Physical review. B, Condensed matter

Accumulated photon echo in ruby and alexandrite

M.H.F. Overwijk, P. J. Rump, J. I. Dijkhuis, H. W. de Wijn

Published Sep 1, 1991• 3 citations

Abstract

The technique of picosecond accumulated photon echo is applied to 700-at. ppm ruby and 2000-at. ppm alexandrite. The decay of the photon-echo intensity versus the probe-pulse delay displays a beat. A detailed analysis on the basis of Bloch equations shows that the beat frequency is associated with the zero-field splitting of the $^{4}$${\mathit{A}}_{2}$ ground state, and that its phase and amplitude are determined by the amount of population communication within this state. Precise values for the spontaneous decay time of 2A\ifmmode\bar\else\textasciimacron\fi{}${(}^{2}$E) and the $^{4}$${\mathit{A}}_{2}$ zero-field splitting are derived.

DOI: 10.1103/physrevb.44.4157

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Photon Echoes

Isaac D. Abella, Norman A. Kurnit, Sven R. Hartmann

Physical ReviewJan 7, 1966689 citations

Photon echo decay in ruby: Electric dipole interactions and instantaneous diffusion

D. R. Taylor, Jan P. Hessler

Physics Letters ADec 1, 197425 citations

Physical review. B, Condensed matter

Accumulated photon echo in ruby and alexandrite

M.H.F. Overwijk, P. J. Rump, J. I. Dijkhuis, H. W. de Wijn

Published Sep 1, 1991• 3 citations

Publisher

Abstract

^{4}$${\mathit{A}}_{2}

ground state, and that its phase and amplitude are determined by the amount of population communication within this state. Precise values for the spontaneous decay time of 2A\ifmmode\bar\else\textasciimacron\fi{}

{(}^{2}

E) and the

^{4}$${\mathit{A}}_{2}

zero-field splitting are derived.

DOI: 10.1103/physrevb.44.4157

Related papers

Accumulated photon echo in ruby under hydrostatic pressure: Ground-state splitting and spontaneous decay of 2A¯ (2 E)

M.H.F. Overwijk, J. I. Dijkhuis, H. W. de Wijn +3 more

The technique of accumulated photon echo is used in combination with a high-pressure diamond anvil cell to measure the splitting of the $^{4}$ ${\mathit{A}}_{2}$ ground state and the one-phonon spontaneous decay rate of the 2A\ifmmode\bar\else\textasciimacron\fi{} ${(}^{2}$ E) level at 1.5 K in ruby up to 4.3 GPa of hydrostatic pressure. The $^{4}$ ${\mathit{A}}_{2}$ ground-state splitting is found to be 0.383\ifmmode\pm\else\textpm\fi{}0.001 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ at ambient pressure, and increases with a slope of +(6\ifmmode\pm\else\textpm\fi{}1)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$/GPa. The spontaneous decay rate of 2A\ifmmode\bar\else\textasciimacron\fi{} ${(}^{2}$ E) increases only weakly with pressure. The pressure dependences of both quantities are accounted for in terms of the trigonal-field and spin-orbit-coupling parameters.The technique of accumulated photon echo is used in combination with a high-pressure diamond anvil cell to measure the splitting of the $^{4}$${\mathit{A}}_{2}$ ground state and the one-phonon spontaneous decay rate of the 2A\ifmmode\bar\else\textasciimacron\fi{}${(}^{2}$E) level at 1.5 K in ruby up to 4.3 GPa of hydrostatic pressure. The $^{4}$${\mathit{A}}_{2}$ ground-state splitting is found to be 0.383\ifmmode\pm\else\textpm\fi{}0.001 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ at ambient pressure, and increases with a slope of +(6\ifmmode\pm\else\textpm\fi{}1)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$/GPa. The spontaneous decay rate of 2A\ifmmode\bar\else\textasciimacron\fi{}${(}^{2}$E) increases only weakly with pressure. The pressure dependences of both quantities are accounted for in terms of the trigonal-field and spin-orbit-coupling parameters.

Physical review. B, Condensed matterJun 1, 19911 citation

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.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.

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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

Accumulated Photon-Echo Measurements In Ruby under Hydrostatic Pressure

M.H.F. Overwijk, J. I. Dijkhuis, H. W. de Wijn +3 more

Photon-echo techniques are widely applied nowadays to study optically active ions in solids. The first photon echoes were observed for the R1 transition in ruby (Al2O3: Cr3+) by Kurnit et al1 using the high-power pulses of a ruby laser. Very recently,2 phase relaxation of both the R1 and R2 transitions in ruby was studied at 1.5 K and ambient pressure. Here, use was ma.de of the technique of accun1ulated photon echo,3 which despite the low average laser power offers greatly enhanced detection sensitivity by virtue of the high repetition rate.Photon-echo techniques are widely applied nowadays to study optically active ions in solids. The first photon echoes were observed for the R1 transition in ruby (Al2O3: Cr3+) by Kurnit et al1 using the high-power pulses of a ruby laser. Very recently,2 phase relaxation of both the R1 and R2 transitions in ruby was studied at 1.5 K and ambient pressure. Here, use was ma.de of the technique of accun1ulated photon echo,3 which despite the low average laser power offers greatly enhanced detection sensitivity by virtue of the high repetition rate.

Quantum Electronics and Laser Science ConferenceApr 24, 19890 citations

Photon Echoes

Isaac D. Abella, Norman A. Kurnit, Sven R. Hartmann

Experiments are described in which a dilute ruby crystal is found to emit spontaneously a short pulse of light, the photon echo, at a time $\ensuremath{\approx}{\ensuremath{\tau}}_{s}$ after irradiation by two successive ruby-laser pulses separated by ${\ensuremath{\tau}}_{s}$. The phenomenon is explained in terms of a macroscopic oscillating electric dipole moment, which is momentarily reformed at the time the photon echo is observed. The analysis predicts the echo polarization as well as the propagation direction relative to the input pulses. A necessary condition for obtaining echoes in ruby is the application of a moderate magnetic field close to the optic axis of the crystal, and a simple model based on ${\mathrm{Cr}}^{3+}$ -Al interactions is offered to account for this magnetic-field behavior. The relaxation time of the echo is found to exceed 250 nsec at 4.2\ifmmode^\circ\else\textdegree\fi{}K but to be less than 70 nsec at 14\ifmmode^\circ\else\textdegree\fi{}K, and is thought to be due to phonon-induced transitions in the excited $^{2}E(\overline{E})$ level. Multiple echo formation is also described.Experiments are described in which a dilute ruby crystal is found to emit spontaneously a short pulse of light, the photon echo, at a time $\ensuremath{\approx}{\ensuremath{\tau}}_{s}$ after irradiation by two successive ruby-laser pulses separated by ${\ensuremath{\tau}}_{s}$. The phenomenon is explained in terms of a macroscopic oscillating electric dipole moment, which is momentarily reformed at the time the photon echo is observed. The analysis predicts the echo polarization as well as the propagation direction relative to the input pulses. A necessary condition for obtaining echoes in ruby is the application of a moderate magnetic field close to the optic axis of the crystal, and a simple model based on ${\mathrm{Cr}}^{3+}$-Al interactions is offered to account for this magnetic-field behavior. The relaxation time of the echo is found to exceed 250 nsec at 4.2\ifmmode^\circ\else\textdegree\fi{}K but to be less than 70 nsec at 14\ifmmode^\circ\else\textdegree\fi{}K, and is thought to be due to phonon-induced transitions in the excited $^{2}E(\overline{E})$ level. Multiple echo formation is also described.

Physical ReviewJan 7, 1966689 citations

Photon echo decay in ruby: Electric dipole interactions and instantaneous diffusion

D. R. Taylor, Jan P. Hessler

Physics Letters ADec 1, 197425 citations

^{4}$${\mathit{A}}_{2}

{(}^{2}

E) and the

^{4}$${\mathit{A}}_{2}

zero-field splitting are derived.

The technique of accumulated photon echo is used in combination with a high-pressure diamond anvil cell to measure the splitting of the

^{4}

{\mathit{A}}_{2}

ground state and the one-phonon spontaneous decay rate of the 2A\ifmmode\bar\else\textasciimacron\fi{}

{(}^{2}

E) level at 1.5 K in ruby up to 4.3 GPa of hydrostatic pressure. The

^{4}

{\mathit{A}}_{2}

ground-state splitting is found to be 0.383\ifmmode\pm\else\textpm\fi{}0.001 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ at ambient pressure, and increases with a slope of +(6\ifmmode\pm\else\textpm\fi{}1)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$/GPa. The spontaneous decay rate of 2A\ifmmode\bar\else\textasciimacron\fi{}

{(}^{2}

E) increases only weakly with pressure. The pressure dependences of both quantities are accounted for in terms of the trigonal-field and spin-orbit-coupling parameters.

{\mathrm{Cr}}^{3+}

ions effecting a spatially dependent phase accumulation which compensates for the phase mismatch.

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.

{\mathrm{Cr}}^{3+}

-Al interactions is offered to account for this magnetic-field behavior. The relaxation time of the echo is found to exceed 250 nsec at 4.2\ifmmode^\circ\else\textdegree\fi{}K but to be less than 70 nsec at 14\ifmmode^\circ\else\textdegree\fi{}K, and is thought to be due to phonon-induced transitions in the excited

^{2}E(\overline{E})

level. Multiple echo formation is also described.