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

Raman heterodyne detected magnetic resonance of the nitrogen-vacancy centre in diamond

Xing-Fei He

Published Jan 1, 1991• 0 citations
Publisher

Abstract

This thesis describes the Raman heterodyne detection of magnetic resonance in the ³A ground state of the nitrogen-vacancy C'-1· V) centre in diamond. The recently developed theory of Raman heterodyne spectroscopy was tested and compared with the spectra measured on the N-V centre. Among those results, the electron-nuclear double resonance (ENDOR), nuclear-nuclear double resonance (double NMR), Autler-Townes effect, coherence transfer and Zeeman quantum beat were observed for the first time using such techniques. Raman heterodyne techniques were also used to investigate the level anticrossing, hyperfine and nuclear quadrupole interactions, and spin relaxations of the N-V centre with high sensitivity and precision. This thesis is comprised of three parts. Part one includes Chapters 1 to 3, providing introductory accounts. Chapter l is an introduction to the N-V colour centre, which describes the defect configuration, the spin Hamiltonian and the calculations of energy levels and wave functions of the ³A ground state. Chapter 2 briefly describes the theory of Raman heterodyne spectroscopy - a coherent optical radio-frequency (RF) double resonance technique, in particular the Raman heterodyne signals at weak and intense RF fields. Chapter 3 deals with experimental details and techniques utilized in the studies. Part two consists of Chapters 4 and 5, where the Raman heterodyne theory is compared with experimental results. Chapter 4 presents the Raman heterodyne detected nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR) lineshapes compared with theoretical results at various RF power levels, laser intensities and laser frequencies within the 6380A zero-phonon line. The double resonance spectra obtained by Raman heterodyne techniques are discussed in Chapter 5, where attention is paid to the analysis of their spectral profiles depending on the detection scheme. The application of Raman heterodyne techniques to the studies of magnetic resonance of the N-V centre is described in part three, consisting of Chapters 6 to 9. The EPR measurements are described in Chapter 6, which were used to study various interactions near the level anticrossing, in particular the spin alignment. The hyperfine and nuclear quadrupole interactions probed by the NMR, ENDOR and hole burning measurements are described in Chapter 7. From these measurements, the hyperfine and quadrupole parameters in the spin Hamiltonian were fully determined. Chapter 8 deals with the Autler-Townes effect in the NMR and EPR transitions. By measuring the Autler-Townes spittings, the magnitudes of matrix elements of the NMR transitions were examined and compared. Chapter 9 presents the coherent spin transient properties, including nutations, echoes, Zeeman beating and coherence transfer. The dephasing time and homogeneous linewidths of the NMR and EPR transitions were then determined from the echo measurements. Finally, the thesis is summarized in Chapter 10.

DOI
10.25911/5d778571c4730

Related papers

Optical-radio-frequency double-resonance studies of two- and three-level systems

Changjiang Wei

This thesis studies the interaction between two-and three-level systems and strong, coherent radio-frequency (rf) electrom agnetic fields.The investigations were carried out in both the frequency domain, where steady state properties are examined, and the time domain, where transient behaviours are studied.The two-and three-level systems studied arise from the nuclear spin I = 1 triplet within the 3 A ground state of the nitrogen-vacancy (N-V) centre in diamond.The nuclear magnetic resonance (NMR) is detected optically using a coherent optical-rf double resonance Raman heterodyne technique.Owing to the unique features of both the nuclear spin triplet and the detection technique, many interesting experimental results have been obtained.The thesis is comprised of four parts.Part 1 includes Chapters 1 to 3, which provides introductory accounts.The two-level system concept and associated theoretical treatments in the density matrix formalism are introduced in Chapter 1.The theory is given in a very general form and is developed later in relevant chapters for specific situations.Chapter 2 gives an introduction to the N-V centre and its electronic and hyperfine energy levels.The Raman heterodyne technique and the experimental details are described in Chapter 3.In Part 2, consisting of Chapters 4 and 5, the nuclear magnetic transition of interest is characterized.Chapter 4 describes various coherent transient observations including nutation, free-induction-decay (FID), spin echo, spin locking, delayed FID, and rotary echo, from which important parameters such as the transition strength, population decay time T 1? and dephasing time T2 can be deduced.The dependence of these parameters upon the wave function mixing due to the level anti-crossing is discussed in Chapter 5.Part 3 is the most significant part of the thesis and consists of Chapters 6 to 9. In these chapters the interaction of a two-and three-level system with electromagnetic fields are studied in the frequency domain using pump-probe spectroscopy.This technique involves driving the systems with a strong (pump) field and monitoring it with a separate (probe) field.The absorption and dispersion profiles of a driven two-level system probed by a weak field are discussed in Chapter 6. Topics include the dynamic "Stark" effect and amplification without inversion.When the probe intensity is increased from weak to strong, multiphoton transitions and multiphoton gain without inversion are observed.These effects are described in Chapter 7. When the pump and probe fields interact separately with two transitions which share one common level the two-level system is extended to a three-level one.The power broadening of the Autler-Townes spectrum in such a three-level system is the topic presented in Chapter 8. Chapter 9 considers the case where there are two strong fields and a weak probe field.The discussion is in terms of the dressed state picture and it is shown that the dressed state can be also dressed.Experimental results of the transient nutation in dressed states are presented in part 4 which consists of Chapter 10.The dressed states transition strength is determined for the first time experimentally.Finally, Chapter 11 presents a summary of this thesis.

•Jan 1, 1994•1 citation

Paramagnetic resonance of photoexcited N-Vdefects in diamond. I. Level anticrossing in the 3 Aground state

Xing-Fei He, Neil B. Manson, Peter Fisk

Raman-heterodyne-detected paramagnetic resonance has been used to study the level anticrossing in the $^{3}$A state of the N-V defect in diamond. The electron-paramagnetic-resonance (EPR) frequencies are well accounted for by a triplet-spin Hamiltonian. Comparison of the EPR spectra with the calculated transition dipole strengths indicates that optical pumping determines, to a large extent, the Raman-heterodyne-signal intensity. Spin alignment in the $^{3}$A ground state under optical pumping leads to the collapse of the EPR signal at the level anticrossing, where the population is equalized due to the mixing of the spin states. This is substantiated by transient nutation and spin-echo measurements, from which the dipole moment and dephasing time are examined. Laser detuning within the 638-nm zero-phonon line shows that the Raman signal is only detectable when the laser frequency is tuned to the low-energy part of the optical line.

Physical review. B, Condensed matter•Apr 1, 1993•88 citations

Autler–Townes effect of the photoexcited diamond nitrogen-vacancy center in its triplet ground state

Xing-Fei He, Peter Fisk, Neil B. Manson

The Autler–Townes effect in nuclear magnetic resonance (NMR) and electron paramagnetic resonance has been observed using recently developed Raman heterodyne techniques. The measurements were carried out on the nitrogen-vacancy color center in diamond, where the 3A↔3E optical transition was driven by a single mode dye laser at 638 nm while the magnetic transitions in the 3A ground state were driven by two rf fields. The measured splittings in the NMR lines were found to be in good agreement with theoretical predictions. Using the Autler–Townes effect, the magnitude of the dipole moments of the mI=0↔±1 (mS=0) transitions in the ground state was determined, and found to be the same. Comparison of this latter result with the NMR spectra shows that Raman heterodyne signal intensities are determined by population factors.

Journal of Applied Physics•Jul 1, 1992•31 citations

Raman heterodyne detection of electron paramagnetic resonance

Keith Holliday, X.-F. He, Peter Fisk +1 more

We report the detection of an electron paramagnetic resonance signal using Raman heterodyne spectroscopy, a rf -optical double-resonance technique. The signals are associated with the nitrogen-vacancy center in diamond, which has a spin-triplet ground state. A three-line spectrum associated with the nitrogen hyperfine structure is observed for various magnetic field strengths and crystal orientations.

Optics Letters•Apr 1, 1990•34 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.

•Jan 1, 1995•0 citations

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.

Physical review. B, Condensed matter•Nov 1, 1983•110 citations
This thesis describes the Raman heterodyne detection of magnetic resonance in the ³A ground state of the nitrogen-vacancy C'-1· V) centre in diamond. The recently developed theory of Raman heterodyne spectroscopy was tested and compared with the spectra measured on the N-V centre. Among those results, the electron-nuclear double resonance (ENDOR), nuclear-nuclear double resonance (double NMR), Autler-Townes effect, coherence transfer and Zeeman quantum beat were observed for the first time using such techniques. Raman heterodyne techniques were also used to investigate the level anticrossing, hyperfine and nuclear quadrupole interactions, and spin relaxations of the N-V centre with high sensitivity and precision. This thesis is comprised of three parts. Part one includes Chapters 1 to 3, providing introductory accounts. Chapter l is an introduction to the N-V colour centre, which describes the defect configuration, the spin Hamiltonian and the calculations of energy levels and wave functions of the ³A ground state. Chapter 2 briefly describes the theory of Raman heterodyne spectroscopy - a coherent optical radio-frequency (RF) double resonance technique, in particular the Raman heterodyne signals at weak and intense RF fields. Chapter 3 deals with experimental details and techniques utilized in the studies. Part two consists of Chapters 4 and 5, where the Raman heterodyne theory is compared with experimental results. Chapter 4 presents the Raman heterodyne detected nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR) lineshapes compared with theoretical results at various RF power levels, laser intensities and laser frequencies within the 6380A zero-phonon line. The double resonance spectra obtained by Raman heterodyne techniques are discussed in Chapter 5, where attention is paid to the analysis of their spectral profiles depending on the detection scheme. The application of Raman heterodyne techniques to the studies of magnetic resonance of the N-V centre is described in part three, consisting of Chapters 6 to 9. The EPR measurements are described in Chapter 6, which were used to study various interactions near the level anticrossing, in particular the spin alignment. The hyperfine and nuclear quadrupole interactions probed by the NMR, ENDOR and hole burning measurements are described in Chapter 7. From these measurements, the hyperfine and quadrupole parameters in the spin Hamiltonian were fully determined. Chapter 8 deals with the Autler-Townes effect in the NMR and EPR transitions. By measuring the Autler-Townes spittings, the magnitudes of matrix elements of the NMR transitions were examined and compared. Chapter 9 presents the coherent spin transient properties, including nutations, echoes, Zeeman beating and coherence transfer. The dephasing time and homogeneous linewidths of the NMR and EPR transitions were then determined from the echo measurements. Finally, the thesis is summarized in Chapter 10.
This thesis studies the interaction between two-and three-level systems and strong, coherent radio-frequency (rf) electrom agnetic fields.The investigations were carried out in both the frequency domain, where steady state properties are examined, and the time domain, where transient behaviours are studied.The two-and three-level systems studied arise from the nuclear spin I = 1 triplet within the 3 A ground state of the nitrogen-vacancy (N-V) centre in diamond.The nuclear magnetic resonance (NMR) is detected optically using a coherent optical-rf double resonance Raman heterodyne technique.Owing to the unique features of both the nuclear spin triplet and the detection technique, many interesting experimental results have been obtained.The thesis is comprised of four parts.Part 1 includes Chapters 1 to 3, which provides introductory accounts.The two-level system concept and associated theoretical treatments in the density matrix formalism are introduced in Chapter 1.The theory is given in a very general form and is developed later in relevant chapters for specific situations.Chapter 2 gives an introduction to the N-V centre and its electronic and hyperfine energy levels.The Raman heterodyne technique and the experimental details are described in Chapter 3.In Part 2, consisting of Chapters 4 and 5, the nuclear magnetic transition of interest is characterized.Chapter 4 describes various coherent transient observations including nutation, free-induction-decay (FID), spin echo, spin locking, delayed FID, and rotary echo, from which important parameters such as the transition strength, population decay time T 1? and dephasing time T2 can be deduced.The dependence of these parameters upon the wave function mixing due to the level anti-crossing is discussed in Chapter 5.Part 3 is the most significant part of the thesis and consists of Chapters 6 to 9. In these chapters the interaction of a two-and three-level system with electromagnetic fields are studied in the frequency domain using pump-probe spectroscopy.This technique involves driving the systems with a strong (pump) field and monitoring it with a separate (probe) field.The absorption and dispersion profiles of a driven two-level system probed by a weak field are discussed in Chapter 6. Topics include the dynamic "Stark" effect and amplification without inversion.When the probe intensity is increased from weak to strong, multiphoton transitions and multiphoton gain without inversion are observed.These effects are described in Chapter 7. When the pump and probe fields interact separately with two transitions which share one common level the two-level system is extended to a three-level one.The power broadening of the Autler-Townes spectrum in such a three-level system is the topic presented in Chapter 8. Chapter 9 considers the case where there are two strong fields and a weak probe field.The discussion is in terms of the dressed state picture and it is shown that the dressed state can be also dressed.Experimental results of the transient nutation in dressed states are presented in part 4 which consists of Chapter 10.The dressed states transition strength is determined for the first time experimentally.Finally, Chapter 11 presents a summary of this thesis.
Raman-heterodyne-detected paramagnetic resonance has been used to study the level anticrossing in the 3^{3}3A state of the N-V defect in diamond. The electron-paramagnetic-resonance (EPR) frequencies are well accounted for by a triplet-spin Hamiltonian. Comparison of the EPR spectra with the calculated transition dipole strengths indicates that optical pumping determines, to a large extent, the Raman-heterodyne-signal intensity. Spin alignment in the 3^{3}3A ground state under optical pumping leads to the collapse of the EPR signal at the level anticrossing, where the population is equalized due to the mixing of the spin states. This is substantiated by transient nutation and spin-echo measurements, from which the dipole moment and dephasing time are examined. Laser detuning within the 638-nm zero-phonon line shows that the Raman signal is only detectable when the laser frequency is tuned to the low-energy part of the optical line.
The Autler–Townes effect in nuclear magnetic resonance (NMR) and electron paramagnetic resonance has been observed using recently developed Raman heterodyne techniques. The measurements were carried out on the nitrogen-vacancy color center in diamond, where the 3A↔3E optical transition was driven by a single mode dye laser at 638 nm while the magnetic transitions in the 3A ground state were driven by two rf fields. The measured splittings in the NMR lines were found to be in good agreement with theoretical predictions. Using the Autler–Townes effect, the magnitude of the dipole moments of the mI=0↔±1 (mS=0) transitions in the ground state was determined, and found to be the same. Comparison of this latter result with the NMR spectra shows that Raman heterodyne signal intensities are determined by population factors.
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.
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.