Physical review. B, Condensed matter

Influence of excited-state Pr3+ on the relaxation of the Pr3+ : YAlO3 3 H4 −1 D2 transition

Stefan Kröll, E. Y. Xu, Ravinder Kachru

Published Jul 1, 1991• 18 citations

Abstract

Two-pulse photon-echo measurements on the 0.1 at. % ${\mathrm{Pr}}^{3+}$:${\mathrm{YAlO}}_{3}$ $^{3}$${\mathit{H}}_{4}$${\mathrm{\ensuremath{-}}}^{1}$${\mathit{D}}_{2}$ transition suggest that the relaxation time depends on the density of excited states created by the excitation pulses. The dependence of the relaxation time on the intensity of each excitation pulse shows that our results are inconsistent with instantaneous spectral diffusion, a model often invoked in this type of experiment, where excited states created by the second pulse chiefly influence the relaxation time. A homogeneous linewidth contribution, noted in previous work as being of unknown origin, is eliminated at low excitation fluences.

DOI: 10.1103/physrevb.44.30

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Optically induced shifts in the frequency of the 3 H4 −1 D2 transition of Pr3+ in LaF3

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Spectroscopic and relaxation character of the P03−H43 transition in La F3 : Pr3+ measured by photon echoes

Y.C. Chen, Kophu P. Chiang, Sven R. Hartmann

Physical review. B, Condensed matterJan 1, 198064 citations

Physical review. B, Condensed matter

Influence of excited-state Pr3+ on the relaxation of the Pr3+ : YAlO3 3 H4 −1 D2 transition

Stefan Kröll, E. Y. Xu, Ravinder Kachru

Published Jul 1, 1991• 18 citations

Publisher

Abstract

Two-pulse photon-echo measurements on the 0.1 at. %

{\mathrm{Pr}}^{3+}

{\mathrm{YAlO}}_{3}

^{3}$${\mathit{H}}_{4}$${\mathrm{\ensuremath{-}}}^{1}$${\mathit{D}}_{2}

transition suggest that the relaxation time depends on the density of excited states created by the excitation pulses. The dependence of the relaxation time on the intensity of each excitation pulse shows that our results are inconsistent with instantaneous spectral diffusion, a model often invoked in this type of experiment, where excited states created by the second pulse chiefly influence the relaxation time. A homogeneous linewidth contribution, noted in previous work as being of unknown origin, is eliminated at low excitation fluences.

DOI: 10.1103/physrevb.44.30

Related papers

Intensity-dependent photon-echo relaxation in rare-earth-doped crystals

Stefan Kröll, E. Y. Xu, M. K. Kim +2 more

Photon-echo-relaxation measurements made on the $^{3}\mathrm{H}_{4}$ ${\mathrm{\ensuremath{-}}}^{3}$ ${\mathrm{P}}_{0}$ transition of 0.01 at. % ${\mathrm{Pr}}^{3+}$ :YAG (where YAG represents yttrium aluminum garnet), $^{3}\mathrm{H}_{4}$ ${\mathrm{\ensuremath{-}}}^{1}$ ${\mathrm{D}}_{2}$ transition in 0.1 at. % ${\mathrm{Pr}}^{3+}$ : ${\mathrm{YAlO}}_{3}$ , and $^{7}\mathrm{F}_{0}$ ${\mathrm{\ensuremath{-}}}^{5}$ ${\mathrm{D}}_{0}$ transition in 0.25 at. % ${\mathrm{Eu}}^{3+}$ : ${\mathrm{YAlO}}_{3}$ show that the photon-echo relaxation rate increases when the intensities of the excitation pulses are increased. Although a part of the relaxation-rate increase in ${\mathrm{Pr}}^{3+}$ :YAG may be attributed to an instantaneous spectral diffusion (ISD) in which the presence of excited neighboring ${\mathrm{Pr}}^{3+}$ ions change the local field and the absorption frequency of the rare-earth ions, our data deviate significantly from the ISD-model predictions. An additional intensity-dependent relaxation mechanism is required to explain the results.Photon-echo-relaxation measurements made on the $^{3}\mathrm{H}_{4}$${\mathrm{\ensuremath{-}}}^{3}$${\mathrm{P}}_{0}$ transition of 0.01 at. % ${\mathrm{Pr}}^{3+}$:YAG (where YAG represents yttrium aluminum garnet), $^{3}\mathrm{H}_{4}$${\mathrm{\ensuremath{-}}}^{1}$${\mathrm{D}}_{2}$ transition in 0.1 at. % ${\mathrm{Pr}}^{3+}$:${\mathrm{YAlO}}_{3}$, and $^{7}\mathrm{F}_{0}$${\mathrm{\ensuremath{-}}}^{5}$${\mathrm{D}}_{0}$ transition in 0.25 at. % ${\mathrm{Eu}}^{3+}$:${\mathrm{YAlO}}_{3}$ show that the photon-echo relaxation rate increases when the intensities of the excitation pulses are increased. Although a part of the relaxation-rate increase in ${\mathrm{Pr}}^{3+}$:YAG may be attributed to an instantaneous spectral diffusion (ISD) in which the presence of excited neighboring ${\mathrm{Pr}}^{3+}$ ions change the local field and the absorption frequency of the rare-earth ions, our data deviate significantly from the ISD-model predictions. An additional intensity-dependent relaxation mechanism is required to explain the results.

Physical review. B, Condensed matterJun 1, 199033 citations

Observation of a magnetic-field-induced resonance in the homogeneous dephasing time for the 1 D2 −3 H4 transition in Pr3+ : YAlO3

Baozhu Luo, Stefan Kröll

Using two-pulse photon echo excitation a strong resonance in the measured homogeneous dephasing time as a function of magnetic field is observed in the $^{3}$ ${\mathit{H}}_{4}$ ${\mathrm{\ensuremath{-}}}^{1}$ ${\mathit{D}}_{2}$ transition of ${\mathrm{Pr}}^{3+}$ : ${\mathrm{YAlO}}_{3}$ . The resonance could only be observed at low excitation energies since it otherwise was masked by excitation intensity dependent extra dephasing processes in the crystal. Thus intensity dependent dephasing processes may not only affect the apparent dephasing time of a system but may also mask other more subtle interactions in the materials studied. It is reasonable to assume that the type of resonance observed could be caused by Zeeman induced level crossings in the active ion or in the host crystal ions or, possibly, that it could be due to coincidences between Zeeman level transition frequencies. However, based on current data of the Pr: ${\mathrm{YAlO}}_{3}$ system the observed resonance could not be unambiguously tied to such effects. \textcopyright{} 1996 The American Physical Society.Using two-pulse photon echo excitation a strong resonance in the measured homogeneous dephasing time as a function of magnetic field is observed in the $^{3}$${\mathit{H}}_{4}$${\mathrm{\ensuremath{-}}}^{1}$${\mathit{D}}_{2}$ transition of ${\mathrm{Pr}}^{3+}$:${\mathrm{YAlO}}_{3}$. The resonance could only be observed at low excitation energies since it otherwise was masked by excitation intensity dependent extra dephasing processes in the crystal. Thus intensity dependent dephasing processes may not only affect the apparent dephasing time of a system but may also mask other more subtle interactions in the materials studied. It is reasonable to assume that the type of resonance observed could be caused by Zeeman induced level crossings in the active ion or in the host crystal ions or, possibly, that it could be due to coincidences between Zeeman level transition frequencies. However, based on current data of the Pr:${\mathrm{YAlO}}_{3}$ system the observed resonance could not be unambiguously tied to such effects. \textcopyright{} 1996 The American Physical Society.

Physical review. B, Condensed matterOct 1, 19962 citations

Stimulated-photon-echo spectroscopy. II. Echo modulation in Pr3+ : YAlO3

Masaharu Mitsunaga, Ryuzi Yano, Naoshi Uesugi

Stimulated-photon-echo measurements as a function of both the first-to-second (\ensuremath{\tau}) and the second-to-third (T) pulse separations were conducted to study the echo-modulation behavior for the $^{3}$ ${\mathit{H}}_{4}$ ${\mathrm{\ensuremath{-}}}^{1}$ ${\mathit{D}}_{2}$ transition of a cryogenic ${\mathrm{Pr}}^{3+}$ : ${\mathrm{YAlO}}_{3}$ sample. When T is shorter than the excited-state lifetime ${\mathit{T}}_{1}$ , deep echo modulations along both the \ensuremath{\tau} and T axes are observed, the frequencies of which correspond to the excited-state sublevel splittings. When T exceeds ${\mathit{T}}_{1}$ , the modulation is still observed, although only along the \ensuremath{\tau} axis. A density-matrix theory is developed in a perturbative manner to explain these coherent dynamical properties. The numerically simulated three-dimensional plots of the echo intensity versus \ensuremath{\tau} and T are presented, predicting quite satisfactorily the seemingly complicated experimental modulation patterns.Stimulated-photon-echo measurements as a function of both the first-to-second (\ensuremath{\tau}) and the second-to-third (T) pulse separations were conducted to study the echo-modulation behavior for the $^{3}$${\mathit{H}}_{4}$${\mathrm{\ensuremath{-}}}^{1}$${\mathit{D}}_{2}$ transition of a cryogenic ${\mathrm{Pr}}^{3+}$:${\mathrm{YAlO}}_{3}$ sample. When T is shorter than the excited-state lifetime ${\mathit{T}}_{1}$, deep echo modulations along both the \ensuremath{\tau} and T axes are observed, the frequencies of which correspond to the excited-state sublevel splittings. When T exceeds ${\mathit{T}}_{1}$, the modulation is still observed, although only along the \ensuremath{\tau} axis. A density-matrix theory is developed in a perturbative manner to explain these coherent dynamical properties. The numerically simulated three-dimensional plots of the echo intensity versus \ensuremath{\tau} and T are presented, predicting quite satisfactorily the seemingly complicated experimental modulation patterns.

Physical review. B, Condensed matterJun 1, 199227 citations

Hyperfine structure and homogeneous broadening in Pr3+:KY(WO4)2

H. L. Xu, M. Nilsson, S. Ohser +4 more

As part of a search for suitable materials for coherent quantum operations, relaxation times and hyperfine structure of the $^{1}D_{2}(1)\text{\ensuremath{-}}^{3}H_{4}(1)$ transition in ${\mathrm{Pr}}^{3+}:\mathrm{KY}{({\mathrm{WO}}_{4})}_{2}$ (0.29 at. %) at 4 K have been obtained using photon-echo and spectral hole burning techniques. The homogeneous linewidth and the effect of excitation-induced dephasing were measured using two-pulse photon-echo techniques. Linewidths of $23.4\ifmmode\pm\else\textpm\fi{}1.0$ and $17.6\ifmmode\pm\else\textpm\fi{}0.9\phantom{\rule{0.3em}{0ex}}\mathrm{kHz}$ were obtained in the absence and presence of an external magnetic field of about 9 mT. The radiative lifetime $({T}_{1})$ of the $^{1}D_{2}$ state was measured to be $43\ifmmode\pm\else\textpm\fi{}2\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$ using time-resolved laser-induced fluorescence and three-pulse photon-echo measurements. The transmission hole spectra were measured and directly yielded the quadrupole level splitting in the $^{1}D_{2}$ ($3.77\ifmmode\pm\else\textpm\fi{}0.03$ and $4.58\ifmmode\pm\else\textpm\fi{}0.04\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$) and $^{3}H_{4}$ ($17.1\ifmmode\pm\else\textpm\fi{}0.1$ and $33.2\ifmmode\pm\else\textpm\fi{}0.3\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$) states. The spectral hole lifetime due to population redistribution between the ground-state nuclear levels was also determined to be $70\ifmmode\pm\else\textpm\fi{}10\phantom{\rule{0.3em}{0ex}}\mathrm{ms}$. A strong dipole-dipole interaction observed in this crystal opens for potential applications in quantum computing schemes for performing quantum logic operations, but the short dephasing time makes it less useful in data storage applications.As part of a search for suitable materials for coherent quantum operations, relaxation times and hyperfine structure of the $^{1}D_{2}(1)\text{\ensuremath{-}}^{3}H_{4}(1)$ transition in ${\mathrm{Pr}}^{3+}:\mathrm{KY}{({\mathrm{WO}}_{4})}_{2}$ (0.29 at. %) at 4 K have been obtained using photon-echo and spectral hole burning techniques. The homogeneous linewidth and the effect of excitation-induced dephasing were measured using two-pulse photon-echo techniques. Linewidths of $23.4\ifmmode\pm\else\textpm\fi{}1.0$ and $17.6\ifmmode\pm\else\textpm\fi{}0.9\phantom{\rule{0.3em}{0ex}}\mathrm{kHz}$ were obtained in the absence and presence of an external magnetic field of about 9 mT. The radiative lifetime $({T}_{1})$ of the $^{1}D_{2}$ state was measured to be $43\ifmmode\pm\else\textpm\fi{}2\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$ using time-resolved laser-induced fluorescence and three-pulse photon-echo measurements. The transmission hole spectra were measured and directly yielded the quadrupole level splitting in the $^{1}D_{2}$ ($3.77\ifmmode\pm\else\textpm\fi{}0.03$ and $4.58\ifmmode\pm\else\textpm\fi{}0.04\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$) and $^{3}H_{4}$ ($17.1\ifmmode\pm\else\textpm\fi{}0.1$ and $33.2\ifmmode\pm\else\textpm\fi{}0.3\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$) states. The spectral hole lifetime due to population redistribution between the ground-state nuclear levels was also determined to be $70\ifmmode\pm\else\textpm\fi{}10\phantom{\rule{0.3em}{0ex}}\mathrm{ms}$. A strong dipole-dipole interaction observed in this crystal opens for potential applications in quantum computing schemes for performing quantum logic operations, but the short dephasing time makes it less useful in data storage applications.

Physical Review BDec 30, 20048 citations

Optically induced shifts in the frequency of the 3 H4 −1 D2 transition of Pr3+ in LaF3

Jiamin Zhang, THOMAS W. MOSSBERG

Photon-echo techniques were employed to measure the homogeneous dephasing rate of the 592.5-nm, $^{3}$ ${\mathit{H}}_{4\mathrm{\ensuremath{-}}}^{1}$ ${\mathit{D}}_{2}$ , transition of ${\mathrm{Pr}}^{3+}$ as experimental parameters affecting the number of ${\mathrm{Pr}}^{3+}$ ions optically excited were varied. These parameters include the dopant concentration and the intensity, carrier frequency, and bandwidth of the excitation pulses. Dephasing rates are found to contain a background contribution whose magnitude is dependent upon the specific crystal sample studied and a second contribution whose magnitude increases with the number of ${\mathrm{Pr}}^{3+}$ ions changing state in the course of the echo excitation sequence. The second contribution to the dephasing rate is attributed to the presence of optical instantaneous diffusion, i.e., the redistribution of ionic transition frequencies consequent to optical excitation, in the samples.Photon-echo techniques were employed to measure the homogeneous dephasing rate of the 592.5-nm, $^{3}$${\mathit{H}}_{4\mathrm{\ensuremath{-}}}^{1}$${\mathit{D}}_{2}$, transition of ${\mathrm{Pr}}^{3+}$ as experimental parameters affecting the number of ${\mathrm{Pr}}^{3+}$ ions optically excited were varied. These parameters include the dopant concentration and the intensity, carrier frequency, and bandwidth of the excitation pulses. Dephasing rates are found to contain a background contribution whose magnitude is dependent upon the specific crystal sample studied and a second contribution whose magnitude increases with the number of ${\mathrm{Pr}}^{3+}$ ions changing state in the course of the echo excitation sequence. The second contribution to the dephasing rate is attributed to the presence of optical instantaneous diffusion, i.e., the redistribution of ionic transition frequencies consequent to optical excitation, in the samples.

Physical review. B, Condensed matterSep 1, 19938 citations

Spectroscopic and relaxation character of the P03−H43 transition in La F3 : Pr3+ measured by photon echoes

Y.C. Chen, Kophu P. Chiang, Sven R. Hartmann

The hyperfine structure and relaxation character of the terminal levels of the $^{3}P_{0}\ensuremath{-}^{3}H_{4}$ (4777 \AA{}) transition in La ${\mathrm{F}}_{3}$ : ${\mathrm{Pr}}^{3+}$ (0.03 at.%) were studied using the photon-echo technique. Using two independent nitrogen-laser pumped dye lasers we have observed modulated photon echoes for pulse separations over a \ensuremath{\sim}10-\ensuremath{\mu}sec range. In this interval our modulated photon echoes decay in a simple exponential manner by a factor of ${10}^{5}$ and yield a homogeneous linewidth of 70 kHz [full width at half maximum (FWHM)]. Fourier transformation of the echo-modulation data yields directly the nuclear level splittings and their associated linewidths in the $^{3}P_{0}$ and $^{3}H_{4}$ states. In the $^{3}P_{0}(^{3}H_{4})$ state the nuclear splittings are 0.73 and 1.12 MHz (8.48 and 16.68 MHz). The measurements for the nuclear level splittings and associated linewidths in the $^{3}H_{4}$ state are in excellent agreement with those obtained from the optical-rf double-resonance experiments of Erickson. We find that the calculated echo modulation is a sensitive function of the relative orientation of the principal axes associated with the ground-and excited-state Hamiltonians. By comparing our experimental and calculated echo-modulation patterns we are able to determine their relative orientations.The hyperfine structure and relaxation character of the terminal levels of the $^{3}P_{0}\ensuremath{-}^{3}H_{4}$ (4777 \AA{}) transition in La${\mathrm{F}}_{3}$: ${\mathrm{Pr}}^{3+}$ (0.03 at.%) were studied using the photon-echo technique. Using two independent nitrogen-laser pumped dye lasers we have observed modulated photon echoes for pulse separations over a \ensuremath{\sim}10-\ensuremath{\mu}sec range. In this interval our modulated photon echoes decay in a simple exponential manner by a factor of ${10}^{5}$ and yield a homogeneous linewidth of 70 kHz [full width at half maximum (FWHM)]. Fourier transformation of the echo-modulation data yields directly the nuclear level splittings and their associated linewidths in the $^{3}P_{0}$ and $^{3}H_{4}$ states. In the $^{3}P_{0}(^{3}H_{4})$ state the nuclear splittings are 0.73 and 1.12 MHz (8.48 and 16.68 MHz). The measurements for the nuclear level splittings and associated linewidths in the $^{3}H_{4}$ state are in excellent agreement with those obtained from the optical-rf double-resonance experiments of Erickson. We find that the calculated echo modulation is a sensitive function of the relative orientation of the principal axes associated with the ground-and excited-state Hamiltonians. By comparing our experimental and calculated echo-modulation patterns we are able to determine their relative orientations.

Physical review. B, Condensed matterJan 1, 198064 citations

Two-pulse photon-echo measurements on the 0.1 at. %

{\mathrm{Pr}}^{3+}

{\mathrm{YAlO}}_{3}

^{3}$${\mathit{H}}_{4}$${\mathrm{\ensuremath{-}}}^{1}$${\mathit{D}}_{2}

Photon-echo-relaxation measurements made on the

^{3}\mathrm{H}_{4}

${\mathrm{\ensuremath{-}}}^{3}$

{\mathrm{P}}_{0}

transition of 0.01 at. %

{\mathrm{Pr}}^{3+}

:YAG (where YAG represents yttrium aluminum garnet),

^{3}\mathrm{H}_{4}

${\mathrm{\ensuremath{-}}}^{1}$

{\mathrm{D}}_{2}

transition in 0.1 at. %

{\mathrm{Pr}}^{3+}

{\mathrm{YAlO}}_{3}

, and

^{7}\mathrm{F}_{0}

${\mathrm{\ensuremath{-}}}^{5}$

{\mathrm{D}}_{0}

transition in 0.25 at. %

{\mathrm{Eu}}^{3+}

{\mathrm{YAlO}}_{3}

show that the photon-echo relaxation rate increases when the intensities of the excitation pulses are increased. Although a part of the relaxation-rate increase in

{\mathrm{Pr}}^{3+}

:YAG may be attributed to an instantaneous spectral diffusion (ISD) in which the presence of excited neighboring

{\mathrm{Pr}}^{3+}

ions change the local field and the absorption frequency of the rare-earth ions, our data deviate significantly from the ISD-model predictions. An additional intensity-dependent relaxation mechanism is required to explain the results.

Using two-pulse photon echo excitation a strong resonance in the measured homogeneous dephasing time as a function of magnetic field is observed in the

^{3}

{\mathit{H}}_{4}

${\mathrm{\ensuremath{-}}}^{1}$

{\mathit{D}}_{2}

transition of

{\mathrm{Pr}}^{3+}

{\mathrm{YAlO}}_{3}

. The resonance could only be observed at low excitation energies since it otherwise was masked by excitation intensity dependent extra dephasing processes in the crystal. Thus intensity dependent dephasing processes may not only affect the apparent dephasing time of a system but may also mask other more subtle interactions in the materials studied. It is reasonable to assume that the type of resonance observed could be caused by Zeeman induced level crossings in the active ion or in the host crystal ions or, possibly, that it could be due to coincidences between Zeeman level transition frequencies. However, based on current data of the Pr:

{\mathrm{YAlO}}_{3}

system the observed resonance could not be unambiguously tied to such effects. \textcopyright{} 1996 The American Physical Society.

^{3}

{\mathit{H}}_{4}

${\mathrm{\ensuremath{-}}}^{1}$

{\mathit{D}}_{2}

transition of a cryogenic

{\mathrm{Pr}}^{3+}

{\mathrm{YAlO}}_{3}

sample. When T is shorter than the excited-state lifetime

{\mathit{T}}_{1}

, deep echo modulations along both the \ensuremath{\tau} and T axes are observed, the frequencies of which correspond to the excited-state sublevel splittings. When T exceeds

{\mathit{T}}_{1}

, the modulation is still observed, although only along the \ensuremath{\tau} axis. A density-matrix theory is developed in a perturbative manner to explain these coherent dynamical properties. The numerically simulated three-dimensional plots of the echo intensity versus \ensuremath{\tau} and T are presented, predicting quite satisfactorily the seemingly complicated experimental modulation patterns.

As part of a search for suitable materials for coherent quantum operations, relaxation times and hyperfine structure of the $^{1}D_{2}(1)\text{\ensuremath{-}}^{3}H_{4}(1)$ transition in

{\mathrm{Pr}}^{3+}:\mathrm{KY}{({\mathrm{WO}}_{4})}_{2}

(0.29 at. %) at 4 K have been obtained using photon-echo and spectral hole burning techniques. The homogeneous linewidth and the effect of excitation-induced dephasing were measured using two-pulse photon-echo techniques. Linewidths of $23.4\ifmmode\pm\else\textpm\fi{}1.0$ and $17.6\ifmmode\pm\else\textpm\fi{}0.9\phantom{\rule{0.3em}{0ex}}\mathrm{kHz}$ were obtained in the absence and presence of an external magnetic field of about 9 mT. The radiative lifetime

({T}_{1})

of the

^{1}D_{2}

state was measured to be $43\ifmmode\pm\else\textpm\fi{}2\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$ using time-resolved laser-induced fluorescence and three-pulse photon-echo measurements. The transmission hole spectra were measured and directly yielded the quadrupole level splitting in the

^{1}D_{2}

($3.77\ifmmode\pm\else\textpm\fi{}0.03$ and $4.58\ifmmode\pm\else\textpm\fi{}0.04\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$) and

^{3}H_{4}

($17.1\ifmmode\pm\else\textpm\fi{}0.1$ and $33.2\ifmmode\pm\else\textpm\fi{}0.3\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$) states. The spectral hole lifetime due to population redistribution between the ground-state nuclear levels was also determined to be $70\ifmmode\pm\else\textpm\fi{}10\phantom{\rule{0.3em}{0ex}}\mathrm{ms}$. A strong dipole-dipole interaction observed in this crystal opens for potential applications in quantum computing schemes for performing quantum logic operations, but the short dephasing time makes it less useful in data storage applications.

Photon-echo techniques were employed to measure the homogeneous dephasing rate of the 592.5-nm,

^{3}

${\mathit{H}}_{4\mathrm{\ensuremath{-}}}^{1}$

{\mathit{D}}_{2}

, transition of

{\mathrm{Pr}}^{3+}

as experimental parameters affecting the number of

{\mathrm{Pr}}^{3+}

ions optically excited were varied. These parameters include the dopant concentration and the intensity, carrier frequency, and bandwidth of the excitation pulses. Dephasing rates are found to contain a background contribution whose magnitude is dependent upon the specific crystal sample studied and a second contribution whose magnitude increases with the number of

{\mathrm{Pr}}^{3+}

ions changing state in the course of the echo excitation sequence. The second contribution to the dephasing rate is attributed to the presence of optical instantaneous diffusion, i.e., the redistribution of ionic transition frequencies consequent to optical excitation, in the samples.

The hyperfine structure and relaxation character of the terminal levels of the $^{3}P_{0}\ensuremath{-}^{3}H_{4}$ (4777 \AA{}) transition in La

{\mathrm{F}}_{3}

{\mathrm{Pr}}^{3+}

(0.03 at.%) were studied using the photon-echo technique. Using two independent nitrogen-laser pumped dye lasers we have observed modulated photon echoes for pulse separations over a \ensuremath{\sim}10-\ensuremath{\mu}sec range. In this interval our modulated photon echoes decay in a simple exponential manner by a factor of

{10}^{5}

and yield a homogeneous linewidth of 70 kHz [full width at half maximum (FWHM)]. Fourier transformation of the echo-modulation data yields directly the nuclear level splittings and their associated linewidths in the

^{3}P_{0}

and

^{3}H_{4}

states. In the

^{3}P_{0}(^{3}H_{4})

state the nuclear splittings are 0.73 and 1.12 MHz (8.48 and 16.68 MHz). The measurements for the nuclear level splittings and associated linewidths in the

^{3}H_{4}

state are in excellent agreement with those obtained from the optical-rf double-resonance experiments of Erickson. We find that the calculated echo modulation is a sensitive function of the relative orientation of the principal axes associated with the ground-and excited-state Hamiltonians. By comparing our experimental and calculated echo-modulation patterns we are able to determine their relative orientations.