ion and hence varies according to the ion-pair separation. The decay under the inhomogeneous width is nonexponential in general. Based on the number of the distinguished ion pair levels, a concept of the sphere of influence is introduced. Following this model, an approach has been developed which allows us to study the decay characteristics. Systematical trends emerge from such analysis. The cross-relaxation coupling constants for ion pairs have been extracted from the decay curves and profiles of the ion-pairs line shape have been mapped out. Their peak positions agree with those obtained from 1D2^{1}D_{2}1D2​ ion-pair up-conversion fluorescence measurements.
We identify and analyze dephasing mechanisms that broaden the optical transitions of rare-earth ions in randomly oriented transparent ceramics. The study examines the narrow $^{7}F_{0}\phantom{\rule{4pt}{0ex}}\ensuremath{\leftrightarrow}\phantom{\rule{4pt}{0ex}}^{5}D_{0}$ transition of Eu3+{\mathrm{Eu}}^{3+}Eu3+ dopants in a series of Y2O3{\mathrm{Y}}_{2}{\mathrm{O}}_{3}Y2​O3​ ceramic samples prepared under varying conditions. We characterize the temperature and magnetic field dependence of the homogeneous linewidth, as well as long-term spectral diffusion on time scales up to 1 s. The results highlight significant differences between samples with differing thermal treatments and Zr4+{\mathrm{Zr}}^{4+}Zr4+ additive concentrations. In particular, several distinct magnetic interactions from defect centers are observed, which are clearly distinguished from the broadening due to interactions with two-level systems and phonons. By minimizing the broadening due to the different defect centers, linewidths of the order of 4 kHz are achieved for all samples. The linewidths are limited by temperature-dependent interactions and by an interaction that is yet to be identified. Although the homogeneous linewidth can be narrowed further in these ceramic samples, the broadening is now comparable to the linewidths achieved in rare-earth-ion--doped single crystals. Thus, this work emphasizes the usefulness of studying ceramics to gain insights into dephasing mechanisms relevant to single crystals and suggests that ceramics may be an interesting alternative for applications in classical and quantum information processing.
The relation between absorption and emission spectra in a rare-earth doped solid is explored analytically and through numerical simulations on a model system. It is found that the widely used theory of McCumber [D. E. McCumber, Phys. Rev. 136, A954 (1964)] is strictly valid only when the linewidth of each individual transition between Stark levels is ≪kBT. When this assumption is relaxed, deviations between actual simulated spectra and McCumber-calculated spectra are found for both homogeneous and inhomogeneous broadening. The McCumber transform introduces a characteristic distortion of each component transition, in which the low-energy side of the spectrum is increased, and the high-energy side is decreased. The average degree of distortion for the model system is calculated to be 5% for a homogeneous width of 50 cm−1 at room temperature, but only 1% for a purely inhomogeneous width of 50 cm−1. For both homogeneous and inhomogeneous spectra, the distortion varies with the linewidth Δν as (Δν)3/2. The dependence of the distortion on temperature is different for the two types of line shapes, however: ∼T2 for homogeneous and ∼T−1 for inhomogeneous broadening. For most rare-earth doped glasses and crystals at room temperature, the average degree of distortion is expected to be on the order of 5% or less, although the actual discrepancy in the spectral wings can be much larger. The effects described here are likely to be of importance when using McCumber’s theory to obtain accurate cross section values in the spectral wings of rare-earth transitions.
Rare Earth (RE) ion doped nanomaterials are promising candidates for a range of quantum technology applications. Among RE ions, the so-called Kramers' ions possess spin transitions in the GHz range at low magnetic fields, which allows for high-bandwidth multimode quantum storage, fast qubit operations as well as interfacing with superconducting circuits. They also present relevant optical transitions in the infrared. In particular, Er3+{\mathrm{Er}}^{3+}Er3+ has an optical transition in the telecom band, while Nd3+{\mathrm{Nd}}^{3+}Nd3+ presents a high-emission-rate transition close to 890 nm. In this paper, we measure spectroscopic properties that are of relevance to using these materials in quantum technology applications. We find the inhomogeneous linewidth to be 10.7 GHz for Er3+{\mathrm{Er}}^{3+}Er3+ and 8.2 GHz for Nd3+{\mathrm{Nd}}^{3+}Nd3+, and the excited state lifetime T1{T}_{1}T1​ to be 13.68 ms for Er3+{\mathrm{Er}}^{3+}Er3+ and $540\phantom{\rule{0.16em}{0ex}}\textmu{}\mathrm{s}$ for Nd3+{\mathrm{Nd}}^{3+}Nd3+. We study the dependence of homogeneous linewidth on temperature for both samples, with the narrowest linewidth being 379 kHz (T2=839{T}_{2}=839T2​=839 ns) for Er3+{\mathrm{Er}}^{3+}Er3+ measured at 3 K, and 62 kHz (${T}_{2}=5.14\phantom{\rule{4pt}{0ex}}\textmu{}\mathrm{s}$) for Nd3+{\mathrm{Nd}}^{3+}Nd3+ measured at 1.6 K. Further, we investigate time-dependent homogeneous linewidth broadening due to spectral diffusion and the dependence of the homogeneous linewidth on magnetic field to get additional clarity of mechanisms that can influence the coherence time. In light of our results, we discuss two applications: single qubit-state readout and a Fourier-limited single photon source.