Physical Review Letters

Low-Temperature Optical Dephasing of Rare-Earth Ions in Glass

David L. Huber, Matthijs M. Broer, Brage Golding

Published Jun 18, 1984• 166 citations

Abstract

A theoretical description of the temperature-dependent dephasing rate of rare-earth ions in glass is given for temperatures $T<1$ K. The model invokes elastic dipole-dipole interactions between the rare-earth ions and atomic tunneling systems. The calculation explains features of a recent photon-echo experiment on Si${\mathrm{O}}_{2}$:${\mathrm{Nd}}^{3+}$, namely, the magnitude and ${T}^{1.3}$ dependence of the dephasing rate.

DOI: 10.1103/physrevlett.52.2281

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Physical Review Letters

Low-Temperature Optical Dephasing of Rare-Earth Ions in Glass

David L. Huber, Matthijs M. Broer, Brage Golding

Published Jun 18, 1984• 166 citations

Publisher

Abstract

A theoretical description of the temperature-dependent dephasing rate of rare-earth ions in glass is given for temperatures

T<1

K. The model invokes elastic dipole-dipole interactions between the rare-earth ions and atomic tunneling systems. The calculation explains features of a recent photon-echo experiment on Si

{\mathrm{O}}_{2}

{\mathrm{Nd}}^{3+}

, namely, the magnitude and

{T}^{1.3}

dependence of the dephasing rate.

DOI: 10.1103/physrevlett.52.2281

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Stefan B. Altner, G. Zumofen, Urs P. Wild +1 more

We study the optical properties of rare-earth-ion-doped inorganic crystals with an emphasis on the dependence of two-pulse photon echoes on the excitation density in the system. The experimental investigations concentrate on ${\mathrm{Pr}}^{3+}$ : ${\mathrm{Nd}}^{3+}$ : ${\mathrm{Eu}}^{3+}$ codoped ${\mathrm{Y}}_{2}$ Si ${\mathrm{O}}_{5}$ and YAl ${\mathrm{O}}_{3}$ crystals at low temperatures. With two pulses of one laser the echo is induced in one ion species and with a third, "scrambler" pulse of a second laser another species is excited. These scrambler excitations lead to a dephasing and thus to an echo attenuation which depends on the strength, frequency, and time of the scrambler pulse. The spectral sensitivity of the echo attenuation is used for a spectroscopic technique: "photon-echo attenuation spectroscopy." As a function of the delay time ${t}_{s}$ between the scrambler pulse and the onset of the two-pulse echo sequence the attenuation shows a very specific behavior dictated by the excitation-induced frequency shifts (EFS's). For ${t}_{s}$ between the two echo-inducing pulses the echo intensity is partially regained by the "dephasing-rephasing balancing" of the reversible EFS's. For the theoretical description a stochastic model is introduced and the dephasing by excitation-induced lattice vibrations and by EFS's are analyzed in detail. The present results are discussed in the light of previous experimental and theoretical investigations.We study the optical properties of rare-earth-ion-doped inorganic crystals with an emphasis on the dependence of two-pulse photon echoes on the excitation density in the system. The experimental investigations concentrate on ${\mathrm{Pr}}^{3+}$:${\mathrm{Nd}}^{3+}$:${\mathrm{Eu}}^{3+}$ codoped ${\mathrm{Y}}_{2}$Si${\mathrm{O}}_{5}$ and YAl${\mathrm{O}}_{3}$ crystals at low temperatures. With two pulses of one laser the echo is induced in one ion species and with a third, "scrambler" pulse of a second laser another species is excited. These scrambler excitations lead to a dephasing and thus to an echo attenuation which depends on the strength, frequency, and time of the scrambler pulse. The spectral sensitivity of the echo attenuation is used for a spectroscopic technique: "photon-echo attenuation spectroscopy." As a function of the delay time ${t}_{s}$ between the scrambler pulse and the onset of the two-pulse echo sequence the attenuation shows a very specific behavior dictated by the excitation-induced frequency shifts (EFS's). For ${t}_{s}$ between the two echo-inducing pulses the echo intensity is partially regained by the "dephasing-rephasing balancing" of the reversible EFS's. For the theoretical description a stochastic model is introduced and the dephasing by excitation-induced lattice vibrations and by EFS's are analyzed in detail. The present results are discussed in the light of previous experimental and theoretical investigations.

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Optical linewidths and photon-echo decays of impurities in glasses

W. O. Putikka, David L. Huber

Using a stochastic model, we calculate the temperature dependence of the homogeneous linewidth and the two-pulse photon-echo decay rate of optically active impurities in glasses. The theory applies to the low-temperature regime T\ensuremath{\lesssim}10 K, where it is assumed that the dephasing arises from an elastic dipole interaction of the impurity with an array of thermally excited tunneling systems. Averaging over the tunneling parameters and using relaxation rates appropriate to vitreous silica, we find that the photon-echo decay rate varies as ${T}^{1.1}$ and the homogeneous linewidth as ${T}^{1.2}$ for 0.1\ensuremath{\le}T\ensuremath{\le}1 K, assuming a constant density of states for the tunneling systems. Both the photon-echo amplitude and the optical dipole-moment correlation function decay exponentially in time. The rates, however, are different, with a ratio of photon-echo dephasing time to optical-absorption dephasing time of 6.9 at T=1 K, assuming a constant density of states. The relation of our results to various experimental studies is discussed.Using a stochastic model, we calculate the temperature dependence of the homogeneous linewidth and the two-pulse photon-echo decay rate of optically active impurities in glasses. The theory applies to the low-temperature regime T\ensuremath{\lesssim}10 K, where it is assumed that the dephasing arises from an elastic dipole interaction of the impurity with an array of thermally excited tunneling systems. Averaging over the tunneling parameters and using relaxation rates appropriate to vitreous silica, we find that the photon-echo decay rate varies as ${T}^{1.1}$ and the homogeneous linewidth as ${T}^{1.2}$ for 0.1\ensuremath{\le}T\ensuremath{\le}1 K, assuming a constant density of states for the tunneling systems. Both the photon-echo amplitude and the optical dipole-moment correlation function decay exponentially in time. The rates, however, are different, with a ratio of photon-echo dephasing time to optical-absorption dephasing time of 6.9 at T=1 K, assuming a constant density of states. The relation of our results to various experimental studies is discussed.

Physical review. B, Condensed matterAug 15, 198752 citations

A theoretical description of the temperature-dependent dephasing rate of rare-earth ions in glass is given for temperatures

T<1

K. The model invokes elastic dipole-dipole interactions between the rare-earth ions and atomic tunneling systems. The calculation explains features of a recent photon-echo experiment on Si

{\mathrm{O}}_{2}

{\mathrm{Nd}}^{3+}

, namely, the magnitude and

{T}^{1.3}

dependence of the dephasing rate.

A detailed description is presented of photon echo experiments in

{\mathrm{Nd}}^{3+}

-doped silica optical fibers at temperatures below 1 K. Dephasing rates ${T}_{2}^{\mathrm{\ensuremath{-}}1}$ have been obtained from two-pulse echo sequences at 0.89 \ensuremath{\mu}m and are found to follow a

{T}^{1.3}

temperature dependence. An interpretation of this result is presented which invokes the interaction of tunneling systems with the optical ions via a dipole-dipole elastic interaction. The dynamics of the interaction originates in a spectral diffusion process and three pulse stimulated echo experiments confirm this interpretation.

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

{\mathrm{Nd}}^{3+}

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

codoped

{\mathrm{Y}}_{2}

{\mathrm{O}}_{5}

and YAl

{\mathrm{O}}_{3}

crystals at low temperatures. With two pulses of one laser the echo is induced in one ion species and with a third, "scrambler" pulse of a second laser another species is excited. These scrambler excitations lead to a dephasing and thus to an echo attenuation which depends on the strength, frequency, and time of the scrambler pulse. The spectral sensitivity of the echo attenuation is used for a spectroscopic technique: "photon-echo attenuation spectroscopy." As a function of the delay time

{t}_{s}

between the scrambler pulse and the onset of the two-pulse echo sequence the attenuation shows a very specific behavior dictated by the excitation-induced frequency shifts (EFS's). For

{t}_{s}

between the two echo-inducing pulses the echo intensity is partially regained by the "dephasing-rephasing balancing" of the reversible EFS's. For the theoretical description a stochastic model is introduced and the dephasing by excitation-induced lattice vibrations and by EFS's are analyzed in detail. The present results are discussed in the light of previous experimental and theoretical investigations.

{T}^{1.1}

and the homogeneous linewidth as

{T}^{1.2}

for 0.1\ensuremath{\le}T\ensuremath{\le}1 K, assuming a constant density of states for the tunneling systems. Both the photon-echo amplitude and the optical dipole-moment correlation function decay exponentially in time. The rates, however, are different, with a ratio of photon-echo dephasing time to optical-absorption dephasing time of 6.9 at T=1 K, assuming a constant density of states. The relation of our results to various experimental studies is discussed.