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Physical review. B, Solid state

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

L. Q. Lambert

Published Mar 1, 1973• 59 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.7.1834

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

Joseph Ganem, Y. P. Wang, D.M. Boye +3 more

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.

Physical Review Letters•Feb 11, 1991•66 citations
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 4A(ms=32)^{4}A({m}_{s}=\frac{3}{2})4A(ms​=23​) to 2E(ms=12)^{2}E({m}_{s}=\frac{1}{2})2E(ms​=21​) 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 2E^{2}E2E excited state are roughly the same as the corresponding interactions in the 4A2^{4}A_{2}4A2​ ground state. The relationship of the photon-echo results to recent fluorescence-linewidth measurements is discussed.
Measurements of photon-echo decays in dilute ruby (Cr2{\mathrm{Cr}}_{2}Cr2​O3{\mathrm{O}}_{3}O3​ concentration of 0.018 at. %) in magnetic fields up to 29.5 kG are reported. Echoes from the 4^{4}4A2{\mathit{A}}_{2}A2​(-3/2)${\mathrm{\ensuremath{\leftrightarrows}}}^{2}$E,E\ifmmode\bar\else\textasciimacron\fi{}(-1/2) and 4^{4}4A2{\mathit{A}}_{2}A2​(-1/2)${\mathrm{\ensuremath{\leftrightarrows}}}^{2}$E,E\ifmmode\bar\else\textasciimacron\fi{}(-1/2) transitions have dephasing times (T2{\mathit{T}}_{2}T2​) 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^{4}4A2{\mathit{A}}_{2}A2​(-1/2)${\mathrm{\ensuremath{\leftrightarrows}}}^{2}$E,E(-1/2) echo are roughly a factor of 3 longer than for the 4^{4}4A2{\mathit{A}}_{2}A2​(-3/2)${\mathrm{\ensuremath{\leftrightarrows}}}^{2}$E,E\ifmmode\bar\else\textasciimacron\fi{}(-1/2) echo. We attribute the lengthening of T2{\mathit{T}}_{2}T2​ with increasing B/T to the suppression of Cr-Cr spin flip-flops as the population of the upper 4^{4}4A2{\mathit{A}}_{2}A2​ levels decreases.
The behavior of photon echoes near level anticrossings is described in terms of the magnetic-field-dependent mixing parameters. The general features of level-crossing behavior are obscured for most cases in dilute ruby and are dominated instead by strong spin-dependent decay resulting from Cr-Al interactions. However, new experiments at short time separation ($\ensuremath{\tau}=32$ nsec) between pulses have permitted observation of the predicted photon-echo anticrossing signals in ruby, and may be applied to other atomic systems.
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.% Cr2{\mathrm{Cr}}_{2}Cr2​O3{\mathrm{O}}_{3}O3​ in Al2{\mathrm{Al}}_{2}Al2​O3{\mathrm{O}}_{3}O3​. 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 KKK 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.
Theoretical and experimental studies of photon-echo modulation for the four σ transitions of the R1 line in ruby with an on-axis magnetic field are described. Echoes originating from the Cr3+ ground-state 4A2 (−3/2) spin level (−3/2 echo) are studied for the first time. Unlike ±½ echoes, the −3/2-echo modulation is found to be dominated by Cr–Al interactions occurring outside the 13 inner-shell ions. The +½-echo modulation is observed to be in major disagreement with the theory using previously determined superhyperfine parameters. Regression-analysis studies indicate that this cannot be due solely to parameter errors. Finite nuclear linewidths and/or optical pumping effects are shown to be a plausible source of the disagreement.
The amplitude of the electron-spin or photon echo from an ensemble of isolated atoms (echo atoms) interacting with magnetic-nuclear neighbors is calculated as a function of the magnitude and the orientation of an applied magnetic field $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$ and the separation between the two excitation pulses, in the limit that the magnitude of $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$ is large compared to the effective local fields at the echo-atom sites due to the nuclear neighbors. The general problem is reduced to the equivalent problem of two-level echo atoms interacting with nuclear neighbors. The latter problem is readily solved and applied to both spin and photon echoes. Experimentally observed spin-echo behavior in ruby is compared to calculated spin-echo behavior using no adjustable parameters, and is found to be in good agreement even when the magnetic field is tilted away from the optic axis thereby causing the echoes to disappear. Calculated photon-echo behavior, in which it is assumed that the interaction constants in the excited state are simply related to those in the ground state, shows the same general features as those that have been observed in experiment. Several results are presented to show the wide range of photon-echo behavior for different values of the interaction constants. A simple theory is presented which explains most observed echo behavior in a straightforward way.
Nonexponential photon-echo decays are observed in ruby, Er3+{\mathrm{Er}}^{3+}Er3+:YLiF4{\mathrm{YLiF}}_{4}YLiF4​, and Er3+{\mathrm{Er}}^{3+}Er3+:LaF3{\mathrm{LaF}}_{3}LaF3​ 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.