Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review Letters

Evidence of Strong Optical Super-Radiant Damping in Ruby

Alvin D Compaan, Isaac D. Abella

Published Jul 5, 1971• 32 citations
Publisher

Abstract

We report measurements of direct photon-echo intensity versus Cr concentration which indicate the presence of sizable radiation-damping effects in dark ruby. The departure from ${n}^{2}$ dependence for concentrations above 0.03% Cr demonstrates that modifications of self-induced transparency analyses are necessary in dense resonant media.

DOI
10.1103/physrevlett.27.23

Related papers

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.

Physical review. B, Solid state•Jun 1, 1972•38 citations

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.

Physical review. B, Condensed matter•Apr 1, 1991•10 citations

Some experimental peculiarities of photon echo in ruby

Самарцев Виталий Владимирович, Alexei A. Kalachev, Ramil G. Usmanov

Photon-echo measurements have been performed in gamma- irradiated ruby and in ruby with 53 Cr 3+ .

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jul 12, 2002•0 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.

Physical review. B, Solid state•Mar 1, 1973•59 citations

Incoherent photon echo in spectroscopy of optically dense impurity media

В. А. Зуйков, Каримуллин Камиль Равкатович, Tatiana G. Mitrofanova +3 more

The possibility of using incoherent photon echo in spectroscopy of optically dense impurity media is considered. A theoretical approach to description of this phenomenon is presented. The experimental data on incoherent photon echo in ruby at liquid-helium temperature, with transport of an excitation pulse through a fiber, are reported. The spectral dependence of the echo intensity is studied. The decay curve for an incoherent echo signal is investigated, and the phase relaxation time is found to be 98 ns.

Bulletin of the Russian Academy of Sciences Physics•Jan 1, 2008•0 citations

Modulation of Photon Echo Intensities by Ultrasonic Waves in Ruby and Alexandrite

D.M. Boye, Wolfgang Grill, John E. Rives +1 more

Modulations of the intensity of two-pulse photon echoes due to ultrasonic waves are described for alexandrite and ruby. Enhancements (up to a factor of 8) of the echo intensity are observed. The main features of the echo intensity changes are well described by a model in which the ultrasonic waves modulate the optical transition frequencies of the echo-producing ${\mathrm{Cr}}^{3+}$ ions effecting a spatially dependent phase accumulation which compensates for the phase mismatch.

Physical Review Letters•Oct 24, 1988•4 citations
We report measurements of direct photon-echo intensity versus Cr concentration which indicate the presence of sizable radiation-damping effects in dark ruby. The departure from n2{n}^{2}n2 dependence for concentrations above 0.03% Cr demonstrates that modifications of self-induced transparency analyses are necessary in dense resonant media.
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.
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.
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.
The possibility of using incoherent photon echo in spectroscopy of optically dense impurity media is considered. A theoretical approach to description of this phenomenon is presented. The experimental data on incoherent photon echo in ruby at liquid-helium temperature, with transport of an excitation pulse through a fiber, are reported. The spectral dependence of the echo intensity is studied. The decay curve for an incoherent echo signal is investigated, and the phase relaxation time is found to be 98 ns.
Modulations of the intensity of two-pulse photon echoes due to ultrasonic waves are described for alexandrite and ruby. Enhancements (up to a factor of 8) of the echo intensity are observed. The main features of the echo intensity changes are well described by a model in which the ultrasonic waves modulate the optical transition frequencies of the echo-producing Cr3+{\mathrm{Cr}}^{3+}Cr3+ ions effecting a spatially dependent phase accumulation which compensates for the phase mismatch.