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 141Pr in the electronic ground state of Pr3+:YAlO3 show that the relaxation rates for the three transitions differ by a factor of 3.
Early in the study of nuclear magnetic resonance, it was recognized that coherent transient signals could possess shapes highly correlated with the radio frequency pulses used to generate them.1 Similar results were observed in the case of optical coherent transients.2 The information necessary to recreate the excitation pulse shapes has traditionally been seen to reside in the polarization of the sample or in the population difference between two energy states. Information so stored is constrained to relax at rates determined by the transverse T2 or the longitudinal T1, relaxation times of the excited nuclear or optical transition. Owing to the shortness of T1 and T2, coherent transient pulse shape storage has been viewed previously as having limited utility.
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 goal of this project was to improve our control over nuclear spins in the solid state, and to extend this control to coupled electron-nuclear spins. Our key results are summarized below. 1. We extended the control techniques developed in liquid state NMR quantum information processing to the control of a three-qubit solid state NMR quantum information processor. 2. To explore multi-body spin dynamics and their sensitivity to decoherence, we have measured the decay of NMR multiple quantum coherence intensities in the presence and absence of the dipolar Hamiltonian, in a cubic and a one-dimensional spin system. 3. We also studied the transport of polarization in the one-dimensional fluoroapatite system, both experimentally and theoretically, and created special states in which the polarization is localized to the ends of the chain. This enables both universal Quantum Computing and Quantum Simulation in 1-D systems. 4. We devised a novel scheme for electron-nuclear quantum information processing that exploits the anisotropic hyperfine coupling. This scheme enables universal control over a 1-electron, N-nuclear spin system, addressing only a single electron spin transition. Not having to address the nuclear spins directly significantly speeds up the control. We designed and fabricated a pulsed electron spin resonance spectrometer, along with a cryogenic probe which we used to experimentally implement this scheme on a single crystal sample of irradiated malonic acid. 5. We demonstrated the role of nuclear spin dipolar diffusion in dynamic nuclear polarization (DNP) experiments, in dielectric samples with abundant nuclear spins. We achieved a 29Si polarization of 8.3% at 66 GHz and 1.1 K in single crystal P-doped, the highest ever reported, using DNP.
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.
Precision measurements based on optically detected nuclear magnetic resonance offer exquisite sensitivity to absolute shifts in spin transition frequencies, with potential applications in fundamental physics experiments and inertial sensing. We investigate 13C nuclear spins in diamond as a candidate system for solid-state implementations, which hold the promise for high-fidelity readout of large numbers of coherent nuclear spins in millitesla or lower magnetic fields. We demonstrate a technique that allows for both optical polarization and readout of large ensembles of ~10^{16} polarized nuclear spins. Our method takes advantage of state-selective Landau-Zener transitions under microwave frequency sweeping, which bidirectionally transfer spin polarization between Nitrogen-Vacancy (NV) electron spins and remote 13C nuclear spins. Using natural isotopic abundance diamonds with nitrogen densities of ~0.5-10 ppm, we perform optically-detected 13C Ramsey spectroscopy and realize a nuclear-spin-dependent fluorescence contrast exceeding 0.5% peak-to-peak. We observe nuclear spin dephasing times T2*~2 ms that only modestly improve with homonuclear dipolar decoupling, indicating that they are limited by the longitudinal spin relaxation of nearby NV electron spins. We study the magnetic field dependence of the optical readout and find comparable contrast and dephasing times for magnetic fields in the range 8-20 mT. Our method can be interpreted as a type of repetitive readout, where each NV center optically reads out the spin state of ~10^2 nuclei before nuclear spins depolarize.
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.