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Physical Review A

Photon-echo nuclear double resonance and its application in ruby

P. F. Liao, Pan Hu, R. W. Leigh, Sven R. Hartmann

Published Jan 1, 1974• 43 citations
Publisher

Abstract

A photon-echo nuclear double resonance (PENDOR) experiment which detects nuclear magnetic resonances by monitoring the stimulated photon-echo intensity after the application of an rf pulse is described and used to determine the Cr-Al hyperfine and electric-quadrupole interaction parameters associated with the ${\mathrm{Cr}}^{3+}$ ion in the $^{2}E(\overline{E})$ optically excited state in ruby. Most of these parameters are found to be within a few percent of the values associated with ${\mathrm{Cr}}^{3+}$ in the $^{4}A_{2}$ ground state. Resonances are also observed associated with the latter, state, and they are in agreement with previous spin-echo ENDOR work. High resolution is obtained by using a gated cw ruby laser which generates a rapid train of three-pulse stimulated-photon echoes with a long time interval between the second and third excitation pulses. The theoretical behavior of the PENDOR effect is discussed with emphasis on the ability to disentangle complicated multiple overlapping resonances by causing whole sets of resonances to disappear in a controlled way.

DOI
10.1103/physreva.9.332

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Two-pulse photon echo electron-nuclear double resonance (or PENDOR) has been used to measure the second-order hyperfine splittings in the ground state and the lowest component of the excited $^{1}D_{2}$ state of YAl${\mathrm{O}}_{3}$:${\mathrm{Pr}}^{3+}$. The excited-state splittings are 0.923 and 1.565 MHz and are significantly different from previous hole-burning results because of greatly increased resolution. The mechanism for two-pulse PENDOR involves a modulation of the photon echo decay at the rf Rabi frequency. This modulation has been observed directly. A brief theoretical analysis is given which shows that the echo modulation is a result of phase and amplitude changes in the oscillating opitical dipole moment which are indirectly produced by the rf field.

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A novel coherent Raman effect induced by a laser and a radio-frequency (rf) field is used to detect cw and pulsed nuclear magnetic resonance (NMR) in ground and excited electronic states. The effect is illustrated in the impurity-ion solid ${\mathrm{Pr}}^{3+}$: La${\mathrm{F}}_{3}$ at 1.6 K utilizing the ${\mathrm{Pr}}^{3+}$ optical transition $^{3}H_{4}({\ensuremath{\Gamma}}_{1})\ensuremath{\rightarrow}^{1}D_{2}({\ensuremath{\Gamma}}_{1})$. The laser field of frequency ${\ensuremath{\omega}}_{E}$ and the rf field (${\ensuremath{\omega}}_{H}$) induce a light wave at the sum ${\ensuremath{\omega}}_{E}+{\ensuremath{\omega}}_{H}$ (anti-Stokes) and difference ${\ensuremath{\omega}}_{E}\ensuremath{-}{\ensuremath{\omega}}_{H}$ (Stokes) frequencies, generating an absorptive or dispersive heterodyne beat signal (${\ensuremath{\omega}}_{H}$) with the laser field at a photodetector. The theory of this effect is characterized in a new three-level perturbation calculation which requires, unlike the usual stimulated Raman effect, that all three transitions be electric- or magnetic-dipole allowed. Detailed predictions are confirmed by cw measurements of the ${\mathrm{Pr}}^{3+}$: La${\mathrm{F}}_{3}$ hyperfine splittings where the optical heterodyne signals are shot-noise limited. The ${\mathrm{Pr}}^{3+}$ nuclear quadrupole parameters are obtained for the $^{3}H_{4}$ and $^{1}D_{2}$ states where the line centers are determined with kilohertz precision. The corresponding wave functions show significant hyperfine-state mixing, as required for all three transitions to be dipole allowed. The cw line shapes are narrow (30-160 kHz), inhomogeneously broadened by nuclear magnetic interactions, and reveal either a Gaussian or an anomalous second-derivative---like line shape. The spin-echo measurements for the $^{3}H_{4}$ and $^{1}D_{2}$ hyperfine transitions yield homogeneous line shapes which are Lorentzian, and rather surprisingly, linewidths in the narrow range 10-20 kHz, a result which tests current line-broadening theories.

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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.

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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.

Laser Physics Letters•Apr 22, 2008•5 citations
A photon-echo nuclear double resonance (PENDOR) experiment which detects nuclear magnetic resonances by monitoring the stimulated photon-echo intensity after the application of an rf pulse is described and used to determine the Cr-Al hyperfine and electric-quadrupole interaction parameters associated with the Cr3+{\mathrm{Cr}}^{3+}Cr3+ ion in the 2E(E‾)^{2}E(\overline{E})2E(E) optically excited state in ruby. Most of these parameters are found to be within a few percent of the values associated with Cr3+{\mathrm{Cr}}^{3+}Cr3+ in the 4A2^{4}A_{2}4A2​ ground state. Resonances are also observed associated with the latter, state, and they are in agreement with previous spin-echo ENDOR work. High resolution is obtained by using a gated cw ruby laser which generates a rapid train of three-pulse stimulated-photon echoes with a long time interval between the second and third excitation pulses. The theoretical behavior of the PENDOR effect is discussed with emphasis on the ability to disentangle complicated multiple overlapping resonances by causing whole sets of resonances to disappear in a controlled way.
Two-pulse photon echo electron-nuclear double resonance (or PENDOR) has been used to measure the second-order hyperfine splittings in the ground state and the lowest component of the excited 1D2^{1}D_{2}1D2​ state of YAlO3{\mathrm{O}}_{3}O3​:Pr3+{\mathrm{Pr}}^{3+}Pr3+. The excited-state splittings are 0.923 and 1.565 MHz and are significantly different from previous hole-burning results because of greatly increased resolution. The mechanism for two-pulse PENDOR involves a modulation of the photon echo decay at the rf Rabi frequency. This modulation has been observed directly. A brief theoretical analysis is given which shows that the echo modulation is a result of phase and amplitude changes in the oscillating opitical dipole moment which are indirectly produced by the rf field.
A novel coherent Raman effect induced by a laser and a radio-frequency (rf) field is used to detect cw and pulsed nuclear magnetic resonance (NMR) in ground and excited electronic states. The effect is illustrated in the impurity-ion solid Pr3+{\mathrm{Pr}}^{3+}Pr3+: LaF3{\mathrm{F}}_{3}F3​ at 1.6 K utilizing the Pr3+{\mathrm{Pr}}^{3+}Pr3+ optical transition $^{3}H_{4}({\ensuremath{\Gamma}}_{1})\ensuremath{\rightarrow}^{1}D_{2}({\ensuremath{\Gamma}}_{1})$. The laser field of frequency ${\ensuremath{\omega}}_{E}$ and the rf field (${\ensuremath{\omega}}_{H}$) induce a light wave at the sum ${\ensuremath{\omega}}_{E}+{\ensuremath{\omega}}_{H}$ (anti-Stokes) and difference ${\ensuremath{\omega}}_{E}\ensuremath{-}{\ensuremath{\omega}}_{H}$ (Stokes) frequencies, generating an absorptive or dispersive heterodyne beat signal (${\ensuremath{\omega}}_{H}$) with the laser field at a photodetector. The theory of this effect is characterized in a new three-level perturbation calculation which requires, unlike the usual stimulated Raman effect, that all three transitions be electric- or magnetic-dipole allowed. Detailed predictions are confirmed by cw measurements of the Pr3+{\mathrm{Pr}}^{3+}Pr3+: LaF3{\mathrm{F}}_{3}F3​ hyperfine splittings where the optical heterodyne signals are shot-noise limited. The Pr3+{\mathrm{Pr}}^{3+}Pr3+ nuclear quadrupole parameters are obtained for the 3H4^{3}H_{4}3H4​ and 1D2^{1}D_{2}1D2​ states where the line centers are determined with kilohertz precision. The corresponding wave functions show significant hyperfine-state mixing, as required for all three transitions to be dipole allowed. The cw line shapes are narrow (30-160 kHz), inhomogeneously broadened by nuclear magnetic interactions, and reveal either a Gaussian or an anomalous second-derivative---like line shape. The spin-echo measurements for the 3H4^{3}H_{4}3H4​ and 1D2^{1}D_{2}1D2​ hyperfine transitions yield homogeneous line shapes which are Lorentzian, and rather surprisingly, linewidths in the narrow range 10-20 kHz, a result which tests current line-broadening theories.
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.
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 .
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 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.