Physical Review Letters

Nonexponential photon-echo decays of paramagnetic ions in the superhyperfine limit

Joseph Ganem, Y. P. Wang, D.M. Boye, Richard S. Meltzer, William M. Yen, R. M. Macfarlane

Published Feb 11, 1991• 66 citations

Abstract

Nonexponential photon-echo decays are observed in ruby, ${\mathrm{Er}}^{3+}$:${\mathrm{YLiF}}_{4}$, and ${\mathrm{Er}}^{3+}$:${\mathrm{LaF}}_{3}$ with samples of low ion concentrations in high (10--50 kG) magnetic fields. At the highest fields, photon-echo decays are field independent and their temporal forms are identical for all three systems. This behavior is attributed to optical dephasing arising from electron-spin nuclear-spin superhyperfine interactions in the presence of a frozen core.

DOI: 10.1103/physrevlett.66.695

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Magnetic-field dependence of photon-echo decays in ruby

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Effects of Superhyperfine Interactions on Photon-Echo Behavior in Dilute Ruby

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Nonexponential Photon-Echo Decays of Paramagnetic Ions in the Superhyperfine Limit

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Physical Review Letters

Nonexponential photon-echo decays of paramagnetic ions in the superhyperfine limit

Joseph Ganem, Y. P. Wang, D.M. Boye, Richard S. Meltzer, William M. Yen, R. M. Macfarlane

Published Feb 11, 1991• 66 citations

Publisher

Abstract

Nonexponential photon-echo decays are observed in ruby,

{\mathrm{Er}}^{3+}

{\mathrm{YLiF}}_{4}

, and

{\mathrm{Er}}^{3+}

{\mathrm{LaF}}_{3}

with samples of low ion concentrations in high (10--50 kG) magnetic fields. At the highest fields, photon-echo decays are field independent and their temporal forms are identical for all three systems. This behavior is attributed to optical dephasing arising from electron-spin nuclear-spin superhyperfine interactions in the presence of a frozen core.

DOI: 10.1103/physrevlett.66.695

Related papers

Magnetic-field dependence of photon-echo decays in ruby

Joseph Ganem, Y. P. Wang, Richard S. Meltzer +1 more

Measurements of photon-echo decays in dilute ruby ( ${\mathrm{Cr}}_{2}$ ${\mathrm{O}}_{3}$ concentration of 0.018 at. %) in magnetic fields up to 29.5 kG are reported. Echoes from the $^{4}$ ${\mathit{A}}_{2}$ (-3/2)${\mathrm{\ensuremath{\leftrightarrows}}}^{2}$E,E\ifmmode\bar\else\textasciimacron\fi{}(-1/2) and $^{4}$ ${\mathit{A}}_{2}$ (-1/2)${\mathrm{\ensuremath{\leftrightarrows}}}^{2}$E,E\ifmmode\bar\else\textasciimacron\fi{}(-1/2) transitions have dephasing times ( ${\mathit{T}}_{2}$ ) that are directly proportional to the ratio of the magnetic field (B) to the temperature (T), for the range 2.5B/T20 kG/K. A transition in the decay from exponential to nonexponential behavior for B/T>10 kG/K is observed. Decay times for the $^{4}$ ${\mathit{A}}_{2}$ (-1/2)${\mathrm{\ensuremath{\leftrightarrows}}}^{2}$E,E(-1/2) echo are roughly a factor of 3 longer than for the $^{4}$ ${\mathit{A}}_{2}$ (-3/2)${\mathrm{\ensuremath{\leftrightarrows}}}^{2}$E,E\ifmmode\bar\else\textasciimacron\fi{}(-1/2) echo. We attribute the lengthening of ${\mathit{T}}_{2}$ with increasing B/T to the suppression of Cr-Cr spin flip-flops as the population of the upper $^{4}$ ${\mathit{A}}_{2}$ levels decreases.Measurements of photon-echo decays in dilute ruby (${\mathrm{Cr}}_{2}$${\mathrm{O}}_{3}$ concentration of 0.018 at. %) in magnetic fields up to 29.5 kG are reported. Echoes from the $^{4}$${\mathit{A}}_{2}$(-3/2)${\mathrm{\ensuremath{\leftrightarrows}}}^{2}$E,E\ifmmode\bar\else\textasciimacron\fi{}(-1/2) and $^{4}$${\mathit{A}}_{2}$(-1/2)${\mathrm{\ensuremath{\leftrightarrows}}}^{2}$E,E\ifmmode\bar\else\textasciimacron\fi{}(-1/2) transitions have dephasing times (${\mathit{T}}_{2}$) that are directly proportional to the ratio of the magnetic field (B) to the temperature (T), for the range 2.5B/T20 kG/K. A transition in the decay from exponential to nonexponential behavior for B/T>10 kG/K is observed. Decay times for the $^{4}$${\mathit{A}}_{2}$(-1/2)${\mathrm{\ensuremath{\leftrightarrows}}}^{2}$E,E(-1/2) echo are roughly a factor of 3 longer than for the $^{4}$${\mathit{A}}_{2}$(-3/2)${\mathrm{\ensuremath{\leftrightarrows}}}^{2}$E,E\ifmmode\bar\else\textasciimacron\fi{}(-1/2) echo. We attribute the lengthening of ${\mathit{T}}_{2}$ with increasing B/T to the suppression of Cr-Cr spin flip-flops as the population of the upper $^{4}$${\mathit{A}}_{2}$ levels decreases.

Physical review. B, Condensed matterApr 1, 199110 citations

Effects of Superhyperfine Interactions on Photon-Echo Behavior in Dilute Ruby

L. Q. Lambert

A detailed analysis of the photon-echo decay in dilute ruby is presented. The experimental results are in quantitative agreement with an echo-decay theory based on the magnetic interaction between the Cr electronic spin and neighboring Al nuclear magnetic moments. Specifically, the following photon-echo properties are explained by the Cr-Al interaction: (i) modulation of the echo as a function of pulse separation time, (ii) the rapid decay of the echo from the $^{4}A({m}_{s}=\frac{3}{2})$ to $^{2}E({m}_{s}=\frac{1}{2})$ transition, (iii) the dependence of the echo on the direction and magnitude of an external magnetic field, (iv) the echo behavior at the 2.06- and 4.12-kG level crossings, and (v) the photon-echo decay in low magnetic fields. In addition, the experiments presented here show that the Cr-Al magnetic interactions in the $^{2}E$ excited state are roughly the same as the corresponding interactions in the $^{4}A_{2}$ ground state. The relationship of the photon-echo results to recent fluorescence-linewidth measurements is discussed.A detailed analysis of the photon-echo decay in dilute ruby is presented. The experimental results are in quantitative agreement with an echo-decay theory based on the magnetic interaction between the Cr electronic spin and neighboring Al nuclear magnetic moments. Specifically, the following photon-echo properties are explained by the Cr-Al interaction: (i) modulation of the echo as a function of pulse separation time, (ii) the rapid decay of the echo from the $^{4}A({m}_{s}=\frac{3}{2})$ to $^{2}E({m}_{s}=\frac{1}{2})$ transition, (iii) the dependence of the echo on the direction and magnitude of an external magnetic field, (iv) the echo behavior at the 2.06- and 4.12-kG level crossings, and (v) the photon-echo decay in low magnetic fields. In addition, the experiments presented here show that the Cr-Al magnetic interactions in the $^{2}E$ excited state are roughly the same as the corresponding interactions in the $^{4}A_{2}$ ground state. The relationship of the photon-echo results to recent fluorescence-linewidth measurements is discussed.

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Concentration-Dependent Photon-Echo Decay in Ruby

Alvin D Compaan

A detailed experimental study is reported of the decay of circularly polarized photon echoes as a function of Cr concentration in samples ranging from 0.006 to 1.2 wt.% ${\mathrm{Cr}}_{2}$ ${\mathrm{O}}_{3}$ in ${\mathrm{Al}}_{2}$ ${\mathrm{O}}_{3}$ . The decay is found to be independent of temperature in the liquid-helium range and generally depends on the pulse separation $\ensuremath{\tau}$ as $\mathrm{exp}(\ensuremath{-}K{\ensuremath{\tau}}^{\frac{1}{2}})$ with the decay constant $K$ proportional to the square root of the Cr concentration. The measured decay is independent of external magnetic field in the range 1.5-6 kG except at 1.06 kG, where modified decays are observed. A theoretical analysis is made of photon-echo decay in terms of spin flips of echo ions resulting from Cr-Cr magnetic interactions and yields good agreement with the observed decays. Spectral diffusion, modified for photon echoes, is shown not to be an important effect. However, anomalously slow decay is observed in some samples when the laser is tuned to the long-wavelength tail of the sample absorption line and the spectral-diffusion mechanism may apply here. The photon-echo-decay measurements are compared with spin-resonance and available spin-echo data in ruby. Also, it is inferred that resonant optical energy transfer is not an important photon-echo-decay mechanism even in the darkest sample studied.A detailed experimental study is reported of the decay of circularly polarized photon echoes as a function of Cr concentration in samples ranging from 0.006 to 1.2 wt.% ${\mathrm{Cr}}_{2}$${\mathrm{O}}_{3}$ in ${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$. The decay is found to be independent of temperature in the liquid-helium range and generally depends on the pulse separation $\ensuremath{\tau}$ as $\mathrm{exp}(\ensuremath{-}K{\ensuremath{\tau}}^{\frac{1}{2}})$ with the decay constant $K$ proportional to the square root of the Cr concentration. The measured decay is independent of external magnetic field in the range 1.5-6 kG except at 1.06 kG, where modified decays are observed. A theoretical analysis is made of photon-echo decay in terms of spin flips of echo ions resulting from Cr-Cr magnetic interactions and yields good agreement with the observed decays. Spectral diffusion, modified for photon echoes, is shown not to be an important effect. However, anomalously slow decay is observed in some samples when the laser is tuned to the long-wavelength tail of the sample absorption line and the spectral-diffusion mechanism may apply here. The photon-echo-decay measurements are compared with spin-resonance and available spin-echo data in ruby. Also, it is inferred that resonant optical energy transfer is not an important photon-echo-decay mechanism even in the darkest sample studied.

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Frozen core effects on nonexponential photon echo decay in ruby at high fields

Alex Szabo

Journal of LuminescenceJan 1, 19947 citations

Photon echo in ruby doped only by53Cr isotope ions

В. В. Самарцев, Шегеда Анатолий Михайлович, A. V. Shkalikov +1 more

The signals of photon echo (PE) are investigated firstly in a ruby crystal doped only by the 53 Cr isotope ions in a concentration of 0.03 – 0,05 wt%. The optical experiments were performed in backward regime at the wavelength of 693.4 nm both with a low magnetic field (200 G) and without it. Since the 53 Cr isotope ions have hyperfine structure of levels the special attention was paid to the study of the stimulated photon echo and primarily to the investigation of its decay kinetics. It is established that this decay has a form which is typical to the signals of long-lived PE. But in contrast to the long-lived PE the decay time in our case is less than the lifetime of the excited 2E(Ē) state. The signals of primary photon echo and stimulated photon echo at a low longitudinal magnetic field and their decay curves are investigated. We observed the beats of temporal shape of these signals with a period of several tens of nanoseconds. Theoretical analysis shows that they are due to the hyperfine interaction of valence electrons of 53 Cr isotope ions with their own nuclei. The obtained decay curves allow us to estimate the phase relaxation time at the presence of a magnetic field. It proves to be equal to 98 ns. The spectrum of stimulated photon echo signal in the doped ruby exposed to a magnetic field is measured.The signals of photon echo (PE) are investigated firstly in a ruby crystal doped only by the 53 Cr isotope ions in a concentration of 0.03 – 0,05 wt%. The optical experiments were performed in backward regime at the wavelength of 693.4 nm both with a low magnetic field (200 G) and without it. Since the 53 Cr isotope ions have hyperfine structure of levels the special attention was paid to the study of the stimulated photon echo and primarily to the investigation of its decay kinetics. It is established that this decay has a form which is typical to the signals of long-lived PE. But in contrast to the long-lived PE the decay time in our case is less than the lifetime of the excited 2E(Ē) state. The signals of primary photon echo and stimulated photon echo at a low longitudinal magnetic field and their decay curves are investigated. We observed the beats of temporal shape of these signals with a period of several tens of nanoseconds. Theoretical analysis shows that they are due to the hyperfine interaction of valence electrons of 53 Cr isotope ions with their own nuclei. The obtained decay curves allow us to estimate the phase relaxation time at the presence of a magnetic field. It proves to be equal to 98 ns. The spectrum of stimulated photon echo signal in the doped ruby exposed to a magnetic field is measured.

Laser Physics LettersApr 22, 20085 citations

Nonexponential photon-echo decays are observed in ruby,

{\mathrm{Er}}^{3+}

{\mathrm{YLiF}}_{4}

, and

{\mathrm{Er}}^{3+}

{\mathrm{LaF}}_{3}

Measurements of photon-echo decays in dilute ruby (

{\mathrm{Cr}}_{2}

{\mathrm{O}}_{3}

concentration of 0.018 at. %) in magnetic fields up to 29.5 kG are reported. Echoes from the

^{4}

{\mathit{A}}_{2}

(-3/2)${\mathrm{\ensuremath{\leftrightarrows}}}^{2}$E,E\ifmmode\bar\else\textasciimacron\fi{}(-1/2) and

^{4}

{\mathit{A}}_{2}

(-1/2)${\mathrm{\ensuremath{\leftrightarrows}}}^{2}$E,E\ifmmode\bar\else\textasciimacron\fi{}(-1/2) transitions have dephasing times (

{\mathit{T}}_{2}

) that are directly proportional to the ratio of the magnetic field (B) to the temperature (T), for the range 2.5B/T20 kG/K. A transition in the decay from exponential to nonexponential behavior for B/T>10 kG/K is observed. Decay times for the

^{4}

{\mathit{A}}_{2}

(-1/2)${\mathrm{\ensuremath{\leftrightarrows}}}^{2}$E,E(-1/2) echo are roughly a factor of 3 longer than for the

^{4}

{\mathit{A}}_{2}

(-3/2)${\mathrm{\ensuremath{\leftrightarrows}}}^{2}$E,E\ifmmode\bar\else\textasciimacron\fi{}(-1/2) echo. We attribute the lengthening of

{\mathit{T}}_{2}

with increasing B/T to the suppression of Cr-Cr spin flip-flops as the population of the upper

^{4}

{\mathit{A}}_{2}

levels decreases.

^{4}A({m}_{s}=\frac{3}{2})

^{2}E({m}_{s}=\frac{1}{2})

transition, (iii) the dependence of the echo on the direction and magnitude of an external magnetic field, (iv) the echo behavior at the 2.06- and 4.12-kG level crossings, and (v) the photon-echo decay in low magnetic fields. In addition, the experiments presented here show that the Cr-Al magnetic interactions in the

^{2}E

excited state are roughly the same as the corresponding interactions in the

^{4}A_{2}

ground state. The relationship of the photon-echo results to recent fluorescence-linewidth measurements is discussed.

A detailed experimental study is reported of the decay of circularly polarized photon echoes as a function of Cr concentration in samples ranging from 0.006 to 1.2 wt.%

{\mathrm{Cr}}_{2}

{\mathrm{O}}_{3}

{\mathrm{Al}}_{2}

{\mathrm{O}}_{3}

. The decay is found to be independent of temperature in the liquid-helium range and generally depends on the pulse separation $\ensuremath{\tau}$ as $\mathrm{exp}(\ensuremath{-}K{\ensuremath{\tau}}^{\frac{1}{2}})$ with the decay constant

K

proportional to the square root of the Cr concentration. The measured decay is independent of external magnetic field in the range 1.5-6 kG except at 1.06 kG, where modified decays are observed. A theoretical analysis is made of photon-echo decay in terms of spin flips of echo ions resulting from Cr-Cr magnetic interactions and yields good agreement with the observed decays. Spectral diffusion, modified for photon echoes, is shown not to be an important effect. However, anomalously slow decay is observed in some samples when the laser is tuned to the long-wavelength tail of the sample absorption line and the spectral-diffusion mechanism may apply here. The photon-echo-decay measurements are compared with spin-resonance and available spin-echo data in ruby. Also, it is inferred that resonant optical energy transfer is not an important photon-echo-decay mechanism even in the darkest sample studied.