Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review Letters

Optical Homogeneous Linewidths of Pr+ in Be F2 and Ge O2 Glasses

John Hegarty, William M. Yen

Published Oct 8, 1979• 123 citations
Publisher

Abstract

Optical homogeneous linewidths of the $^{3}P_{0}\ensuremath{-}^{3}H_{4}(1)$ transition of ${\mathrm{Pr}}^{3+}$ in Be${\mathrm{F}}_{2}$ and Ge${\mathrm{O}}_{2}$ glasses reveal an anomalously smooth quadratic dependence on temperature from 8 to 300 K. The low-temperature behavior is consistent with a recent model of Lyo and Orbach involving an interaction with a single two-level system but the smooth quadratic behavior at all temperatures has deep consequences for the relative roles played by the ordinary phonons and the two-level system in line broadening.

DOI
10.1103/physrevlett.43.1126

Related papers

Spectroscopy and multiwave mixing in Pr3+ : LaF3

Fred Moshary, R. Kichinski, Raymond John Beach +1 more

Photon-echo and stimulated-photon-echo experiments in ${\mathrm{Pr}}^{3+}$:${\mathrm{LaF}}_{3}$ on the three transitions, $^{3}\mathrm{P}_{0}$-${(}^{3}$${\mathrm{H}}_{5}$${)}_{1}$, $^{3}\mathrm{P}_{0}$-${(}^{3}$${\mathrm{H}}_{5}$${)}_{2}$, and $^{3}\mathrm{P}_{0}$-${(}^{3}$${\mathrm{H}}_{6}$${)}_{1}$ [none of which, therefore, involves the ${(}^{3}$${\mathrm{H}}_{4}$${)}_{1}$ ground state] at liquid-He temperatures have revealed the presence of anomalously large residual homogeneous linewidths. The subscripts (e.g., 1,2) denote the crystal-field-split levels of the ${\mathrm{Pr}}^{3+}$ ion states. Amplitude-modulated trilevel echoes were observed involving the $^{3}\mathrm{P}_{0}$-${(}^{3}$${\mathrm{H}}_{5}$${)}_{1}$ and $^{3}\mathrm{P}_{0}$-${(}^{3}$${\mathrm{H}}_{5}$${)}_{2}$ transitions while no trilevel echoes were observed involving the $^{3}\mathrm{P}_{0}$-${(}^{3}$${\mathrm{H}}_{4}$${)}_{1}$ and $^{3}\mathrm{P}_{0}$-${(}^{3}$${\mathrm{H}}_{6}$${)}_{1}$ transitions. Photon echoes were observed on many of the satellite lines of the principal resonance $^{3}\mathrm{P}_{0}$-${(}^{3}$${\mathrm{H}}_{4}$${)}_{1}$ transitions.

Physical Review A•Oct 1, 1989•3 citations

Temperature dependence of optical linewidths and specific heat of rare-earth-doped silicate glasses

Thomas Schmidt, J. Baak, D. A. van de Straat +2 more

Optical dephasing and specific heat measurements were performed on two rare-earth-doped silicate glasses. The effective homogeneous linewidth of the optical transition, ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{hom}}$ was compared to the two-level-system (TLS) contribution to the specific heat, ${\mathit{C}}_{\mathit{v}}^{\mathrm{TLS}}$, between 0.4 and 12 K. Both ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{hom}}$ and ${\mathit{C}}_{\mathit{v}}^{\mathrm{TLS}}$ vary as ${\mathit{T}}^{\mathrm{\ensuremath{\alpha}}}$ with the same value of \ensuremath{\alpha} for a given rare-earth/glass sample, but with different \ensuremath{\alpha} for the two samples (\ensuremath{\alpha}=1.3 for the ${\mathrm{Pr}}^{3+}$/glass, \ensuremath{\alpha}=1.0 for ${\mathrm{Eu}}^{3+}$/glass). From the ratio of ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{hom}}$ to ${\mathit{C}}_{\mathit{v}}^{\mathrm{TLS}}$ for each glass, it appears that the coupling strengths to the TLS for each rare-earth optical transition are similar, but that the density of TLS differ due to their different compositions.

Physical Review Letters•Nov 1, 1993•32 citations

Low-temperature homogeneous linewidths of Yb3+ in inorganic glasses

Richard T. Brundage, William M. Yen

We have measured the homogeneous linewidth of the $^{2}\mathrm{F}_{5/2}$(1)${\mathrm{\ensuremath{-}}}^{2}$${\mathrm{F}}_{7/2}$(1) transition of ${\mathrm{Yb}}^{3+}$ in silicate and phosphate glasses using fluorescence line narrowing between 6.5 and 70 K. The linewidth is observed to vary as ${T}^{1.9\ifmmode\pm\else\textpm\fi{}0.1}$ at high temperature, changing to ${T}^{1.3\ifmmode\pm\else\textpm\fi{}0.1}$ below 40 K. This behavior is compared to that observed in other systems and examined in light of current theories of dephasing in disordered systems.

Physical review. B, Condensed matter•Mar 15, 1986•37 citations

Temperature Dependence of Fluorescence Linewidths in Pr F3 : A Comment on "Excited-State Exchange Broadening of Optical Transitions in Pr Cl3 "

J. W. Allen

Data are reported which show that the temperature dependence of fluorescence linewidths in Pr${\mathrm{F}}_{3}$ are qualitatively like those in La${\mathrm{F}}_{3}$: ${\mathrm{Pr}}^{3+}$. This result is interpreted as supporting the explanation of German and Kiel for the anomalous temperature dependence of fluorescence linewidths in Pr${\mathrm{Cl}}_{3}$.

Physical Review Letters•Jul 14, 1975•2 citations

Homogeneous broadening and hyperfine structure of optical transitions in Pr 3 + : Y 2 SiO 5

Randy W. Equall, R. L. Cone, R. M. Macfarlane

Contributions to the homogeneous linewidth of the $^{3}$${\mathit{H}}_{4}$(1)${\ensuremath{\rightarrow}}^{1}$${\mathit{D}}_{2}$(1) transition for the two crystallographic sites of ${\mathrm{Pr}}^{3+}$ in ${\mathrm{Y}}_{2}$${\mathrm{SiO}}_{5}$ have been investigated using photon echoes. The effects of excitation-intensity-dependent dephasing or instantaneous diffusion were systematically studied to allow accurate determination of the optical resonance widths. Homogeneous linewidths of 2.8 kHz (site 1) and 1 kHz (site 2) were measured with no applied magnetic field and with sufficiently low laser intensity to minimize the effects of instantaneous diffusion. Using the same excitation intensity, widths of 2.1 kHz (site 1) and 0.85 kHz (site 2) were obtained with an applied magnetic field of 77 G, demonstrating a significant contribution of $^{89}\mathrm{Y}$ nuclear-spin fluctuations to the zero-field homogeneous linewidth. Extrapolation to zero excitation intensity yielded optical resonance widths that were only slightly narrower than the measured values. Optically detected nuclear magnetic resonance measurements determined the hyperfine structure of the $^{3}$${\mathit{H}}_{4}$ ground state for each site; the hyperfine levels of the lowest component of the $^{1}$${\mathit{D}}_{2}$ manifold for each site were determined using photon echo nuclear double resonance. The relatively large oscillator strength of 3\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}7}$ for a rare-earth ion, in conjunction with long dephasing times makes this material a useful candidate for demonstration of time-domain signal processing and optical data storage.

Physical review. B, Condensed matter•Aug 1, 1995•213 citations

Phonon-Induced Relaxation in Excited Optical States of Trivalent Praseodymium in La F3

William M. Yen, W. C. Scott, ARTHUR L. SCHAWLOW

Phonon-ion interactions have recently been shown to satisfactorily explain the temperature dependence of widths and positions of the $R$ lines of some $3d$ ions in crystals. These interactions give rise to phonon relaxation processes and are investigated here as the mechanisms responsible for the widths and positions of sharp optical transitions in ($4f$) ions, in particular La${\mathrm{F}}_{3}$: ${\mathrm{Pr}}^{3+}$. The widths of transitions originating or terminating in the metastable $^{3}P_{0}$ state and involving the $^{3}H_{4}$, $^{3}H_{6}$, $^{3}F_{2}$, and $^{3}F_{4}$ states of ${\mathrm{Pr}}^{3+}$ in La${\mathrm{F}}_{3}$ have been investigated as a function of temperature and are found to be both qualitatively and quantitatively explainable in terms of lifetime broadening of the interacting states via nonradiative processes. Temperature-dependent shifts have also been measured for the above four groups of transitions and are shown to be in qualitative agreement with theoretical predictions. Additional features of the La${\mathrm{F}}_{3}$: ${\mathrm{Pr}}^{3+}$ spectrum, including several unreported weak transitions and vibrational sidebands, are also reported.

Physical Review•Oct 5, 1964•270 citations
Optical homogeneous linewidths of the 3P0\ensuremath−3H4(1)^{3}P_{0}\ensuremath{-}^{3}H_{4}(1)3P0​\ensuremath−3H4​(1) transition of Pr3+{\mathrm{Pr}}^{3+}Pr3+ in BeF2{\mathrm{F}}_{2}F2​ and GeO2{\mathrm{O}}_{2}O2​ glasses reveal an anomalously smooth quadratic dependence on temperature from 8 to 300 K. The low-temperature behavior is consistent with a recent model of Lyo and Orbach involving an interaction with a single two-level system but the smooth quadratic behavior at all temperatures has deep consequences for the relative roles played by the ordinary phonons and the two-level system in line broadening.
Photon-echo and stimulated-photon-echo experiments in Pr3+{\mathrm{Pr}}^{3+}Pr3+:LaF3{\mathrm{LaF}}_{3}LaF3​ on the three transitions, 3P0^{3}\mathrm{P}_{0}3P0​-(3{(}^{3}(3H5{\mathrm{H}}_{5}H5​)1{)}_{1})1​, 3P0^{3}\mathrm{P}_{0}3P0​-(3{(}^{3}(3H5{\mathrm{H}}_{5}H5​)2{)}_{2})2​, and 3P0^{3}\mathrm{P}_{0}3P0​-(3{(}^{3}(3H6{\mathrm{H}}_{6}H6​)1{)}_{1})1​ [none of which, therefore, involves the (3{(}^{3}(3H4{\mathrm{H}}_{4}H4​)1{)}_{1})1​ ground state] at liquid-He temperatures have revealed the presence of anomalously large residual homogeneous linewidths. The subscripts (e.g., 1,2) denote the crystal-field-split levels of the Pr3+{\mathrm{Pr}}^{3+}Pr3+ ion states. Amplitude-modulated trilevel echoes were observed involving the 3P0^{3}\mathrm{P}_{0}3P0​-(3{(}^{3}(3H5{\mathrm{H}}_{5}H5​)1{)}_{1})1​ and 3P0^{3}\mathrm{P}_{0}3P0​-(3{(}^{3}(3H5{\mathrm{H}}_{5}H5​)2{)}_{2})2​ transitions while no trilevel echoes were observed involving the 3P0^{3}\mathrm{P}_{0}3P0​-(3{(}^{3}(3H4{\mathrm{H}}_{4}H4​)1{)}_{1})1​ and 3P0^{3}\mathrm{P}_{0}3P0​-(3{(}^{3}(3H6{\mathrm{H}}_{6}H6​)1{)}_{1})1​ transitions. Photon echoes were observed on many of the satellite lines of the principal resonance 3P0^{3}\mathrm{P}_{0}3P0​-(3{(}^{3}(3H4{\mathrm{H}}_{4}H4​)1{)}_{1})1​ transitions.
Optical dephasing and specific heat measurements were performed on two rare-earth-doped silicate glasses. The effective homogeneous linewidth of the optical transition, ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{hom}}$ was compared to the two-level-system (TLS) contribution to the specific heat, CvTLS{\mathit{C}}_{\mathit{v}}^{\mathrm{TLS}}CvTLS​, between 0.4 and 12 K. Both ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{hom}}$ and CvTLS{\mathit{C}}_{\mathit{v}}^{\mathrm{TLS}}CvTLS​ vary as ${\mathit{T}}^{\mathrm{\ensuremath{\alpha}}}$ with the same value of \ensuremath{\alpha} for a given rare-earth/glass sample, but with different \ensuremath{\alpha} for the two samples (\ensuremath{\alpha}=1.3 for the Pr3+{\mathrm{Pr}}^{3+}Pr3+/glass, \ensuremath{\alpha}=1.0 for Eu3+{\mathrm{Eu}}^{3+}Eu3+/glass). From the ratio of ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{hom}}$ to CvTLS{\mathit{C}}_{\mathit{v}}^{\mathrm{TLS}}CvTLS​ for each glass, it appears that the coupling strengths to the TLS for each rare-earth optical transition are similar, but that the density of TLS differ due to their different compositions.
We have measured the homogeneous linewidth of the 2F5/2^{2}\mathrm{F}_{5/2}2F5/2​(1)${\mathrm{\ensuremath{-}}}^{2}$F7/2{\mathrm{F}}_{7/2}F7/2​(1) transition of Yb3+{\mathrm{Yb}}^{3+}Yb3+ in silicate and phosphate glasses using fluorescence line narrowing between 6.5 and 70 K. The linewidth is observed to vary as ${T}^{1.9\ifmmode\pm\else\textpm\fi{}0.1}$ at high temperature, changing to ${T}^{1.3\ifmmode\pm\else\textpm\fi{}0.1}$ below 40 K. This behavior is compared to that observed in other systems and examined in light of current theories of dephasing in disordered systems.
Data are reported which show that the temperature dependence of fluorescence linewidths in PrF3{\mathrm{F}}_{3}F3​ are qualitatively like those in LaF3{\mathrm{F}}_{3}F3​: Pr3+{\mathrm{Pr}}^{3+}Pr3+. This result is interpreted as supporting the explanation of German and Kiel for the anomalous temperature dependence of fluorescence linewidths in PrCl3{\mathrm{Cl}}_{3}Cl3​.
Contributions to the homogeneous linewidth of the 3^{3}3H4{\mathit{H}}_{4}H4​(1)${\ensuremath{\rightarrow}}^{1}$D2{\mathit{D}}_{2}D2​(1) transition for the two crystallographic sites of Pr3+{\mathrm{Pr}}^{3+}Pr3+ in Y2{\mathrm{Y}}_{2}Y2​SiO5{\mathrm{SiO}}_{5}SiO5​ have been investigated using photon echoes. The effects of excitation-intensity-dependent dephasing or instantaneous diffusion were systematically studied to allow accurate determination of the optical resonance widths. Homogeneous linewidths of 2.8 kHz (site 1) and 1 kHz (site 2) were measured with no applied magnetic field and with sufficiently low laser intensity to minimize the effects of instantaneous diffusion. Using the same excitation intensity, widths of 2.1 kHz (site 1) and 0.85 kHz (site 2) were obtained with an applied magnetic field of 77 G, demonstrating a significant contribution of 89Y^{89}\mathrm{Y}89Y nuclear-spin fluctuations to the zero-field homogeneous linewidth. Extrapolation to zero excitation intensity yielded optical resonance widths that were only slightly narrower than the measured values. Optically detected nuclear magnetic resonance measurements determined the hyperfine structure of the 3^{3}3H4{\mathit{H}}_{4}H4​ ground state for each site; the hyperfine levels of the lowest component of the 1^{1}1D2{\mathit{D}}_{2}D2​ manifold for each site were determined using photon echo nuclear double resonance. The relatively large oscillator strength of 3\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}7}$ for a rare-earth ion, in conjunction with long dephasing times makes this material a useful candidate for demonstration of time-domain signal processing and optical data storage.
Phonon-ion interactions have recently been shown to satisfactorily explain the temperature dependence of widths and positions of the RRR lines of some 3d3d3d ions in crystals. These interactions give rise to phonon relaxation processes and are investigated here as the mechanisms responsible for the widths and positions of sharp optical transitions in (4f4f4f) ions, in particular LaF3{\mathrm{F}}_{3}F3​: Pr3+{\mathrm{Pr}}^{3+}Pr3+. The widths of transitions originating or terminating in the metastable 3P0^{3}P_{0}3P0​ state and involving the 3H4^{3}H_{4}3H4​, 3H6^{3}H_{6}3H6​, 3F2^{3}F_{2}3F2​, and 3F4^{3}F_{4}3F4​ states of Pr3+{\mathrm{Pr}}^{3+}Pr3+ in LaF3{\mathrm{F}}_{3}F3​ have been investigated as a function of temperature and are found to be both qualitatively and quantitatively explainable in terms of lifetime broadening of the interacting states via nonradiative processes. Temperature-dependent shifts have also been measured for the above four groups of transitions and are shown to be in qualitative agreement with theoretical predictions. Additional features of the LaF3{\mathrm{F}}_{3}F3​: Pr3+{\mathrm{Pr}}^{3+}Pr3+ spectrum, including several unreported weak transitions and vibrational sidebands, are also reported.