CaltechDATA: Book Chapter
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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenThu, 28 Mar 2024 11:21:25 -0700Quantum-mechanical chemical exchange. Stochastic averaging in magnetic resonance
https://resolver.caltech.edu/CaltechTHESIS:12172012-092540697
Year: 1993
DOI: 10.7907/nr9w-1k51
<p> I. Quantum-Mechanical Chemical Exchange</p>
<p>A quantum-mechanical treatment of both spin and space degrees of freedom is derived which accounts for both tunnelling splittings and lineshape behavior in the observed NMR of exchanging proton pairs. In this self-consistent treatment, the chemical exchange rate is expressed in terms of a correlation function of the operator which couples space and spin. A master equation formulation of the correlation function is presented which can be solved for any model of discrete rovibrational states. In contrast to previous descriptions of intramolecular chemical exchange, which either use transition state theory and the notion of molecular tunnelling or ad hoc ideas of incoherent tunnelling, the present treatment places chemical exchange among the class of transport and relaxation rates described by the quantum-statistical fluctuation-dissipation theorem. Results from simple models of the tunnelling system are analyzed in order to relate the observed NMR lineshape of certain transition metal hydrides to the underlying Born-Oppenheimer potential for the quantized nuclear motion.</p>
<p> II. Stochastic Averaging in Magnetic Resonance</p>
<p>As a result of the typical smallness of spin Hamiltonian parameters relative to the rates of relaxation of spatial degrees of freedom, many magnetic resonance spectra are
understood to be stochastic averages over thermally accessible molecular configurations or spatial (e.g., rovibrational) eigenstates. The temperature dependence of the average spin parameters is widely used to provide information on the potential energy functions which determine molecular conformation. It is universal practice in computing these averages that the energies (or free energies) multiplying β(=1/kT) in the Boltzmann probability factors are the spatial contributions only. It is argued that any such averaging procedure is inconsistent with statistical mechanics and an alternative procedure is
presented for calculating the stochastically-averaged spin Hamiltonian. The experimental conditions and possible test systems for validating the traditional or alternative forms of the stochastic average are discussed.</p>
https://resolver.caltech.edu/CaltechTHESIS:12172012-092540697Efficient Generation of Hyperpolarized Molecules Utilizing the Scalar Order of Parahydrogen
https://resolver.caltech.edu/CaltechTHESIS:05212010-154212167
Year: 2010
DOI: 10.7907/57FW-1060
<p>This dissertation describes methods that polarize the spin of a specific nucleus in molecules synthesized by molecular addition of parahydrogen to a precursor molecule. Nuclear magnetic resonance (NMR) pulse sequences are designed to perform efficient transfer of spin order by way of the scalar spin couplings between the two nascent protons and a heteronuclear spin label target. The result is an increase in the NMR signal from that nucleus by several orders of magnitude, approaching unity polarization. Algorithms are presented to effect the desired unitary evolution of this three-spin system over the range of couplings found in diverse molecules and in the presence of interfering spins. These methods are explored theoretically and comparisons are made to select the most advantageous method given a specific problem.</p>
<p>Issues concerning the choice of target molecule, portable equipment, and automation are discussed. Some design choices made for convenience in one aspect of the execution of the methods raise difficulties in other aspects. These difficulties are elucidated and methods of mitigation are discussed.</p>
<p>Pulse design issues are elucidated with numerical calculations which confirm analytical results for the time dependence obtained in the multiply rotating frame approximation. Failures of this approximation at low frequencies are explored numerically leading to novel pulse sequence design rules which ameliorate undesirable phenomena peculiar to low field NMR, enabling its employment for this and other applications requiring precise control of the spin degrees of freedom. Experimental results, primarily aimed at biomedical applications, are reviewed.</p>
https://resolver.caltech.edu/CaltechTHESIS:05212010-154212167Chemical Exchange in Nuclear Magnetic Resonance
https://resolver.caltech.edu/CaltechTHESIS:02212018-140937311
Year: 1997
DOI: 10.7907/fx7d-jf45
<p>Nuclear magnetic resonance spectra of molecules undergoing chemical exchange
have traditionally been quantified using a theory that combines a quantum-mechanical treatment of the spin dynamics with a kinetic model for the molecular exchange. This implicit factorization of spin and spatial degrees of freedom is without theoretical justification and yet it has been widely relied upon in chemical studies. In this thesis, a quantum-statistical theory of chemical exchange is presented for the calculation of lineshapes in dynamic nuclear magnetic resonance. In this treatment, the rates describing the exchange of spin coherence are shown to be complex valued due to the incomplete cancellation of the imaginary components of the spectral density of purely spatial perturbations. These imaginary components give rise to the previously unrecognized phenomena of exchange shifts, new contributions to the line positions which depend on spatial rates even in the fast-exchange limit. These shifts can be orders of magnitude greater than the experimental resolution. The same purely spatial fluctuations responsible for chemical exchange determine these shifts through a Hilbert-transform relationship.</p>
<p>New measurements on the <sup>13</sup>C NMR of methylcyclohexane show that, indeed, the traditional theory fails to relate spectra obtained in the regimes of fast and slow exchange. If interpreted using the traditional theory, the fast-exchange line positions in methylcyclohexane lead to an extracted equilibrium constant with an error of up to 30% and differing between isotopomers by up to 30%. With plausible assumptions on the temperature dependence of the chemical shifts and free energy, an overall fit of the fast and slow-exchange methylcyclohexane data is unsatisfactory, rigorously excluding the traditional theory. The exchange-shift theory indicates why additional information is needed to fit the fast-exchange line positions and allows a fit consistent with the observed experimental data on methylcyclohexane using a single conformer free energy difference linear in temperature over the entire experimental range.</p>https://resolver.caltech.edu/CaltechTHESIS:02212018-140937311I. Quantum-mechanical chemical exchange. II. NMR of semiconductors
https://resolver.caltech.edu/CaltechTHESIS:09022011-090934651
Year: 1992
DOI: 10.7907/0TQK-G720
<p>Part I. Quantum-Mechanical Chemical Exchange:</p>
<p>The requirement that the total wavefunction of a system be antisymmetric to the exchange of identical fermions manifests itself as a scalar coupling between the spin angular momenta. In a class of transition metal trihydrides, this effect is observed as multiplet structure in the liquid state NMR spectrum due to proton tunnelling. Numerical fits to the temperature dependence of these couplings are described as the ensemble averaged tunnel splitting over thermally occupied rovibrational states. The accepted concept of stochastic average of the coupling is questioned on theoretical grounds and an alternative prescription given which differs significantly in its numerical predictions. It is also shown how the fluctuations of the tunnel splitting due to dissipative coupling to the lattice contribute to the chemical rate processes that incoherently exchange nuclei between different sites and the coherent exchange effect. A master equation procedure for evaluating such rates numerically is presented.</p>
<p>Part II. NMR of Semiconductors:</p>
<p>NMR is an inherently low-sensitive technique. Moreover, unless special procedures are employed the structural information obtainable from an NMR line in the solid-state is also limited. Both these problems are addressed here. A method is proposed for the high resolution solid-state NMR of nuclei around paramagnetic defects which uses multiple pulse techniques to selectively average spin couplings and extract structural information. It is shown by numerical simulations how the method could resolve a long-standing controversy on the assignment of hyperfine tensors to silicon sites around a phosphorous dopant. Experimental results on a novel time-domain optical nuclear magnetic resonance method are obtained on gallium arsenide. Comparison with an earlier continuous-wave variant of the technique show improved absolute sensitivity and relative sensitivity to low-abundance sites near an optically relevant defect.</p>
https://resolver.caltech.edu/CaltechTHESIS:09022011-090934651Trapped ion magnetic resonance: concepts and designs
https://resolver.caltech.edu/CaltechTHESIS:05102013-144219320
Year: 1994
DOI: 10.7907/eeq1-kw72
<p>A novel spectroscopy of trapped ions is proposed which will bring single-ion
detection sensitivity to the observation of magnetic resonance spectra. The approaches
developed here are aimed at resolving one of the fundamental problems of molecular
spectroscopy, the apparent incompatibility in existing techniques between high information
content (and therefore good species discrimination) and high sensitivity. Methods for
studying both electron spin resonance (ESR) and nuclear magnetic resonance (NMR) are
designed. They assume established methods for trapping ions in high magnetic field and
observing the trapping frequencies with high resolution (<1 Hz) and sensitivity (single ion)
by electrical means. The introduction of a magnetic bottle field gradient couples the spin
and spatial motions together and leads to a small spin-dependent force on the ion, which
has been exploited by Dehmelt to observe directly the perturbation of the ground-state
electron's axial frequency by its spin magnetic moment. </p>
<p>A series of fundamental innovations is described m order to extend magnetic
resonance to the higher masses of molecular ions (100 amu = 2x 10^5 electron masses) and smaller magnetic moments (nuclear moments = 10^(-3) of the electron moment). First, it is
demonstrated how time-domain trapping frequency observations before and after magnetic
resonance can be used to make cooling of the particle to its ground state unnecessary.
Second, adiabatic cycling of the magnetic bottle off between detection periods is shown to
be practical and to allow high-resolution magnetic resonance to be encoded pointwise as
the presence or absence of trapping frequency shifts. Third, methods of inducing spindependent
work on the ion orbits with magnetic field gradients and Larmor frequency
irradiation are proposed which greatly amplify the attainable shifts in trapping frequency. </p>
<p>The dissertation explores the basic concepts behind ion trapping, adopting a
variety of classical, semiclassical, numerical, and quantum mechanical approaches to
derive spin-dependent effects, design experimental sequences, and corroborate results
from one approach with those from another. The first proposal presented builds on
Dehmelt's experiment by combining a "before and after" detection sequence with novel
signal processing to reveal ESR spectra. A more powerful technique for ESR is then
designed which uses axially synchronized spin transitions to perform spin-dependent work
in the presence of a magnetic bottle, which also converts axial amplitude changes into
cyclotron frequency shifts. A third use of the magnetic bottle is to selectively trap ions
with small initial kinetic energy. A dechirping algorithm corrects for undesired frequency
shifts associated with damping by the measurement process. </p>
<p>The most general approach presented is spin-locked internally resonant ion
cyclotron excitation, a true continuous Stern-Gerlach effect. A magnetic field gradient
modulated at both the Larmor and cyclotron frequencies is devised which leads to
cyclotron acceleration proportional to the transverse magnetic moment of a coherent state
of the particle and radiation field. A preferred method of using this to observe NMR as an
axial frequency shift is described in detail. In the course of this derivation, a new quantum
mechanical description of ion cyclotron resonance is presented which is easily combined
with spin degrees of freedom to provide a full description of the proposals. </p>
<p>Practical, technical, and experimental issues surrounding the feasibility of the
proposals are addressed throughout the dissertation. Numerical ion trajectory simulations
and analytical models are used to predict the effectiveness of the new designs as well as
their sensitivity and resolution. These checks on the methods proposed provide
convincing evidence of their promise in extending the wealth of magnetic resonance
information to the study of collisionless ions via single-ion spectroscopy. </p>
https://resolver.caltech.edu/CaltechTHESIS:05102013-144219320Force-Detected NMR in a Homogeneous Field: Experiment Design, Apparatus, and Observations
https://resolver.caltech.edu/CaltechTHESIS:04262012-133554077
Year: 2002
DOI: 10.7907/MT9P-7J20
<p>Here I present motivation, experimental progress, and theoretical aspects of the BOOMERANG (better observation of magnetization enhanced resolution and no gradient) method of force-detected NMR, a general approach to extending arbitrary NMR experiments to the micron scale and below. Enabling quality of BOOMERANG is that its sensitivity scales much more favorably than traditional inductive detection for small samples. A reduction in the sample size accessible by NMR is strongly motivated by such goals as massively parallel analysis in support of combinatorial chemistry, portability in support of planetary exploration, and the general advantage of highest sensitivity per unit cost.</p>
<p>The key design insight is that the spin-dependent forces are independent of the field homogeneity across the sample. However, throughput is optimized only by providing field homogeneity during detection sufficient to allow coherent control over all target spins in a sample. I present our BOOMERANG design concepts and strategies, which allow detectors with high geometrical efficiency and good prospects for low mechanical dissipation.</p>
<p>The design principles are quantitatively confirmed using a prototype mm-scale spectrometer. Our experimental results, which include proton and fluorine FT-NMR
spectra in solids and liquids, heteronuclear J spectra, and liquid-state spin echoes with sub-Hz linewidths, emphasize BOOMERANG’s general spectroscopic applicability.</p>
<p>Fabrication of a high-sensitivity spectrometer optimized for 60-micron samples is underway in conjunction with the Microdevices Laboratory (MDL) at the NASA Jet Propulsion Laboratory (JPL). Using state-of-the-art lithography and electrodeposition techniques, we have fabricated magnets and mechanical oscillator structures that show promise for incorporation into spectrometers for in-situ planetary exploration, and for massively parallel analysis.</p>
<p>As the sample size decreases, sensitivity is dominated by quantum-statistical noise in the sample, or spin noise. This fundamental problem is mitigated by the CONQUEST measurement paradigm involving multiple time-correlated measurements on a spin system of interest. This is an essential ingredient in converting polarization
fluctuations to coherent time-domain spectroscopy or to images with arbitrary numbers of spins in each pixel.</p>
https://resolver.caltech.edu/CaltechTHESIS:04262012-133554077I. Multiple-pulse radio-frequency gradient nuclear magnetic resonance imaging of solids ; II. Optical nuclear magnetic resonance analysis of epitaxial gallium arsenide structures
https://resolver.caltech.edu/CaltechTHESIS:02242011-083555306
Year: 1996
DOI: 10.7907/PDK5-7T44
This dissertation details two techniques for materials analysis by nuclear magnetic resonance.
The first is a general strategy for recording spin density maps from solids through improved nuclear
magnetic resonance imaging. The second involves ultrasensitive methods for detecting nuclear magnetic
resonance optically and is applicable to semiconductors at low temperature.
Conventional liquids magnetic resonance imaging (MRJ) protocols fail in solids, where rapid
local-field dephasing of nuclear magnetization precludes the frequency encoding of spatial information
with conventional magnetic field gradients. In our approach, a multiple-pulse line-narrowing sequence is
delivered with a solenoid coil to prolong a solid's effective transverse relaxation time. A radiofrequency
gradient coil, delivering resonant pulses whose amplitude varies across the sample, is driven in concert
with the line-narrowing coil to encode spatial information. The practical implementation of this protocol
demanded the construction of an active Q-spoiling circuit to negate coupling of the two isoresonant coils.
Two-dimensional Fourier-zeugmatographic images of hexamethylbenzene have been obtained that exhibit
300 µm x 300 µm planar resolution. This imaging protocol is one of the highest sensitivity methods for
imaging solids by NMR (the other involves line narrowing and pulsed DC gradients).
Extraordinary increases in detection sensitivity are required for NMR to study epitaxial
semiconductor devices. Optical pumping is one route to such increased sensitivity. Here, a transfer of
angular momentum from polarized light to electrons (via selection rules), and electrons to nuclei (through
hyperfine couplings), can result in > 10 % nuclear spin polarization in less than 5 seconds at 2 K. A total
sensitivity gain of 10^5 follows by detecting this large polarization optically, through the inverse process,
allowing collection of the NMR spectra for several GaAs-based epitaxial devices. Previous workers
observed these spectra to be either power-broadened at the rf levels required to induce optical response, or
distorted due to the presence of photocarriers during optical detection. An innovation of the Weitekamp
group was to time-sequence and separately optimize the periods of optical pumping, NMR evolution, and
optical detection. Although time sequencing in principle allows the collection of multiple-pulse high-resolution
NMR spectra, it appeared inadequate when applied to a semiconductors heterojunction.
In conventional NMR, the entire dipole-allowed spectrum may be collected following a single
pulse. In time-sequenced optical NMR however, the desired interferogram must be built up pointwise by
repetitively incrementing an evolution time. Although sensitive, this experiment is time consuming and
sensitive to drift. A new optical detection protocol has been developed which removes these problems and
allows NMR spectra to be collected optically in real tillle. In this experiment, a circularly polarized
reference nuclear hyperfine field is introduced during the precession of a signal field. The observed
luminescence polarization is sensitive to the instantaneous vector sum of the fields, producing Larmor
beats. With the reference magnetization in equilibrium through the use of either continuous irradiation or
a pulsed spin-lock, the oscillation of luminescence polarization at the Larmor beat frequency is able to
record the spectrum of the signal nucleus alone.
A spectrometer has been constructed for implementing both time-sequenced and Larmer-beat
optical detection of NMR. In order to implement rotation studies in a way compatible with optical
detection at 2K, variable-angle Helmholtz coils have been added to the apparatus so that the direction of
the static field can be varied. The results of preliminary rotation studies put a surprisingly low upper
bound on the electric fields present at the most rapidly polarizable sites in a AlGaAs/GaAs heterojunction.
This can be understood in terms of a model where these sites are neutral donors at locations where the
built-in interfacial electric field has fallen off.https://resolver.caltech.edu/CaltechTHESIS:02242011-083555306Theoretical and Experimental Investigations in MEMS-Based Force-Detected NMR
https://resolver.caltech.edu/CaltechETD:etd-02182006-145814
Year: 2005
DOI: 10.7907/4FSQ-YP59
<p>This thesis describes a method of mechanically detecting magnetic resonance. The detector consists of a ferromagnet harmonically bound to a mechanical resonator and measures a magnetic force of interaction with a nearby sample via dipole-dipole coupling. Flexural modes of vibration of the resonator are induced by inversion of the sample magnetization at the mechanical resonance frequency of the device. In this method, a nominally homogeneous field at the sample allows coherent spectroscopy over the entire sample volume.</p>
<p>Sensitivity analyses suggest that encoding an NMR signal into mechanical oscillations favors inductive detection at the micron scale and below with Brownian motion of the detection being the predominant source of noise and azimuthal eddy currents being the predominant source of damping. As such, the design issues of a MEMS-based spectrometer optimized for 50 micron samples have been investigated. Finite element methods were used and the results for magnetic softening effects, mechanical stresses, field homogeneity, magnet design, radiofrequency excitation, and the utility of capacitive transduction to provide tuning of the oscillator’s mechanical resonance frequency and active shimming are discussed. A piezeoelectrically actuated microvalve is proposed as part of a microfluidic device to allow shuttling of liquid samples. We present a new means of fiber-optic interferometry for geometrically confined regions in which the light exits transverse to core axis. The use of a composite magnetic array of packed nanoparticles may reduce the damping by 10<sup>4</sup>.</p>
<p>The portability of the spectrometer will allow in situ spectroscopy and towards that end 14N overtone experiments were simulated. Force-detection of this transition is superior not only at reduced size scales, but over a broad range of magnetic field strengths. The line narrowing observed by detecting the overtone transition should allow detailed spectroscopic analysis not possible by observing the quadrupolar broadened first-order spectrum. Simulations for a representative class of tholins suggest that the overtone linewidths is of order tens of kHz.</p>
<p>We conclude by discussing the feasibility of nanoscale NMR using torque detection of spin-locked, transverse magnetization, include a derivation of the signal-to-noise and detector optimization, and comment on the fundamental limitations of quantum statistical noise.</p>https://resolver.caltech.edu/CaltechETD:etd-02182006-145814Novel Methods for Force-Detected Nuclear Magnetic Resonance
https://resolver.caltech.edu/CaltechETD:etd-06112008-065533
Year: 2008
DOI: 10.7907/S5K2-NH54
<p>This thesis is concerned with the problem of extending methods for force-detected nuclear magnetic resonance (NMR) to the nanoscale regime. A magnetic mechanical resonator can be used both as a sensitive detector of spins and a means of inducing spin relaxation between detected transients. At the mK temperatures achievable in a dilution refrigerator, spin-lattice interactions are "frozen out," and resonator-induced relaxation can replace spin-lattice relaxation in returning the spins to equilibrium between detected transients. We analyze resonator-induced spin relaxation and the sensitivity of schemes which use a nanoscale mechanical resonator to detect spins.</p>
<p>Relaxation equations are derived from first principles, and a physical interpretation of the processes contributing to resonator-induced relaxation is given. The intrinsically quantum mechanical nature of the relaxation is highlighted by comparing the quantum mechanical relaxation equations with analogous equations derived using a semiclassical model in which all spin components have a definite value simultaneously. In the case where the spins all experience the same field, the semiclassical spins cannot become polarized as a result of their interaction with the resonator, and a quantum mechanical model is necessary even for a qualitative description of the polarization process.</p>
<p>Resonator-induced relaxation of spin systems is complicated by the fact that an indirect spin-spin interaction is present when all spins are coupled to the same resonator, since the resonator's field at a given spin is determined by the interactions which have occurred between the resonator and the other spins of the system. This indirect interaction can prevent the spins from relaxing to a thermal state characterized by a spin temperature. We present a physical interpretation of the mechanism by which an indirect spin-spin torque develops during resonator-induced relaxation, and we estimate the magnitude of this torque and the time T_corr required for it to induce strong spin-spin correlations. A perturbation in the spin Hamiltonian which periodically reverses the direction of the indirect torques within a time period shorter than T_corr will prevent the development of resonator-induced correlations and allow the spins to relax to a thermal state.</p>
<p>The mechanisms by which the spin Hamiltonian H_s modifies resonator-induced relaxation are characterized. In the case where the eigenstates of H_s are weakly perturbed from product states, the system will relax exponentially to thermal equilibrium with the resonator, provided that resonator-induced couplings between populations and certain zero-quantum coherences are suppressed by terms in H_s which shift the frequencies of these coherences sufficiently far from zero. Analysis of longitudinal relaxation in example systems containing three dipole-dipole coupled spins shows that the relaxation occurs in two stages governed by different physical processes, and the three-spin systems do not relax to a thermal state. For substantially larger dipole-dipole coupled system (e.g., N = 50), we propose the hypotheses that the secular dipolar Hamiltonian will quickly equalize the population of states which lie in the same eigenspace of I_z. Simulations of the longitudinal relaxation predicted by this hypothesis suggest that a single resonator could efficiently relax dipole-dipole coupled systems to a thermal state.</p>
<p>Arguments based on general properties of the master equation suggest that the transverse relaxation induced by the mechanical resonator could occur on a shorter time scale than that of the longitudinal relaxation. We derive conditions which guarantee that the time constant for transverse relaxation will be 2/R_h, where 1/R_h is the time constant for resonator-induced longitudinal relaxation of a single-spin sample to thermal equilibrium. Under these conditions, transverse relaxation can be interpreted as the "lifetime broadening" associated with the shortened lifetime of energy eigenstates due to coupling with the resonator. For a two-spin system, however, we show analytically that "turning on" the dipolar coupling can accelerate resonator-induced transverse relaxation, and we give an interpretation of the mechanism by which this occurs. Simulations of four-spin systems also show that the presence of dipolar couplings can substantially accelerate resonator-induced transverse relaxation, and that this accelerated relaxation can be distinguished from so-called radiation damping. In addition, we find that spin-locking limits the rate of resonator-induced transverse relaxation. In the case where the spin-locking field is large enough to average the dipolar Hamiltonian and the superoperator responsible for resonator-induced relaxation, we have T_1rho = 2/R_h.</p>
<p>We propose a general definition of signal-to-noise ratio (SNR) which can be used to compare the sensitivity of methods that measure the amplitude of a signal with the sensitivity of methods that yield a continuous record of a signal. This definition is used to compare the sensitivity of three schemes for detecting the NMR signal of a sample consisting of a few spins: spin-locked detection of a transverse dipole, detection of a freely-precessing dipole, and detection of a correlated product. The dependence of SNR and acquisition time on resonator parameters is analyzed. We find that when the time constant for decay of the signal during the detection period is 2/R_h, with instrument noise substantially larger than spin noise, the only resonator parameter which appears in the SNR expressions is the ratio of the mechanical frequency to the temperature. This result suggests, in particular, that SNR for spin-locked detection will be insensitive to details of resonator design.</p>
<p>A torsional mechanical resonator design is presented. We discuss the advantages of using soft magnetic material and eliminating relative motion between the sample and the resonator, as well as the validity of the models used to characterize the resonator. The possibility of using non-metallic magnetic material as the source of the resonator's magnetic field is introduced. A numerical example is presented for which the calculated time constant for the longitudinal relaxation of a single-spin sample is 1/R_h = 0.77 s. Simulations of detected NMR spectra for two-spin samples suggest the possibility of chemical studies in which force-detected NMR spectroscopy is used with single-spin sensitivity.</p>
<p>The final chapter studies the possibility of using hyperpolarized spins to cool a single mechanical mode. Numerical examples suggest that cooling would be negligible for resonators of size scale ~ 10 um or larger. In the regime characterized by these examples, substantial cooling requires sufficiently strong spin-resonator coupling that neither a mechanical mode nor a spin mode can be distinguished in the spin-resonator system; instead, the modes of the system include equal contributions from the spins and the mechanical resonator. The spin-resonator correlations responsible for cooling make a significant contribution to the symmetric correlation function of the resonator coordinate, with the result that the noisy "thermal torque" acting on the resonator is increased rather than diminished by the presence of the hyperpolarized spins.</p>
https://resolver.caltech.edu/CaltechETD:etd-06112008-065533Laser Synchronized Optical Nuclear Magnetic Resonance via Larmor Beat Detection : Imaging Electronic Wavefunctions in Gallium Arsenide Device Structures
https://resolver.caltech.edu/CaltechETD:etd-12102007-114331
Year: 2001
DOI: 10.7907/ARCE-F837
<p>We have accomplished Optical Nuclear Magnetic Resonance (ONMR) experiments in an Al<sub>0.36</sub>Ga<sub>0.64</sub>As/GaAs heterojunction sample at ~2K with rf-optical pulse synchronization. The hyperfine coupling of the electron spin to the nuclear spins enable this spectroscopy in several ways, which are discussed herein. Moreover, the interactions experienced by nuclear spins in III-V semiconductors, in general, and the phenomena encountered when they are in the vicinity of a shallow donor or pseudo-donor, specifically, are developed. Furthermore, the most accurate calculation of spin diffusion in a spin-three-halves system to date is developed and presented using a methodology can be readily applied to any spin-larger-than-one-half system to a yield a set of coupled differential equations for a set of orthogonal polarizations. The behavior of these equations under a number of physical situations is also investigated.</p>
<p>We have captured the first ever radially resolved Knight shift images from the nuclei near a point defect in GaAs using laser synchronized ONMR. A deconvolution of these images into their constituent physical interactions has been approximately carried out using the theoretical advances developed and presented in this thesis, yielding the shape and size of the electronic orbital in which the electron is trapped, the occupancy of that electronic orbital, and the quadrupolar interactions in the vicinity of the defect, including the charge state of the defect.</p>
<p>Computational approaches include both full, real-time analyses of every one of the hundreds of thousands of nuclei surrounding a defect in GaAs, modeling the time domain evolution for each individual nucleus including its Knight shift, quadrupolar interactions (both secular and nonsecular), individual optical polarization conditions, optical detection weighting, and rigorously exact rf effects, and analyses of a variety of continuous medium approximations. The only computations that fit the experimental spectra are those that calculate spin diffusion along a radial line of spins, and use this approximation to the radial profile of nuclear polarization in a continuous medium approximation. The successful interface of this spin diffusion calculation and the single nucleus calculations, leveraging their individual strengths, is clearly a desirable route to further increase computational accuracy.</p>https://resolver.caltech.edu/CaltechETD:etd-12102007-114331Probing Quantum Confinement at the Atomic Scale with Optically Detected Nuclear Magnetic Resonance
https://resolver.caltech.edu/CaltechETD:etd-08282001-123851
Year: 2001
DOI: 10.7907/0JZB-N948
<p>Near-band-gap circularly polarized excitation in III-V semiconductors provides spin-polarized electrons that transfer spin order to lattice nuclei via fluctuations in the contact hyperfine interaction. This process of optical nuclear polarization and the complementary technique of optical detection of nuclear magnetic resonance (NMR) provide extreme sensitivity enhancement and spatial selectivity in structured samples, enabling collection of NMR spectra from samples such as single quantum wells or dots containing as few as ~10^5 nuclei.</p>
<p>Combining these advances with novel techniques for high spectral resolution, we have probed quantum-confined electronic states near the interface of a single epitaxially grown Al(1-x)Ga(x)As/GaAs (x = 0.36) heterojunction. Using a novel strategy that we refer to as POWER (perturbations observed with enhanced resolution) NMR, multiple-pulse time suspension is synchronized with bandgap optical irradiation to reveal spectra of effective spin Hamiltonians that are differences between those of the occupied and unoccupied photoexcited electronic state. The underlying NMR linewidth is reduced by three orders of magnitude in these experiments, enabling resolution of an asymmetric line shape due to light-induced hyperfine interactions. The results are successfully fit with the coherent nuclear spin evolution and relaxation theoretically expected for sites distributed over the volume of an electronic excitation weakly localized at a point defect. This analysis establishes a one-to-one relationship, which can be used to follow nuclear spin diffusion, between optical Knight shift and the radial position of lattice nuclei.</p>
<p>We have also introduced POWER NMR techniques to characterize the change in electric field associated with cycling from light-on to light-off states via a linear quadrupole Stark effect (LQSE) of the nuclear spins. Simulations of these NMR spectra in terms of the radial electric fields of either donor-bound electrons or excitons indicate differences, where the bound-exciton model provides a significantly better fit to the data. The same spin physics enabled our measurement of the heterojunction interfacial field, which we find to be less than 1.3 kV/cm at the sites responsible for optical NMR. Other simulations show the promise of optical NMR as a tool in future studies aimed at atomic-level characterization of quantum-confined systems such as quantum dots and wells.</p>https://resolver.caltech.edu/CaltechETD:etd-08282001-123851Force-Detected Nuclear Magnetic Resonance Independent of Field Gradients
https://resolver.caltech.edu/CaltechETD:etd-05292003-175447
Year: 2003
DOI: 10.7907/8GH1-CC08
This thesis describes a new method of magnetic resonance detection based on mechanical displacements caused by magnetic forces, which is general with respect to sample and pulse sequence. A spin-bearing sample placed inside a flexible magnet assembly distorts that assembly in proportion to the sample's magnetization. Radio-frequency fields that modulate the sample's spin magnetization at this detector's mechanical resonance frequency encode magnetic resonance spectra into the detector's trajectory. A key insight is that such mechanical detection can be performed within optimized detectors with no need for field gradients inside the sample volume, circumventing the deleterious consequences of such gradients for sensitivity and resolution. The new method is called Better Observation of Magnetization, Enhanced Resolution, and No Gradient (BOOMERANG), and its sensitivity is predicted to exceed that of inductive detection at microscopic size scales.
A prototype BOOMERANG spectrometer optimized for 3 mm diameter liquid and solid samples is described. The device uses direct digital synthesis of radio-frequency waveforms in its operation and fiber-optic interferometry to detect picometer-scale motions of a detector magnet. This magnet is bound to a tuned mechanical oscillator inside a magnet assembly designed for homogeneity of the magnetic field in the sample. Several types of time-domain FT-NMR spectra on test samples are presented. The data confirm theory and design principles.
The favorable scaling of BOOMERANG's sensitivity and the numerous potential uses for NMR at reduced size scales motivate construction of spectrometers optimized for microscopic samples. Geometric concerns in scaling down BOOMERANG are addressed quantitatively. At size scales where the number of spins is such that mean magnetization is smaller than fluctuations, such fluctuations, if not accounted for, can dominate the noise regardless of the physical detection method used. A measurement paradigm using correlations of these fluctuations to encode spectra is proposed to suppress this quantum noise, and the sensitivity of this method, which we call Correlated Observations Narrow Quantum Uncertainty, Enhancing Spectroscopic Transients (CONQUEST), is analyzed. BOOMERANG and CONQUEST promise to extend the applicability of nuclear magnetic resonance (NMR) for chemical analysis to samples and problems that are currently inaccessible by NMR due to poor sensitivity.https://resolver.caltech.edu/CaltechETD:etd-05292003-175447Parahydrogen and Synthesis Allow Dramatically Enhanced Nuclear Alignment
https://resolver.caltech.edu/CaltechETD:etd-04172006-141634
Year: 1991
DOI: 10.7907/R5TV-Z220
<p>The PASADENA effect is a method for transient high-sensitivity proton spin-labelling by molecular addition of dihydrogen. When the parahydrogen mole fraction differs from the high-temperature limit of 1/4, this population difference constitutes a form of spin order which can be converted to magnetization observable by NMR. Large NMR signals are observed, if subsequent to the hydrogen addition, the two protons experience magnetic inequivalence and spin-spin coupling and if observation is made before spin-lattice relaxation restores the equilibrium spin order. The analogous effect for D2 is also possible.</p>
<p>The kinetic mechanisms of the homogeneous hydrogenation catalysts which permit the realization of the PASADENA effect have been the target of the experimental applications. The enhancement of the NMR transitions has facilitated the determination of true molecular rate constants. Ordinarily, the activity of a catalyst is assessed by dividing the observed rate by the total catalyst concentration. However, the question as to whether most of the catalytic rate is due to a tiny fraction of active species or a large fraction with a relatively low molecular rate is not clearly addressed by such an analysis. This ambiguity is entirely avoided in the PASADENA studies, since only active catalyst molecules can contribute to the enhanced signals from which all kinetic inferences are made.</p>
<p>The sensitivity enhancement has also led to the identification of a novel intermediate in the mechanism for the Rh(DIPHOS)+ catalyzed hydrogenation of styrene. The rate of conversion of this species into product and starting material has been studied using two-dimensional NMR. The dramatically improved sensitivity should make it possible to observe key catalytic intermediates which do not build up in sufficient quantity to allow detection by conventional NMR arising from Curie-Law magnetization.</p>
<p>The study of surface sites which bind pairwise with H2 is also a potentially fruitful area for future experimental work. The ambient temperature NMR spectroscopy of surfaces is not often feasible due to sensitivity limitations. Simulations have been performed using typical shift and coupling parameters in an effort to characterize the enhanced lineshapes which can be expected.</p>
<p>The inverse of the PASADENA effect has also been proposed, whereby the spin order of a molecule containing hydrogen is probed by measuring the branching ratio to ortho and para dihydrogen. This RAYMOND phenomenon (radiowave application yields modulated ortho number desorbed) has the potential for measuring precursor NMR with extraordinary sensitivity, since it finesses the need for detection of radiowaves.</p>https://resolver.caltech.edu/CaltechETD:etd-04172006-141634