Physical Review Letters

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

D.M. Boye, Wolfgang Grill, John E. Rives, Richard S. Meltzer

Published Oct 24, 1988• 4 citations

Abstract

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.

DOI: 10.1103/physrevlett.61.1934

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Physical Review Letters

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

D.M. Boye, Wolfgang Grill, John E. Rives, Richard S. Meltzer

Published Oct 24, 1988• 4 citations

Publisher

Abstract

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

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

DOI: 10.1103/physrevlett.61.1934

Related papers

Modulation of photon-echo intensities by electric fields: Pseudo-Stark splittings in alexandrite and YAlO3 : Er3+

Y. P. Wang, Richard S. Meltzer

We describe and demonstrate a method for performing ultrahigh-resolution optical spectroscopy in the time domain which utilizes modulations in the intensity of the two-pulse photon echo in the presence of a perturbation that splits the optical transition frequencies of two or more subgroups of ions. The method is applied to a measurement of the pseudo-Stark effect in alexandrite and ${\mathrm{YAlO}}_{3}$ : ${\mathrm{Er}}^{3+}$ . Stark shifts of \ensuremath{\simeq}100 kHz are observed, but the technique is capable of resolutions 10 kHz in some systems.We describe and demonstrate a method for performing ultrahigh-resolution optical spectroscopy in the time domain which utilizes modulations in the intensity of the two-pulse photon echo in the presence of a perturbation that splits the optical transition frequencies of two or more subgroups of ions. The method is applied to a measurement of the pseudo-Stark effect in alexandrite and ${\mathrm{YAlO}}_{3}$:${\mathrm{Er}}^{3+}$. Stark shifts of \ensuremath{\simeq}100 kHz are observed, but the technique is capable of resolutions 10 kHz in some systems.

Physical review. B, Condensed matterMay 1, 199225 citations

Accumulated photon echo in ruby and alexandrite

M.H.F. Overwijk, P. J. Rump, J. I. Dijkhuis +1 more

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.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.

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A stimulated photon echo modulation varying in T (separation between the second and third pulses) due to the superhyperfine interaction between a Cr ion and neighboring Al nuclei has been observed in ruby by using a Stark switching technique. The modulation was observed for a time much longer than T 2 , and much higher resolution was obtained than by two-pulse photon echo experiments. An apparent disagreement between theoretical and experimental modulation patterns was noticed in the region where T > T 2 .A stimulated photon echo modulation varying in T (separation between the second and third pulses) due to the superhyperfine interaction between a Cr ion and neighboring Al nuclei has been observed in ruby by using a Stark switching technique. The modulation was observed for a time much longer than T 2 , and much higher resolution was obtained than by two-pulse photon echo experiments. An apparent disagreement between theoretical and experimental modulation patterns was noticed in the region where T > T 2 .

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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.

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On-axis photon-echo modulation in ruby

Arthur G. Szabo

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.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.

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Axel Schenzle, S. B. Grossman, Richard G. Brewer

Photon echoes, observed recently in ruby and in ${\mathrm{NH}}_{2}$ D gas by two-pulse laser excitation, exhibit a modulation behavior as the pulse delay time is varied. The effect, which arises in a three-level quantum system, is due to the interference of two optically coupled transitions that share a common level. In this article, the three-level echo problem is treated exactly. Wave-function solutions are incorporated that are handled conveniently by a Laplace-transform technique. We, therefore, extend the earlier theory of echo modulation by Lambert et al., by removing their restriction of on-resonance pulse excitation. This procedure allows us to examine the effect of inhomogeneous broadening on echo amplitude explicitly, and we treat the problem by numerical and also by analytical means for the case of a Doppler-broadened gas. Analytic expressions are derived either for a high or a low laser power regime corresponding to excitation of either a large or a small fraction of the Doppler linewidth. The former case is analogous to pulsed nuclear magnetic resonance and is well known, whereas the latter result is new and applies to current photon echo measurements.Photon echoes, observed recently in ruby and in ${\mathrm{NH}}_{2}$D gas by two-pulse laser excitation, exhibit a modulation behavior as the pulse delay time is varied. The effect, which arises in a three-level quantum system, is due to the interference of two optically coupled transitions that share a common level. In this article, the three-level echo problem is treated exactly. Wave-function solutions are incorporated that are handled conveniently by a Laplace-transform technique. We, therefore, extend the earlier theory of echo modulation by Lambert et al., by removing their restriction of on-resonance pulse excitation. This procedure allows us to examine the effect of inhomogeneous broadening on echo amplitude explicitly, and we treat the problem by numerical and also by analytical means for the case of a Doppler-broadened gas. Analytic expressions are derived either for a high or a low laser power regime corresponding to excitation of either a large or a small fraction of the Doppler linewidth. The former case is analogous to pulsed nuclear magnetic resonance and is well known, whereas the latter result is new and applies to current photon echo measurements.

Physical Review AMay 1, 197623 citations

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

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

{\mathrm{YAlO}}_{3}

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

. Stark shifts of \ensuremath{\simeq}100 kHz are observed, but the technique is capable of resolutions 10 kHz in some systems.

^{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.

Photon echoes, observed recently in ruby and in

{\mathrm{NH}}_{2}

D gas by two-pulse laser excitation, exhibit a modulation behavior as the pulse delay time is varied. The effect, which arises in a three-level quantum system, is due to the interference of two optically coupled transitions that share a common level. In this article, the three-level echo problem is treated exactly. Wave-function solutions are incorporated that are handled conveniently by a Laplace-transform technique. We, therefore, extend the earlier theory of echo modulation by Lambert et al., by removing their restriction of on-resonance pulse excitation. This procedure allows us to examine the effect of inhomogeneous broadening on echo amplitude explicitly, and we treat the problem by numerical and also by analytical means for the case of a Doppler-broadened gas. Analytic expressions are derived either for a high or a low laser power regime corresponding to excitation of either a large or a small fraction of the Doppler linewidth. The former case is analogous to pulsed nuclear magnetic resonance and is well known, whereas the latter result is new and applies to current photon echo measurements.