Physical review. B, Condensed matter

Optical-pumping effects on Raman-heterodyne-detected multipulse rf nuclear-spin-echo decay

L. E. Erickson

Published Sep 1, 1990• 15 citations

Abstract

Raman-heterodyne-detected multipulse rf nuclear-spin-echo decay of ${\mathrm{Pr}}^{3+}$ in ${\mathrm{YAlO}}_{3}$ is measured with continuous-detection light throughout the spin-locking pulse train and with the light on during a short period centered at the echo time only for every sixth echo. The echo decay shows three components: an initial fast decay (\ensuremath{\simeq}400 \ensuremath{\mu}s), an intermediate decay (5.4\ifmmode\pm\else\textpm\fi{}0.6 ms), and a slower decay of 22.5\ifmmode\pm\else\textpm\fi{}1.7 ms for gated echoes. For cw light, the decay is described by the same initial fast decay, but a single decay at 7.6\ifmmode\pm\else\textpm\fi{}0.6 ms is observed at longer times. The difference in the observed echo decay is attributed to optical pumping effects. A rate-equation model is constructed, consisting of three ground-state levels and three excited-state levels. It includes radiative decay, spin-lattice relaxation, the optical pumping and rf pulses, and rf coherence loss due to excited-state occupancy. The model shows three decay times, fast (\ensuremath{\simeq}400 \ensuremath{\mu}s), intermediate (6.08\ifmmode\pm\else\textpm\fi{}0.07 ms), and slow (21.0\ifmmode\pm\else\textpm\fi{}0.1 ms) decay for gated echoes. The last two rates are affected by the strength and duration of the optical field. For continuous light, the calculated echo is seen to decay at \ensuremath{\simeq}400 \ensuremath{\mu}s, 2.04\ifmmode\pm\else\textpm\fi{}0.07 ms, and 3.43\ifmmode\pm\else\textpm\fi{}0.02 ms and then increases at a much slower rate (100 ms). This is only an apparent increase, because significant signal cancellation occurs in the sum of the six ion groups contributing to the signal. If a reduced light level and faster spin-lattice relaxation rates are assumed, the calculated echo-decay times for cw light are 2.44\ifmmode\pm\else\textpm\fi{}0.03 and 7.37\ifmmode\pm\else\textpm\fi{}0.04 ms. This corresponds to a homogeneous linewidth increase of 2.5 times and a spin-lattice relaxation rate increase of 2.5 times equivalent to crystal heating by the cw detecting light of 0.35 K over that of the gated light.

DOI: 10.1103/physrevb.42.3789

Related papers

Raman heterodyne detection of nuclear magnetic resonance

N. C. Wong, Emily S. Kintzer, J. Mlynek +2 more

Physical review. B, Condensed matterNov 1, 1983110 citations

Coherent raman scattering for optical detection of NMR in Pr³⁺:YAIO₃

Tilo Blasberg

Jan 1, 19950 citations

Raman Heterodyne Detection of Nuclear Magnetic Resonance

J. Mlynek, N. C. Wong, Ralph G. DeVoe +2 more

Physical Review LettersMar 28, 1983154 citations

Optically Detected Coherent Transients in Nuclear Hyperfine Levels

Robert M. Shelby, Constantino S. Yannoni, R. M. Macfarlane

Physical Review LettersDec 18, 197891 citations

All-optical measurement of nuclear-spin relaxation

Robert Klieber, Andreas Michalowski, Rudolf Neuhaus +1 more

Physical review. B, Condensed matterAug 26, 20035 citations

Spectroscopic and relaxation character of the P03−H43 transition in La F3 : Pr3+ measured by photon echoes

Y.C. Chen, Kophu P. Chiang, Sven R. Hartmann

Physical review. B, Condensed matterJan 1, 198064 citations

Physical review. B, Condensed matter

Optical-pumping effects on Raman-heterodyne-detected multipulse rf nuclear-spin-echo decay

L. E. Erickson

Published Sep 1, 1990• 15 citations

Publisher

Abstract

Raman-heterodyne-detected multipulse rf nuclear-spin-echo decay of

{\mathrm{Pr}}^{3+}

{\mathrm{YAlO}}_{3}

is measured with continuous-detection light throughout the spin-locking pulse train and with the light on during a short period centered at the echo time only for every sixth echo. The echo decay shows three components: an initial fast decay (\ensuremath{\simeq}400 \ensuremath{\mu}s), an intermediate decay (5.4\ifmmode\pm\else\textpm\fi{}0.6 ms), and a slower decay of 22.5\ifmmode\pm\else\textpm\fi{}1.7 ms for gated echoes. For cw light, the decay is described by the same initial fast decay, but a single decay at 7.6\ifmmode\pm\else\textpm\fi{}0.6 ms is observed at longer times. The difference in the observed echo decay is attributed to optical pumping effects. A rate-equation model is constructed, consisting of three ground-state levels and three excited-state levels. It includes radiative decay, spin-lattice relaxation, the optical pumping and rf pulses, and rf coherence loss due to excited-state occupancy. The model shows three decay times, fast (\ensuremath{\simeq}400 \ensuremath{\mu}s), intermediate (6.08\ifmmode\pm\else\textpm\fi{}0.07 ms), and slow (21.0\ifmmode\pm\else\textpm\fi{}0.1 ms) decay for gated echoes. The last two rates are affected by the strength and duration of the optical field. For continuous light, the calculated echo is seen to decay at \ensuremath{\simeq}400 \ensuremath{\mu}s, 2.04\ifmmode\pm\else\textpm\fi{}0.07 ms, and 3.43\ifmmode\pm\else\textpm\fi{}0.02 ms and then increases at a much slower rate (100 ms). This is only an apparent increase, because significant signal cancellation occurs in the sum of the six ion groups contributing to the signal. If a reduced light level and faster spin-lattice relaxation rates are assumed, the calculated echo-decay times for cw light are 2.44\ifmmode\pm\else\textpm\fi{}0.03 and 7.37\ifmmode\pm\else\textpm\fi{}0.04 ms. This corresponds to a homogeneous linewidth increase of 2.5 times and a spin-lattice relaxation rate increase of 2.5 times equivalent to crystal heating by the cw detecting light of 0.35 K over that of the gated light.

DOI: 10.1103/physrevb.42.3789

Related papers

Raman heterodyne detection of nuclear magnetic resonance

N. C. Wong, Emily S. Kintzer, J. Mlynek +2 more

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.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.

Physical review. B, Condensed matterNov 1, 1983110 citations

Coherent raman scattering for optical detection of NMR in Pr³⁺:YAIO₃

Tilo Blasberg

T. Blasberg: Coherent Raman scattering for optical detecti¬ on of NMR in Pr3+:YA103. Nuclear magnetic resonance (NMR) is a powerful and versatile spec¬ troscopic technique. However, conventional NMR requires samples, which has to consist of at least 1017 nuclear spins. One of the most promising approaches to increase the sensitivity of this method relies on the resonant interaction of laser fields with atoms. The main goal of this thesis was the investigation and the improvement of coherent Raman scattering techniques for an optical heterodyne detection of NMR. All ex¬ periments were performed at cryogenic temperatures on Pr3+-ions, which were added to the host lattice YAIO3 (YAP). The coherent Raman scattering experiments consist of two distinct stages: firstly, the transient or continuous excitation of a coherent superposition between two nuclear spin states and secondly, its optical detection through coherent Raman scattering of a resonant, frequency-tunable test laser field from this sublevel coherence. For the theoretical description of the experiments, coherent Raman scattering in multilevel atoms is discussed in detail and a common solution for the Raman heterodyne beat signal in pump-and-probe experiments is derived. The dynamics of a three-level atom that interacts with two resonant electromagnetic fields is treated making use of the density-matrix formalism. The method of Raman heterodyne detection of NMR uses a resonant radio frequency field to drive the magnetic-dipole transition between two nuclear spin states. This technique was used to determine the orientation of the nuclear quadrupole tensors of Pr3+ at its two non-equivalent lattice sites in YAP by measuring the dependence of the transition frequencies on the orientation of an external magnetic field. In the electronic ground state 3H4, the quantization axes of the nuclear spin eigenfunctions are ro¬ tated by po=±56.4° relative to the crystal b-axis. The corresponding rota¬ tion angle in the electronically excited state !D2 is Po=±105.2°. With this new value for the relative orientation of the quantization axes in both electronic states, the relative strengths of all 3H4 1D2 transitions could be calculated. The different orientation of the quantization axes in the two electronic states gives rise to a strong state mixing of the nuclear spin eigenfunctions and is the reason, why most of the optical transitions be¬ tween nuclear spin substates of different electronic states have similar oscillator strengths. Pr:YAP is therefore an ideal model system for the investigation of coherent Raman scattering. A new rf-optical triple-resonance experiment was developed that is a combination of Raman heterodyne detection of NMR and spectral holeburning. This technique allows the unambiguous determination of the ab¬ solute sign of nuclear quadrupole coupling constants. In the electronic ground state of PnYAP, the quadrupole coupling constant was found to be negative (D=-3.5289 MHz) being the result of dominant pseudoquadrupole contributions. The pump-and-probe technique, which uses a frequency-tunable test laser beam, was used to investigate the influence of an inhomogeneous broadening of the optical resonance line on Raman heterodyne detection of NMR. A hitherto unknown interference effect could be predicted and verified by the experiments. A prerequisite for this interference effect is that coherent Raman scattering in different opti¬ cal transitions can contribute to the total Raman heterodyne beat signal. These optical transitions represent different 'scattering pathways', whose contributions to the total beat signal can interfere destructively with each other, since the heterodyne beat signal depends linearly on the relevant transition matrix elements. The rf-optical triple resonance technique al¬ lows to circumvent this interference effect, since the frequency-tunable test laser field can be used to select only one of the various scattering pathways. A new and efficient excitation scheme was developed, which allows the observation of coherent Raman beats in systems with arbitrary wide sublevel spectra and small oscillator strengths. The method utilizes a bichromatic laser field for the purely optical excitation of a coherent superposition between two nuclear spin substates. For the preparation of the sublevel coherence, the two frequency components couple two different nuclear spin substates of the same electronic state to a different electronic state. With the help of the density-matrix formalism, the dyna¬ mics of a three-level atom during the bichromatic excitation were calcu¬ lated. Those experimental parameters could be identified that determine the excitation efficiency. While in the purely optical method of coherent Raman beats almost 10_1 of the incident test laser photons were coherent¬ ly Raman scattered, the corresponding figure of merit of Raman hetero¬ dyne detection of NMR was less man 10-3. From the decay of hole-burning spectra in the presence of a saturating rf-field the temperature-dependence of the nuclear spin relaxation rates of Pr:YAP was determined in the temperature range 3-9 K. At low tem¬ peratures, the relaxation is dominated by mutual spin flips whereas at higher temperatures Orbach and Raman relaxation become of importan¬ ce. A simple rate-equation model allowed to calculate the entire hole-bur¬ ning spectrum of the crystal.T. Blasberg: Coherent Raman scattering for optical detecti¬ on of NMR in Pr3+:YA103. Nuclear magnetic resonance (NMR) is a powerful and versatile spec¬ troscopic technique. However, conventional NMR requires samples, which has to consist of at least 1017 nuclear spins. One of the most promising approaches to increase the sensitivity of this method relies on the resonant interaction of laser fields with atoms. The main goal of this thesis was the investigation and the improvement of coherent Raman scattering techniques for an optical heterodyne detection of NMR. All ex¬ periments were performed at cryogenic temperatures on Pr3+-ions, which were added to the host lattice YAIO3 (YAP). The coherent Raman scattering experiments consist of two distinct stages: firstly, the transient or continuous excitation of a coherent superposition between two nuclear spin states and secondly, its optical detection through coherent Raman scattering of a resonant, frequency-tunable test laser field from this sublevel coherence. For the theoretical description of the experiments, coherent Raman scattering in multilevel atoms is discussed in detail and a common solution for the Raman heterodyne beat signal in pump-and-probe experiments is derived. The dynamics of a three-level atom that interacts with two resonant electromagnetic fields is treated making use of the density-matrix formalism. The method of Raman heterodyne detection of NMR uses a resonant radio frequency field to drive the magnetic-dipole transition between two nuclear spin states. This technique was used to determine the orientation of the nuclear quadrupole tensors of Pr3+ at its two non-equivalent lattice sites in YAP by measuring the dependence of the transition frequencies on the orientation of an external magnetic field. In the electronic ground state 3H4, the quantization axes of the nuclear spin eigenfunctions are ro¬ tated by po=±56.4° relative to the crystal b-axis. The corresponding rota¬ tion angle in the electronically excited state !D2 is Po=±105.2°. With this new value for the relative orientation of the quantization axes in both electronic states, the relative strengths of all 3H4 1D2 transitions could be calculated. The different orientation of the quantization axes in the two electronic states gives rise to a strong state mixing of the nuclear spin eigenfunctions and is the reason, why most of the optical transitions be¬ tween nuclear spin substates of different electronic states have similar oscillator strengths. Pr:YAP is therefore an ideal model system for the investigation of coherent Raman scattering. A new rf-optical triple-resonance experiment was developed that is a combination of Raman heterodyne detection of NMR and spectral holeburning. This technique allows the unambiguous determination of the ab¬ solute sign of nuclear quadrupole coupling constants. In the electronic ground state of PnYAP, the quadrupole coupling constant was found to be negative (D=-3.5289 MHz) being the result of dominant pseudoquadrupole contributions. The pump-and-probe technique, which uses a frequency-tunable test laser beam, was used to investigate the influence of an inhomogeneous broadening of the optical resonance line on Raman heterodyne detection of NMR. A hitherto unknown interference effect could be predicted and verified by the experiments. A prerequisite for this interference effect is that coherent Raman scattering in different opti¬ cal transitions can contribute to the total Raman heterodyne beat signal. These optical transitions represent different 'scattering pathways', whose contributions to the total beat signal can interfere destructively with each other, since the heterodyne beat signal depends linearly on the relevant transition matrix elements. The rf-optical triple resonance technique al¬ lows to circumvent this interference effect, since the frequency-tunable test laser field can be used to select only one of the various scattering pathways. A new and efficient excitation scheme was developed, which allows the observation of coherent Raman beats in systems with arbitrary wide sublevel spectra and small oscillator strengths. The method utilizes a bichromatic laser field for the purely optical excitation of a coherent superposition between two nuclear spin substates. For the preparation of the sublevel coherence, the two frequency components couple two different nuclear spin substates of the same electronic state to a different electronic state. With the help of the density-matrix formalism, the dyna¬ mics of a three-level atom during the bichromatic excitation were calcu¬ lated. Those experimental parameters could be identified that determine the excitation efficiency. While in the purely optical method of coherent Raman beats almost 10_1 of the incident test laser photons were coherent¬ ly Raman scattered, the corresponding figure of merit of Raman hetero¬ dyne detection of NMR was less man 10-3. From the decay of hole-burning spectra in the presence of a saturating rf-field the temperature-dependence of the nuclear spin relaxation rates of Pr:YAP was determined in the temperature range 3-9 K. At low tem¬ peratures, the relaxation is dominated by mutual spin flips whereas at higher temperatures Orbach and Raman relaxation become of importan¬ ce. A simple rate-equation model allowed to calculate the entire hole-bur¬ ning spectrum of the crystal.

Jan 1, 19950 citations

Raman Heterodyne Detection of Nuclear Magnetic Resonance

J. Mlynek, N. C. Wong, Ralph G. DeVoe +2 more

An optical heterodyne technique based on the coherent Raman effect is demonstrated for detecting nuclear magnetic resonances (NMR) and coherent spin transients in normal and optically excited impurity-ion solids at low temperature. Initial measurements on ${\mathrm{Pr}}^{3+}$ : La ${\mathrm{F}}_{3}$ provide the first spin-echo studies of an electronically excited state, and cw resonances yield NMR line centers and shapes with kilohertz precision.An optical heterodyne technique based on the coherent Raman effect is demonstrated for detecting nuclear magnetic resonances (NMR) and coherent spin transients in normal and optically excited impurity-ion solids at low temperature. Initial measurements on ${\mathrm{Pr}}^{3+}$: La${\mathrm{F}}_{3}$ provide the first spin-echo studies of an electronically excited state, and cw resonances yield NMR line centers and shapes with kilohertz precision.

Physical Review LettersMar 28, 1983154 citations

Optically Detected Coherent Transients in Nuclear Hyperfine Levels

Robert M. Shelby, Constantino S. Yannoni, R. M. Macfarlane

Using optical detection, we have observed rf nutation, free-induction decay, and echoes, on the 16.70-MHz nuclear hyperfine transition of dilute ${\mathrm{Pr}}^{3+}$ in La ${\mathrm{F}}_{3}$ at 2 K. From a comparison of free-induction decay and echo decay we find that the previously observed linewidth of 200 kHz is inhomogeneous and that the homogeneous width is 19 kHz. On the basis of these measurements it is suggested that optical dephasing times for the $^{1}D_{2}\ensuremath{\leftrightarrow}^{3}H_{4}$ and $^{3}P_{0}\ensuremath{\leftrightarrow}^{3}H_{4}$ transitions are as long as \ensuremath{\sim}20 \ensuremath{\mu} sec.Using optical detection, we have observed rf nutation, free-induction decay, and echoes, on the 16.70-MHz nuclear hyperfine transition of dilute ${\mathrm{Pr}}^{3+}$ in La${\mathrm{F}}_{3}$ at 2 K. From a comparison of free-induction decay and echo decay we find that the previously observed linewidth of 200 kHz is inhomogeneous and that the homogeneous width is 19 kHz. On the basis of these measurements it is suggested that optical dephasing times for the $^{1}D_{2}\ensuremath{\leftrightarrow}^{3}H_{4}$ and $^{3}P_{0}\ensuremath{\leftrightarrow}^{3}H_{4}$ transitions are as long as \ensuremath{\sim}20 \ensuremath{\mu} sec.

Physical Review LettersDec 18, 197891 citations

All-optical measurement of nuclear-spin relaxation

Robert Klieber, Andreas Michalowski, Rudolf Neuhaus +1 more

Nuclear-spin relaxation rates are usually measured by pulsed radio frequency excitation of nuclear-spin transitions. When the number of spins is too small for direct detection with conventional nuclear-magnetic-resonance spectrometers, pulsed excitation may be combined with optical detection of the nuclear spins for increased sensitivity. Here we demonstrate that such measurements can also be done purely optically, without radio frequency fields. This is achieved by preparing nonthermal populations by optical hole-burning and time-resolved probing of the populations as a function of the decay time. Measurements of the nuclear-spin relaxation of ${}^{141}\mathrm{Pr}$ in the electronic ground state of ${\mathrm{Pr}}^{3+}:{\mathrm{YAlO}}_{3}$ show that the relaxation rates for the three transitions differ by a factor of 3.Nuclear-spin relaxation rates are usually measured by pulsed radio frequency excitation of nuclear-spin transitions. When the number of spins is too small for direct detection with conventional nuclear-magnetic-resonance spectrometers, pulsed excitation may be combined with optical detection of the nuclear spins for increased sensitivity. Here we demonstrate that such measurements can also be done purely optically, without radio frequency fields. This is achieved by preparing nonthermal populations by optical hole-burning and time-resolved probing of the populations as a function of the decay time. Measurements of the nuclear-spin relaxation of ${}^{141}\mathrm{Pr}$ in the electronic ground state of ${\mathrm{Pr}}^{3+}:{\mathrm{YAlO}}_{3}$ show that the relaxation rates for the three transitions differ by a factor of 3.

Physical review. B, Condensed matterAug 26, 20035 citations

Spectroscopic and relaxation character of the P03−H43 transition in La F3 : Pr3+ measured by photon echoes

Y.C. Chen, Kophu P. Chiang, Sven R. Hartmann

The hyperfine structure and relaxation character of the terminal levels of the $^{3}P_{0}\ensuremath{-}^{3}H_{4}$ (4777 \AA{}) transition in La ${\mathrm{F}}_{3}$ : ${\mathrm{Pr}}^{3+}$ (0.03 at.%) were studied using the photon-echo technique. Using two independent nitrogen-laser pumped dye lasers we have observed modulated photon echoes for pulse separations over a \ensuremath{\sim}10-\ensuremath{\mu}sec range. In this interval our modulated photon echoes decay in a simple exponential manner by a factor of ${10}^{5}$ and yield a homogeneous linewidth of 70 kHz [full width at half maximum (FWHM)]. Fourier transformation of the echo-modulation data yields directly the nuclear level splittings and their associated linewidths in the $^{3}P_{0}$ and $^{3}H_{4}$ states. In the $^{3}P_{0}(^{3}H_{4})$ state the nuclear splittings are 0.73 and 1.12 MHz (8.48 and 16.68 MHz). The measurements for the nuclear level splittings and associated linewidths in the $^{3}H_{4}$ state are in excellent agreement with those obtained from the optical-rf double-resonance experiments of Erickson. We find that the calculated echo modulation is a sensitive function of the relative orientation of the principal axes associated with the ground-and excited-state Hamiltonians. By comparing our experimental and calculated echo-modulation patterns we are able to determine their relative orientations.The hyperfine structure and relaxation character of the terminal levels of the $^{3}P_{0}\ensuremath{-}^{3}H_{4}$ (4777 \AA{}) transition in La${\mathrm{F}}_{3}$: ${\mathrm{Pr}}^{3+}$ (0.03 at.%) were studied using the photon-echo technique. Using two independent nitrogen-laser pumped dye lasers we have observed modulated photon echoes for pulse separations over a \ensuremath{\sim}10-\ensuremath{\mu}sec range. In this interval our modulated photon echoes decay in a simple exponential manner by a factor of ${10}^{5}$ and yield a homogeneous linewidth of 70 kHz [full width at half maximum (FWHM)]. Fourier transformation of the echo-modulation data yields directly the nuclear level splittings and their associated linewidths in the $^{3}P_{0}$ and $^{3}H_{4}$ states. In the $^{3}P_{0}(^{3}H_{4})$ state the nuclear splittings are 0.73 and 1.12 MHz (8.48 and 16.68 MHz). The measurements for the nuclear level splittings and associated linewidths in the $^{3}H_{4}$ state are in excellent agreement with those obtained from the optical-rf double-resonance experiments of Erickson. We find that the calculated echo modulation is a sensitive function of the relative orientation of the principal axes associated with the ground-and excited-state Hamiltonians. By comparing our experimental and calculated echo-modulation patterns we are able to determine their relative orientations.

Physical review. B, Condensed matterJan 1, 198064 citations

Raman-heterodyne-detected multipulse rf nuclear-spin-echo decay of

{\mathrm{Pr}}^{3+}

{\mathrm{YAlO}}_{3}

{\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.

{\mathrm{Pr}}^{3+}

: La

{\mathrm{F}}_{3}

provide the first spin-echo studies of an electronically excited state, and cw resonances yield NMR line centers and shapes with kilohertz precision.

Using optical detection, we have observed rf nutation, free-induction decay, and echoes, on the 16.70-MHz nuclear hyperfine transition of dilute

{\mathrm{Pr}}^{3+}

in La

{\mathrm{F}}_{3}

at 2 K. From a comparison of free-induction decay and echo decay we find that the previously observed linewidth of 200 kHz is inhomogeneous and that the homogeneous width is 19 kHz. On the basis of these measurements it is suggested that optical dephasing times for the $^{1}D_{2}\ensuremath{\leftrightarrow}^{3}H_{4}$ and $^{3}P_{0}\ensuremath{\leftrightarrow}^{3}H_{4}$ transitions are as long as \ensuremath{\sim}20 \ensuremath{\mu} sec.

{}^{141}\mathrm{Pr}

in the electronic ground state of

{\mathrm{Pr}}^{3+}:{\mathrm{YAlO}}_{3}

show that the relaxation rates for the three transitions differ by a factor of 3.

The hyperfine structure and relaxation character of the terminal levels of the $^{3}P_{0}\ensuremath{-}^{3}H_{4}$ (4777 \AA{}) transition in La

{\mathrm{F}}_{3}

{\mathrm{Pr}}^{3+}

(0.03 at.%) were studied using the photon-echo technique. Using two independent nitrogen-laser pumped dye lasers we have observed modulated photon echoes for pulse separations over a \ensuremath{\sim}10-\ensuremath{\mu}sec range. In this interval our modulated photon echoes decay in a simple exponential manner by a factor of

{10}^{5}

and yield a homogeneous linewidth of 70 kHz [full width at half maximum (FWHM)]. Fourier transformation of the echo-modulation data yields directly the nuclear level splittings and their associated linewidths in the

^{3}P_{0}

and

^{3}H_{4}

states. In the

^{3}P_{0}(^{3}H_{4})

state the nuclear splittings are 0.73 and 1.12 MHz (8.48 and 16.68 MHz). The measurements for the nuclear level splittings and associated linewidths in the

^{3}H_{4}

state are in excellent agreement with those obtained from the optical-rf double-resonance experiments of Erickson. We find that the calculated echo modulation is a sensitive function of the relative orientation of the principal axes associated with the ground-and excited-state Hamiltonians. By comparing our experimental and calculated echo-modulation patterns we are able to determine their relative orientations.