Electron dynamics and harmonics emission spectra due to electron oscillation driven by intense laser pulses

The dynamics and harmonics emission spectra due to electron oscillation driven by intense laser pulses have been investigated considering a single electron model. The spectral and angular distributions of the harmonics radiation are numerically analyzed and demonstrate significantly different characteristics from those of the low-intensity field case. Higher-order harmonic radiation is possible for a sufficiently intense driving laser pulse. A complex shifting and broadening structure of the spectrum is observed and analyzed for different polarization. For a realistic pulsed photon beam, the spectrum of the radiation is redshifted for backward radiation and blueshifted for forward radiation, and spectral broadening is noticed. This is due to the changes in the longitudinal velocity of the electron during the laser pulse. These effects are much more pronounced at higher laser intensities giving rise to even higher-order harmonics that eventually leads to a continuous spectrum. Numerical simulations have further shown that broadening of the high harmonic radiation can be limited by increasing the laser pulse width. The complex shifting and broadening of the spectra can be employed to characterize the ultrashort and ultraintense laser pulses and to study the ultrafast dynamics of the electrons. (c) 2006 American Institute of Physics.

Dirac spectra, summation formulae, and the spectral action

Noncommutative geometry is a source of particle physics models with matter Lagrangians coupled to gravity. One may associate to any noncommutative space (A, H, D) its spectral action, which is defined in terms of the Dirac spectrum of its Dirac operator D. When viewing a spin manifold as a noncommutative space, D is the usual Dirac operator. In this paper, we give nonperturbative computations of the spectral action for quotients of SU(2), Bieberbach manifolds, and SU(3) equipped with a variety of geometries. Along the way we will compute several Dirac spectra and refer to applications of this computation.

Trapped ion magnetic resonance: concepts and designs

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.

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.

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.

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.

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.

Reactivity of titanocene methylidene with metal halides, alkene sulfides, and alkene oxides

Titanocene metallacyclobutanes show a wide variety of reactivites with organic and inorganic reagents. Their reactions include methylene transfer to organic carbonyls, formation of enolates, electron transfer from activated alkyl chlorides, olefin metathesis, ring opening polymerization. Recently, preparations of heterobinuclear µ-methylene complexes were reported. In this thesis, mechanistic, synthetic, and structural studies of the heterobinuclear µ-methylene complexes will be described. Also, the reaction of titanocene methylidene trimethylphosphine complex with alkene sulfide and styrene sulfide will be presented.

Heterobinuclear µ-methylene-µ-methyl complexes C_(p2)Ti(µ-CH_2)( µ-CH_3)M(1,5-COD) have been prepared (M = Rh, Ir). X-ray crystallography showed that the methyl group of the complex was bonded to the rhodium and bridges to the titanium through an agostic bond. The ^(1)H,^(13)CNMR, IR spectra along with partial deuteration studies supported the structure in both solution and solid state. Activation of the agostic bond is demonstrated by the equilibration of the µ-CH_3 and µ-CH_2 groups. A nonlinear Arrhenius plot, an unusually large kinetic isotope effect (24(5)), and a large negative activation entropy (-64(3)eu) can be explained by the quantum-mechanical tunneling. Calculated rate constants with Bell-type barrier fitted well with the observed one. This equilibration was best explained by a 4e-4c mechanism (or σ bond metathesis) with the character of quantum-mechanical tunneling.

Heterobinuclear µ-methylene-µ-phenyl complexes were synthesized. Structural study of C_(p2)Ti(µ-CH_(2))(µ-p-Me_(2)NC_(6)H_(4))Rh(l,5-COD) showed that the two metal atoms are bridged by the methylene carbon and the ipso carbon of the p-N,N-dimethylarninophenyl group. The analogous structure of C_(p2))Ti(µ-CH_(2))(µ-o-MeOC_(6)H_(4))Rh(1,5-COD) has been verified by the differential NOE. The aromaticity of the phenyl group observed by ^(1)H NMR, was confirmed by the comparison of the C-C bond lengths in the crystallographic structure. The unusual downfield shifts of the ipso carbon in the ^(13)C NMR are assumed to be an indication of the interaction between the ipso carbon and electron-deficient titanium.

Titanium-platinum heterobinuclear µ-methylene complexes C_(p2)Ti(µ-CH_(2))(µ -X)Pt(Me)(PM_(2)Ph) have been prepared (X= Cl, Me). Structural studies indicate the following:(1) the Ti-CH2 bond possesses residual double bond character, (2) there is a dative Pt→Ti interaction which may be regarded as a π back donation from the platinum atom to the 'Ti=CH_(2)'' group, and (3) the µ-CH_3 group is bound to the titanium atom through a three-center, two-electron agostic bond.

Titanocene (η^(2)-thioformaldehyde)•PMe_3 was prepared from C_(p2)Ti=CH_(2)•PMe_3 and sulfur-containing organic compounds (e.g. alkene sulfide, triphenylphosphine sulfide) including elemental sulfur. Mechanistic studies utilizing trans-styrene sulfide-d_1 suggested the stepwise reaction to explain equimolar mixture of trans- and cis-styrene-d_1 as by-products. The product reacted with methyl iodide to produce cationic titanocene (η_(2)-thiomethoxymethyl) complex. Complexes having less coordinating anion like BF_4 or BPh_4 could be obtained through metathesis. Together with structural analyses, the further reactivities of the complexes have been explored.

The complex C_(p2)TiOCH_(2)CH(Ph)CH_2 was prepared from the compound C_(p2)Ti=CH_(2)-PMe_3 and styrene oxide. The product was characterized with ^(1)H-^(1)H correlated 2-dimensional NMR, selective decoupling of ^(1)H NMR, and differential NOE. Stereospecificity of deuterium in the product was lost when trans-styrene oxide-d_1 was allowed to react. Relative rates of the reaction were measured with varying substituents on the phenyl ring. Better linearity (r = -0.98, p^(+) = -0.79) was observed with σ_(p)^(+)than σ(r = -0.87, p = -1.26). The small magnitude of p^+ value and stereospecificity loss during the formation of product were best explained by the generation of biradicals, but partial generation of charge cannot be excluded. Carbonylation of the product followed by exposure to iodine yields the corresponding β-phenyl γ-lactone.

Fine interference fringes formed in high-order harmonic spectra generated by infrared driving laser pulses

We experimentally investigate the high-order harmonic generation in argon gas using a driving laser pulse at a center wavelength of 1240 nm. High-contrast fine interference fringes could be observed in the harmonic spectra near the propagation axis, which is attributed to the interference between long and short quantum paths. We also systematically examine the variation of the interference fringe pattern with increasing energy of the driving pulse and with different phase-matching conditions.

The effect of electric field maximum on the Rabi flopping and generated higher frequency spectra

We investigate the effect of the electric field maximum on the Rabi flopping and the generated higher frequency spectra properties by solving Maxwell-Bloch equations without invoking any standard approximations. It is found that the maximum of the electric field will lead to carrier-wave Rabi flopping (CWRF) through reversion dynamics which will be more evident when the applied field enters the sub-one-cycle regime. Therefore, under the interaction of sub-one-cycle pulses, the Rabi flopping follows the transient electric field tightly through the oscillation and reversion dynamics, which is in contrast to the conventional envelope Rabi flopping. Complete or incomplete population inversion can be realized through the control of the carrier-envelope phase (CEP). Furthermore, the generated higher frequency spectra will be changed from distinct to continuous or irregular with the variation of the CEP. Our results demonstrate that due to the evident maximum behavior of the electric field, pulses with different CEP give rise to different CWRFs, and then different degree of interferences lead to different higher frequency spectral features.

Pondermotive shift of photoelectron spectra in intense laser field

In a recent experimental work on the excess photon detachment (EPD) of H- ions [Phys. Rev. Lett. 87 (2001) 243001] it has been found that the ponderomotive shift of each EPD peak increases with the order of the EPD channel. By using a nonperturbative quantum scattering theory, we obtain the kinetic energy spectra for the differential detachment rate along the laser polarization for several laser intensities. It is demonstrated that higher order EPD peaks are produced mainly at relatively higher laser intensities. By calculating the overall EPD spectra with varying laser intensities, it is found that the ponderomotive shift of each EPD peak increases with the order of the EPD channel. Our calculations are in good agreement with the experimental observation. It is found that different EPD channels occur mainly when the laser field reaches some values, thus the intensity distribution of the laser field is responsible for the varying ponderomotive shifts.

I. Spectroscopic evidence for slow vibrational relaxation in excited electronic states of diatomics in rare gas solids. II. Static crystal field effects in the electronic spectra of isotopically mixed benzene crystals

Part I

Studies of vibrational relaxation in excited electronic states of simple diatomic molecules trapped in solid rare-gas matrices at low temperatures are reported. The relaxation is investigated by monitoring the emission intensity from vibrational levels of the excited electronic state to vibrational levels of the ground electronic state. The emission was in all cases excited by bombardment of the doped rare-gas solid with X-rays.

The diatomics studied and the band systems seen are: N₂, Vegard-Kaplan and Second Positive systems; O₂, Herzberg system; OH and OD, A ²Σ⁺ - X²II_i system. The latter has been investigated only in solid Ne, where both emission and absorption spectra were recorded; observed fine structure has been partly interpreted in terms of slightly perturbed rotational motion in the solid. For N₂, OH, and OD emission occurred from v' > 0, establishing a vibrational relaxation time in the excited electronic state of the order, of longer than, the electronic radiative lifetime. The relative emission intensity and decay times for different v' progressions in the Vegard-Kaplan system are found to depend on the rare-gas host and the N₂ concentration, but are independent of temperature in the range 1.7°K to 30°K.

Part II

Static crystal field effects on the absorption, fluorescence, and phosphorescence spectra of isotopically mixed benzene crystals were investigated. Evidence is presented which demonstrate that in the crystal the ground, lowest excited singlet, and lowest triplet states of the guest deviate from hexagonal symmetry. The deviation appears largest in the lowest triplet state and may be due to an intrinsic instability of the ³B_1u state. High resolution absorption and phospho- rescence spectra are reported and analyzed in terms of site-splitting of degenerate vibrations and orientational effects. The guest phosphorescence lifetime for various benzene isotopes in C₆D₆ and sym-C₆H₃D₃ hosts is presented and discussed.

Absolute phase control of spectra effects in a two-level medium driven by two-color ultrashort laser pulses

Using a omega-3 omega combination scenario, we investigate the absolute phase control of the spectra effects for ultrashort laser pulses propagating in a two-level medium. It is found that the higher spectral components can be controlled by the absolute phases. In particular, different absolute phase combinations can lead to the buildup or split of the even harmonics. (c) 2006 Elsevier B.V. All rights reserved.

Pulse NMR in solids : chemical shift, lead fluoride and thorium hydride

Part one of this thesis consists of two sections. In the first section the fluorine chemical shift of a single crystal CaF_2 has been measured as a function of external pressure up to 4 kilobar at room temperature using multiple pulse NMR techniques. The pressure dependence of the shift is found to be -1.7 ± 1 ppm/kbar, while a theoretical calculation using an overlap model predicts a shift of -0.46 ppm/kbar. In the second section a separation of the chemical shift tensor into physically meaningful "geometrical" and "chemical" contributions is presented and a comparison of the proposed model calculations with recently reported data on hydroxyl proton chemical shift tensors demonstrates, that for this system, the geometrical portion accounts for the qualitative features of the measured tensors.

Part two of the thesis consists of a study of fluoride ion motion in β-PbF_2 doped with NaF by measurement of the ^(19)F transverse relaxation time (T_2), spin lattice relaxation time (T_1) and the spin lattice relaxation time in the rotating frame (T_(1r)). Measurements over the temperature range of -50°C to 160°C lead to activation energies for T_1, T_(1r) and T_2 of 0.205 ± 0.01, 0.29 + 0.02 and 0.27 ± 0.01 ev/ion, and a T_(1r) minimum at 56°C yields a correlation time of 0.74 μsec. Pressure dependence of T_1 and T_2 yields activation volumes of <0.2 cm^3/g-mole and 1.76 ± 0.05 cm^3/g-mole respectively. These data along with the measured magnetic field independence of T_1 suggest that the measured T_1's are not caused by ^(19)F motion, but by thermally excited carriers.

Part three of the thesis consists of a study of two samples of Th_4H_(15), prepared under different conditions but both having the proper ratio of H/Th (to within 1%). The structure of the Th_4H_(15) as suggested by X-ray measurements is confirmed through a moment analysis of the rigid lattice line shape. T_1 and T_2 measurements above 390 K furnish activation energies of 16.3 ± 1.2 kcal/mole and 18.0 ± 3.0 kcal/mole, respectively. Below 350 K, T_(1r) measurements furnish an activation energy of 10.9 ± 0.7 kcal/mole, indicating most probably more than a single mechanism for proton motion. A time-temperature hysteresis effect of the proton motion was found in one of the two samples and is strongly indicative of a phase change. T_1 at room temperature and below is dominated by relaxation due to conduction electrons with the product T_1T being 180 ± 10 K-sec. Using multiple pulse techniques to greatly reduce homonuclear dipolar broadening, a temperature-dependent line shift was observed, and the chemical shift anisotropy is estimated to be less than 16 ppm.

Spin dynamics of pulsed nuclear magnetic double resonance in solids

In the first part of this thesis, experiments utilizing an NMR phase interferometric concept are presented. The spinor character of two-level systems is explicitly demonstrated by using this concept. Following this is the presentation of an experiment which uses this same idea to measure relaxation times of off-diagonal density matrix elements corresponding to magnetic-dipole-forbidden transitions in a ^(13)C-^1H, AX spin system. The theoretical background for these experiments and the spin dynamics of the interferometry are discussed also.

The second part of this thesis deals with NMR dipolar modulated chemical shift spectroscopy, with which internuclear bond lengths and bond angles with respect to the chemical shift principal axis frame are determined from polycrystalline samples. Experiments using benzene and calcium formate verify the validity of the technique in heteronuclear (^(13)C-^1H) systems. Similar experiments on powdered trichloroacetic acid confirm the validity in homonuclear (^1H- ^1H) systems. The theory and spin dynamics are explored in detail, and the effects of a number of multiple pulse sequences are discussed.

The last part deals with an experiment measuring the ^(13)C chemical shift tensor in K_2Pt(CN)_4Br_(0.3) • 3H_2O, a one-dimensional conductor. The ^(13)C spectra are strongly affected by ^(14)N quadrupolar interactions via the ^(13)C - ^(14)N dipolar interaction. Single crystal rotation spectra are shown.

An appendix discussing the design, construction, and performance of a single-coil double resonance NMR sample probe is included.

The energy spectra of uranium atoms sputtered from uranium metal and uranium dioxide targets

The energy spectra of ²³⁵U atoms sputtered from a 93% enriched ²³⁵U metal foil and a hot pressed ²³⁵U0₂ pellet by an 80 keV ⁴⁰Ar⁺ beam have been measured in the range 1 eV to 1 keV. The measurements were made using a mechanical time-of-flight spectrometer in conjunction with the fission track technique for detecting ²³⁵U. The design and construction of this spectrometer are discussed in detail, and its operation is mathematically analyzed.

The results of the experiment are discussed in the context of the random collision cascade model of sputtering. The spectrum obtained by the sputtering of the ²³⁵U metal target was found to be well described by the functional form E(E+E_b)^-2.77, where E_b = 5.4 eV. The ²³⁵U0₂ target produced a spectrum that peaked at a lower energy (~ 2 eV) and decreased somewhat more rapidly for E ≳ 100 eV.

Buffer-gas-induced narrowing of electromagnetically induced transparent spectra for an open system

We have investigated the spectra of the electromagnetically induced transparency (EIT) when a cell is filled with a buffer gas. Our theoretical results show that the buffer gas can induce a narrower spectra line and steeper dispersion than those of the usual EIT case in a homogeneous and Doppler broadened system. The linewidth decreases with the increase of the buffer gas pressure. This narrow spectra may be applied to quantum information processing, nonlinear optics and atomic frequency standard.