Physical review. B, Condensed matter

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

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

Published Aug 1, 1995• 213 citations

Abstract

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.

DOI: 10.1103/physrevb.52.3963

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Photon echo studies of rare-earth-activated materials for optical memory and signal processing devices

Randy W. Equall

Jan 1, 19951 citation

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

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

Physical Review BDec 30, 20048 citations

Ultraslow optical dephasing in Eu 3 + : Y 2 SiO 5

Randy W. Equall, Yazhou Sun, R. L. Cone +1 more

Physical Review LettersApr 4, 1994257 citations

Hyperfine structure, optical dephasing, and spectral-hole lifetime of single-crystalline Pr3+:La2(WO4)3

O. Guillot-Noël, Philippe Goldner, Y. Le Du +4 more

Physical Review BMay 15, 200719 citations

Optically Detected Coherent Transients in Nuclear Hyperfine Levels

Robert M. Shelby, Constantino S. Yannoni, R. M. Macfarlane

Physical Review LettersDec 18, 197891 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

Physical review. B, Condensed matterJan 1, 198064 citations

Physical review. B, Condensed matter

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

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

Published Aug 1, 1995• 213 citations

Publisher

Abstract

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+}

{\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.

DOI: 10.1103/physrevb.52.3963

Related papers

Photon echo studies of rare-earth-activated materials for optical memory and signal processing devices

Randy W. Equall

The optical spectroscopy and dynamics of three materials; Eu^3+:Y2SiO5, Pr^3+:Y2SiO5, and Tm^3+:Y2SiO5 that are of interest for application in persistent spectral holeburning optical memory and signal processing devices were investigated using linear and nonlinear spectroscopic techniques.Two-pulse photon echoes have been used to measure the homogeneous linewidths.The effects of instantaneous spectral diffusion were systematically studied to allow accurate determination of the optical resonance widths, and external magnetic fields were applied to characterize the effects of fluctuating nuclear spins of the host lattice on dephasing of the dopant ion.The 7F0 → 5D0 transition of 0.1% Eu^3+ in the two crystallographic sites of Y2SiO5 was studied using photon echoes.Using this material, we succeeded in measuring the narrowest optical resonance in a solid by shielding the crystal from stray electromagnetic fields and using sufficiently low laser power to minimize contributions from instantaneous diffusion.The homogeneous linewidths measured in a magnetic field of 100 G are 122 Hz (site 1) and 167 Hz (site 2).These widths are dominated by population decay, but up to 20 Hz is attributed to 89Y spin fluctuations which have been reduced by the applied magnetic field.Similar studies were performed to determine the contributions to the homogeneous linewidth of the 3H4(1) → 1D2(1) transition for both sites of 0.02% Pr^3+ in Y2SiO5.Linewidths of 2.1 kHz (site 1) and 0.85 kHz (site 2) were obtained with an applied magnetic field of 77 G.A significant contribution of 89Y nuclear spin fluctuations to the zero-field homogeneous linewidth was found.Optically detected nuclear magnetic resonance measurements determined the hyperfine structure of the 3H4 ground state for each site, and photon echo nuclear double resonance was used to determine the hyperfine levels of the lowest component of the 1D2 manifold. 3) 2.1? Ec,2SThe optical spectroscopy and dynamics of three materials; Eu^3+:Y2SiO5, Pr^3+:Y2SiO5, and Tm^3+:Y2SiO5 that are of interest for application in persistent spectral holeburning optical memory and signal processing devices were investigated using linear and nonlinear spectroscopic techniques.Two-pulse photon echoes have been used to measure the homogeneous linewidths.The effects of instantaneous spectral diffusion were systematically studied to allow accurate determination of the optical resonance widths, and external magnetic fields were applied to characterize the effects of fluctuating nuclear spins of the host lattice on dephasing of the dopant ion.The 7F0 → 5D0 transition of 0.1% Eu^3+ in the two crystallographic sites of Y2SiO5 was studied using photon echoes.Using this material, we succeeded in measuring the narrowest optical resonance in a solid by shielding the crystal from stray electromagnetic fields and using sufficiently low laser power to minimize contributions from instantaneous diffusion.The homogeneous linewidths measured in a magnetic field of 100 G are 122 Hz (site 1) and 167 Hz (site 2).These widths are dominated by population decay, but up to 20 Hz is attributed to 89Y spin fluctuations which have been reduced by the applied magnetic field.Similar studies were performed to determine the contributions to the homogeneous linewidth of the 3H4(1) → 1D2(1) transition for both sites of 0.02% Pr^3+ in Y2SiO5.Linewidths of 2.1 kHz (site 1) and 0.85 kHz (site 2) were obtained with an applied magnetic field of 77 G.A significant contribution of 89Y nuclear spin fluctuations to the zero-field homogeneous linewidth was found.Optically detected nuclear magnetic resonance measurements determined the hyperfine structure of the 3H4 ground state for each site, and photon echo nuclear double resonance was used to determine the hyperfine levels of the lowest component of the 1D2 manifold. 3) 2.1? Ec,2S

Jan 1, 19951 citation

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

Ultraslow optical dephasing in Eu 3 + : Y 2 SiO 5

Randy W. Equall, Yazhou Sun, R. L. Cone +1 more

We report the measurement of what we believe to be the narrowest known optical resonance in a solid. This was made on the $^{7}$ ${\mathit{F}}_{0}$ ${\ensuremath{\rightarrow}}^{5}$ ${\mathit{D}}_{0}$ transition of ${\mathrm{Eu}}^{3+}$ : ${\mathrm{Y}}_{2}$ ${\mathrm{SiO}}_{5}$ at 1.4 K using photon echoes with sufficiently low laser power to almost eliminate contributions from instantaneous diffusion. The optical resonance widths measured for ${\mathrm{Eu}}^{3+}$ ions in the two crystallographic sites of ${\mathrm{Y}}_{2}$ ${\mathrm{SiO}}_{5}$ and in a magnetic field of 100 G are 122 Hz (site 1) and 167 Hz (site 2). These widths are dominated by population decay, but up to 20 Hz is attributed to $^{89}\mathrm{Y}$ spin fluctuations which have been reduced by the applied magnetic field.We report the measurement of what we believe to be the narrowest known optical resonance in a solid. This was made on the $^{7}$${\mathit{F}}_{0}$${\ensuremath{\rightarrow}}^{5}$${\mathit{D}}_{0}$ transition of ${\mathrm{Eu}}^{3+}$:${\mathrm{Y}}_{2}$${\mathrm{SiO}}_{5}$ at 1.4 K using photon echoes with sufficiently low laser power to almost eliminate contributions from instantaneous diffusion. The optical resonance widths measured for ${\mathrm{Eu}}^{3+}$ ions in the two crystallographic sites of ${\mathrm{Y}}_{2}$${\mathrm{SiO}}_{5}$ and in a magnetic field of 100 G are 122 Hz (site 1) and 167 Hz (site 2). These widths are dominated by population decay, but up to 20 Hz is attributed to $^{89}\mathrm{Y}$ spin fluctuations which have been reduced by the applied magnetic field.

Physical Review LettersApr 4, 1994257 citations

Hyperfine structure, optical dephasing, and spectral-hole lifetime of single-crystalline Pr3+:La2(WO4)3

O. Guillot-Noël, Philippe Goldner, Y. Le Du +4 more

Most of the experiments related to quantum information applications, involving rare-earth doped inorganic crystals, are performed on yttrium orthosilicate single crystals. The work presented here is motivated by the search of new compounds which can be used in the field of quantum computing and/or quantum storage. Relaxation times and hyperfine structure of the $^{3}H_{4}(0)\ensuremath{\rightarrow}^{1}D_{2}(0)$ transition in 1.4% ${\mathrm{Pr}}^{3+}:{\mathrm{La}}_{2}{(\mathrm{W}{\mathrm{O}}_{4})}_{3}$ at $4\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ have been measured by photon-echo and spectral-hole-burning techniques. The hyperfine splittings of the ground $^{3}H_{4}(0)$ and the excited $^{1}D_{2}(0)$ states are $14.9\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$, $24.6\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$ and $5.0\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$, $7.3\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$, respectively. An inhomogeneous linewidth of $18.8\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$ was measured. A homogeneous linewidth of $25.3\ifmmode\pm\else\textpm\fi{}2.0\phantom{\rule{0.3em}{0ex}}\mathrm{kHz}$ was obtained with or without an external magnetic field of about $14\phantom{\rule{0.3em}{0ex}}\mathrm{mT}$ . The fluorescence dynamics of the $^{1}D_{2}$ level obtained by a direct excitation in the $^{3}H_{4}\ensuremath{\rightarrow}^{1}D_{2}$ transition gives a nonexponential decay which indicates energy-transfer processes. This decay can be accurately fitted by the Inokuti-Hirayama model [J. Chem. Phys. 43, 1978 (1965)] with a radiative lifetime of $61\ifmmode\pm\else\textpm\fi{}1\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$ giving a minimal homogeneous linewidth of $2.6\phantom{\rule{0.3em}{0ex}}\mathrm{kHz}$ . The spectral-hole lifetime due to population redistribution within the ground hyperfine levels is $16\ifmmode\pm\else\textpm\fi{}2\phantom{\rule{0.3em}{0ex}}\mathrm{s}$. The results obtained for the ${\mathrm{La}}_{2}{(\mathrm{W}{\mathrm{O}}_{4})}_{3}$ compound make this crystal an interesting host for quantum applications.Most of the experiments related to quantum information applications, involving rare-earth doped inorganic crystals, are performed on yttrium orthosilicate single crystals. The work presented here is motivated by the search of new compounds which can be used in the field of quantum computing and/or quantum storage. Relaxation times and hyperfine structure of the $^{3}H_{4}(0)\ensuremath{\rightarrow}^{1}D_{2}(0)$ transition in 1.4% ${\mathrm{Pr}}^{3+}:{\mathrm{La}}_{2}{(\mathrm{W}{\mathrm{O}}_{4})}_{3}$ at $4\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ have been measured by photon-echo and spectral-hole-burning techniques. The hyperfine splittings of the ground $^{3}H_{4}(0)$ and the excited $^{1}D_{2}(0)$ states are $14.9\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$, $24.6\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$ and $5.0\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$, $7.3\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$, respectively. An inhomogeneous linewidth of $18.8\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$ was measured. A homogeneous linewidth of $25.3\ifmmode\pm\else\textpm\fi{}2.0\phantom{\rule{0.3em}{0ex}}\mathrm{kHz}$ was obtained with or without an external magnetic field of about $14\phantom{\rule{0.3em}{0ex}}\mathrm{mT}$. The fluorescence dynamics of the $^{1}D_{2}$ level obtained by a direct excitation in the $^{3}H_{4}\ensuremath{\rightarrow}^{1}D_{2}$ transition gives a nonexponential decay which indicates energy-transfer processes. This decay can be accurately fitted by the Inokuti-Hirayama model [J. Chem. Phys. 43, 1978 (1965)] with a radiative lifetime of $61\ifmmode\pm\else\textpm\fi{}1\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$ giving a minimal homogeneous linewidth of $2.6\phantom{\rule{0.3em}{0ex}}\mathrm{kHz}$. The spectral-hole lifetime due to population redistribution within the ground hyperfine levels is $16\ifmmode\pm\else\textpm\fi{}2\phantom{\rule{0.3em}{0ex}}\mathrm{s}$. The results obtained for the ${\mathrm{La}}_{2}{(\mathrm{W}{\mathrm{O}}_{4})}_{3}$ compound make this crystal an interesting host for quantum applications.

Physical Review BMay 15, 200719 citations

Optically Detected Coherent Transients in Nuclear Hyperfine Levels

Robert M. Shelby, Constantino S. Yannoni, R. M. Macfarlane

Using optical detection, we have observed rf nutation, free-induction decay, and echoes, on the 16.70-MHz nuclear hyperfine transition of dilute ${\mathrm{Pr}}^{3+}$ in La ${\mathrm{F}}_{3}$ at 2 K. From a comparison of free-induction decay and echo decay we find that the previously observed linewidth of 200 kHz is inhomogeneous and that the homogeneous width is 19 kHz. On the basis of these measurements it is suggested that optical dephasing times for the $^{1}D_{2}\ensuremath{\leftrightarrow}^{3}H_{4}$ and $^{3}P_{0}\ensuremath{\leftrightarrow}^{3}H_{4}$ transitions are as long as \ensuremath{\sim}20 \ensuremath{\mu} sec.Using optical detection, we have observed rf nutation, free-induction decay, and echoes, on the 16.70-MHz nuclear hyperfine transition of dilute ${\mathrm{Pr}}^{3+}$ in La${\mathrm{F}}_{3}$ at 2 K. From a comparison of free-induction decay and echo decay we find that the previously observed linewidth of 200 kHz is inhomogeneous and that the homogeneous width is 19 kHz. On the basis of these measurements it is suggested that optical dephasing times for the $^{1}D_{2}\ensuremath{\leftrightarrow}^{3}H_{4}$ and $^{3}P_{0}\ensuremath{\leftrightarrow}^{3}H_{4}$ transitions are as long as \ensuremath{\sim}20 \ensuremath{\mu} sec.

Physical Review LettersDec 18, 197891 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

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+}

{\mathrm{Y}}_{2}$${\mathrm{SiO}}_{5}

^{89}\mathrm{Y}

^{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.

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.

We report the measurement of what we believe to be the narrowest known optical resonance in a solid. This was made on the

^{7}

{\mathit{F}}_{0}

${\ensuremath{\rightarrow}}^{5}$

{\mathit{D}}_{0}

transition of

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

{\mathrm{Y}}_{2}

{\mathrm{SiO}}_{5}

at 1.4 K using photon echoes with sufficiently low laser power to almost eliminate contributions from instantaneous diffusion. The optical resonance widths measured for

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

ions in the two crystallographic sites of

{\mathrm{Y}}_{2}

{\mathrm{SiO}}_{5}

and in a magnetic field of 100 G are 122 Hz (site 1) and 167 Hz (site 2). These widths are dominated by population decay, but up to 20 Hz is attributed to

^{89}\mathrm{Y}

spin fluctuations which have been reduced by the applied magnetic field.

{\mathrm{Pr}}^{3+}:{\mathrm{La}}_{2}{(\mathrm{W}{\mathrm{O}}_{4})}_{3}

4\phantom{\rule{0.3em}{0ex}}\mathrm{K}

have been measured by photon-echo and spectral-hole-burning techniques. The hyperfine splittings of the ground

^{3}H_{4}(0)

and the excited

^{1}D_{2}(0)

states are $14.9\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$, $24.6\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$ and $5.0\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$, $7.3\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$, respectively. An inhomogeneous linewidth of $18.8\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$ was measured. A homogeneous linewidth of $25.3\ifmmode\pm\else\textpm\fi{}2.0\phantom{\rule{0.3em}{0ex}}\mathrm{kHz}$ was obtained with or without an external magnetic field of about

14\phantom{\rule{0.3em}{0ex}}\mathrm{mT}

. The fluorescence dynamics of the

^{1}D_{2}

level obtained by a direct excitation in the $^{3}H_{4}\ensuremath{\rightarrow}^{1}D_{2}$ transition gives a nonexponential decay which indicates energy-transfer processes. This decay can be accurately fitted by the Inokuti-Hirayama model [J. Chem. Phys. 43, 1978 (1965)] with a radiative lifetime of $61\ifmmode\pm\else\textpm\fi{}1\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$ giving a minimal homogeneous linewidth of

2.6\phantom{\rule{0.3em}{0ex}}\mathrm{kHz}

. The spectral-hole lifetime due to population redistribution within the ground hyperfine levels is $16\ifmmode\pm\else\textpm\fi{}2\phantom{\rule{0.3em}{0ex}}\mathrm{s}$. The results obtained for the

{\mathrm{La}}_{2}{(\mathrm{W}{\mathrm{O}}_{4})}_{3}

compound make this crystal an interesting host for quantum applications.

Using optical detection, we have observed rf nutation, free-induction decay, and echoes, on the 16.70-MHz nuclear hyperfine transition of dilute

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

in La

{\mathrm{F}}_{3}

at 2 K. From a comparison of free-induction decay and echo decay we find that the previously observed linewidth of 200 kHz is inhomogeneous and that the homogeneous width is 19 kHz. On the basis of these measurements it is suggested that optical dephasing times for the $^{1}D_{2}\ensuremath{\leftrightarrow}^{3}H_{4}$ and $^{3}P_{0}\ensuremath{\leftrightarrow}^{3}H_{4}$ transitions are as long as \ensuremath{\sim}20 \ensuremath{\mu} sec.

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.