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 Pr3+: LaF3 provide the first spin-echo studies of an electronically excited state, and cw resonances yield NMR line centers and shapes with kilohertz precision.
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+: LaF3 at 1.6 K utilizing the 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+: LaF3 hyperfine splittings where the optical heterodyne signals are shot-noise limited. The Pr3+ nuclear quadrupole parameters are obtained for the 3H4 and 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 and 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.
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.
Raman heterodyne detection of nuclear magnetic resonance is a sensitive technique for optical detection of an NMR transition, which is driven by a resonant radio-frequency field. The observed signal is linear in the transition matrix elements of the magnetic resonance transition and two optical transitions. This linearity is the reason that signal contributions from different sites or different rf transitions can interfere, in many cases destructively. In this article, we discuss such an interference effect, which appears to have been overlooked in the past. It occurs between signal contributions that originate from the same magnetic resonance transition of atoms with different positions within the inhomogeneously broadened optical resonance line. These atoms contribute to the coherent Raman scattering through different scattering paths, which involve optical transitions to different nuclear spin states of the same electronic state. We show that the interference between all possible scattering paths leads to complete signal cancellation, if the atoms that are involved in the different scattering paths are equally polarized. To study the effect and to eliminate the interference, we used a pump-and-probe technique with two laser beams. With two independent laser frequencies, it becomes possible to separate the individual scattering paths. We calculate the dependence of the signal on the frequency of both laser beams as well as on the radio frequency and compare the results to experimental data from Pr3+:YAlO3. Our results show that the interference reduces the signal amplitude of the conventional Raman heterodyne experiment but can be eliminated in the new experiment.
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.
Raman-heterodyne-detected multipulse rf nuclear-spin-echo decay of Pr3+ in YAlO3 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.
The recently developed technique of Raman heterodyne detection has unveiled a new interference effect in the Zeeman spectrum of hyperfine transitions of impurity-ion solids. An earlier theory had been developed to explain the basic Raman heterodyne process which involves the resonant interaction of a three-level quantum system with coherent optical-frequency and radiofrequency fields. However, it was not realized that impurity-ion crystals can generate more than one type of Raman heterodyne signal and that these signals can interfere. This article describes two examples of interference where one originates from two or more inequivalent nuclear sites and the other from a single site that exhibits interference among Zeeman transitions. An analytical theory covering these two cases is presented and compared to observations for the impurity-ion crystals Pr3+:YAlO3 and Pr3+:LaF3, the interference behavior in the two being dramatically different.