<p>This dissertation discusses theoretical methods for describing photoionization in different systems in the context of time-dependent and time-independent non-relativistic and time-independent relativistic systems. We introduce a multichannel quantum defect theory (MQDT) model for describing photoionization in the context of pump-probe experiments. The basics of MQDT are introduced and specialized to the argon atom. Two energy regimes are studied in detail and compared to the experiment: (i) a perturbative calculation describing the dynamics of an autoionizing wave packet, (ii) a time-resolved calculation describing the two-photon ionization of a deeply bound wave packet. In both cases, the model accurately describes the relative ionization with respect to the two spin-orbit split thresholds of the ion and the oscillations shown in the delay between the pump and probe. We finalize with a brief presentation, which is primarily pedagogical, of how to use MQDT inside a finite box.</p> <p>Next, we use MQDT to describe the ytterbium atom in different energy regimes and varying degrees of approximation. The motivation behind this lies in the context of quantum information science, but our study is only concerned with calculating atomic properties. We start with a minimal MQDT model to describe the data observed in the experiment, followed by the presentation of an ab initio two-electron model. Both models compare very well to the experiment, and the ab initio method compares favorably with older spectroscopic results. In addition, we show unpublished results that incorporate the hyper-fine effects into the approximate model.</p> <p>Finally, we present an implementation of the two-electron variational R-matrix method for the Dirac equation, including the complete derivation of the solution of the Dirac equation in a central potential. We provide explicit analytic forms for the solutions of the Coulomb potential and use them to derive the generalized quantum defect parameters. A discussion of the variational R-matrix method for the Dirac equation in single and multichannel contexts is presented, with sample calculations for the beryllium and radium atoms. A chapter that summarizes and points to future work for each one of the projects concludes the work.</p>

<p dir="ltr">Following the development of laser technology in the 1960s, radiation pressure was soon employed to manipulate particles by Arthur Ashkin in the 1970s. Since then, levitated optomechanics has been widely studied across physics, engineering, chemistry, and biology. In this dissertation, we first experimentally demonstrate GHz rotation and sensing with an optically levitated nanodumbbell near a surface. Then, we propose achieving optical refrigeration below liquid nitrogen temperature using near-field Purcell enhancement.</p><p dir="ltr">The first part of this dissertation focuses on fast rotation and sensing with a non-spherical silica nanoparticle levitated near a surface. Specifically, we optically levitate a nanodumbbell at 430 nm away from a surface in high vacuum and drive it to rotate at 1.6 GHz. This corresponds to a relative linear velocity of 1.4 km/s between the tip of the nanodumbbell and the surface at sub-micrometer separation. The near-surface rotating nanodumbbell demonstrates a superior torque sensitivity of (5.0 +/- 1.1 ) x 10^-26 Nm at room temperature. Our numerical simulation shows that such an ultra-sensitive nanodumbbell levitated near nanostructures can be used to detect fundamental physics, such as Casimir torque and non-Newtonian gravity. </p><p dir="ltr">In the latter part of this dissertation, we propose that optical refrigeration of solid with anti-Stokes fluorescence can be enhanced by Purcell effect. The spontaneous emission rate of high-energy photons is Purcell enhanced by coupling with a near-field cavity. The enhanced emission shifts the mean emission wavelength and enables optical refrigeration with high-absorption cooling laser. We estimate a minimum achievable temperature of 38 K with a Yb³⁺:YLiF₄ nanocrystal near a cavity using our proposed Purcell enhanced optical refrigeration method. This method can be applied to other rare-earth ion doped materials and enable applications that require solid-state cooling below liquid nitrogen temperature.</p>

Understanding the complexities of the interior of planets and stars requires the help of analyzing the effects of high pressures on certain elements believed to be found within. The Hartree-Fock method uses the Schr¨odinger equation, Kummer’s differential equations and a confinement potential to simulate an atom being squeezed to high pressures. The Hartree-Fock method was used to calculate the total energies of atoms. After being compared to Gaussian03 and VASP, the results were deemed accurate. It was also observed that the pressure versus density data closely approximated those pairs found in outer space in the interiors of, for example, Jupiter.

This thesis addresses the investigation of doubly excited 2l´nl states in helium atoms and double core excitations in solid lithium compounds. Measurements on He are made in field free environments and under the influence of electric and magnetic fields, using synchrotron based inelastic photon scattering. Cross sections for scattering to singly excited final states are directly determined and compared to theoretical results and are found to be in excellent agreement. Radiative and spin-orbit effects are quantified and are shown to play an important role in the overall characterization of highly excited He states below the N =2 threshold. A dramatic electric field dependence is also observed in the flourecence yield already for relatively weak fields. This signal increase, induced by electric as well as magnetic fields, is interpreted in terms of mixing with states of higher fluorescence branching ratios. Double core excitations at the lithium site in solid lithium compounds are investigated using resonant inelastic x-ray scattering (RIXS). The lithium halides LiF, LiCl, LiBr and LiI are studied as well as the molecular compounds Li2O, Li2CO3 and LiBF4. States with one, as well as both, of the excited electrons localized at the site of the bare lithium nucleus are identified, and transitions which involve additional band excitations are observed. A strong influence of the chemical surrounding is found, and it is discussed in terms of the ionic character of the chemical bond.

<p>This thesis addresses the investigation of doubly excited <i>2l´nl</i> states in helium atoms and double core excitations in solid lithium compounds.</p><p>Measurements on <i>He</i> are made in field free environments and under the influence of electric and magnetic fields, using synchrotron based inelastic photon scattering. Cross sections for scattering to singly excited final states are directly determined and compared to theoretical results and are found to be in excellent agreement. Radiative and spin-orbit effects are quantified and are shown to play an important role in the overall characterization of highly excited <i>He </i>states below the <i>N =2</i> threshold. A dramatic electric field dependence is also observed in the flourecence yield already for relatively weak fields. This signal increase, induced by electric as well as magnetic fields, is interpreted in terms of mixing with states of higher fluorescence branching ratios.</p><p>Double core excitations at the lithium site in solid lithium compounds are investigated using resonant inelastic x-ray scattering (RIXS). The lithium halides <i>LiF, LiCl, LiBr</i> and <i>LiI </i>are studied as well as the molecular compounds <i>Li</i><i>2</i><i>O, Li</i><i>2</i><i>CO</i><i>3</i> and <i>LiBF</i><i>4</i>. States with one, as well as both, of the excited electrons localized at the site of the bare lithium nucleus are identified, and transitions which involve additional band excitations are observed. A strong influence of the chemical surrounding is found, and it is discussed in terms of the ionic character of the chemical bond.</p>

Polymer electrolytes are the most obvious candidates for safe "all-solid" Li-ion batteries and other electrochemical devices. However, they still have relatively poor ionic conductivities, which limits their wider adoption in commercial applications. It has earlier been the conventional wisdom that only amorphous phases of polymer electrolytes show usefully high ionic conduction, while crystalline forms are insulators. However, this has been challenged in the last decade by the discovery of highly organized, low-dimensional ion-conducting materials. Specifically, the crystalline phases of LiXF6.PEO6 exhibit higher ionic conductivities than their amorphous counterparts, with the Li-ion conduction taking place along the PEO channels. Polymer chain-length and chain-end registry has emerged as potentially significant in determining ionic conduction in these materials. Molecular Dynamics simulations have therefore been made of short-chain, monodisperse (Mw~1000), methoxy end-capped LiPF6.PEO6 to examine relationships between ion conduction and mode of chain-ordering. Studies of smectic and nematic arrangements of PEO chains have revealed that ion-transport mechanisms within the smectic planes formed by cooperative chain-end registry appear to be more suppressed by ion-pairing than in-channel conduction. Disorder phenomena in the chain-end regions emerge as a critical factor in promoting Li-ion migration across chain-gaps, as does the structural continuity of the PEO channels. Simulations incorporating ~1% aliovalent SiF62- dopants further suggest an increase in Li-ion conduction when the extra Li-ions reside within the PEO channels, with the anion influencing charge-carrier concentration through enhanced ion-pair formation. XRD techniques alone are shown to be inadequate in ascertaining the significance of the various short-chain models proposed; atomistic modelling is clearly a helpful complement in distinguishing more or less favourable situations for ion conduction. Though providing valuable insights, it must be concluded that this work has hardly brought us significantly closer to breakthroughs in polymer electrolyte design; the critical factors which will make this possible remain as yet obscure.

We are developing a novel classical over-the barrier model for electron transfer from an in nitely thin conducting disc to a point charge projectile to model multiple electron capture in e.g. keV collisions of atomic ions with poly-cyclic aromatic hydrocarbons (PAHs). In its nal form, the present model will incorporate the polarization of the PAH molecules due to the active electron and the point charge projectile at a general angle of incidence. This will drastically improve the description of the potential barrier in comparisons with simpler versions of the model where the nite size and polarizability of the target molecule is neglected or treated in an averaged fashion. In this work we arrive at expressions for the electrostatic potential energy barrier experienced by the active electron in the two spatial orientations where the point charge projectile is located along the normal symmetry axis and in the tangent plane of the disc. Applied to coronene (C24H12) such barriers compare better with high level density functional theory (DFT) calculations than with the results from the simpler versions of the classical over-the-barrier models for atomic and spherical cluster targets. These results thus strongly supports the conducting disc approximation of PAHs. Finally we discuss the nal steps in the model development and possible extensions of the model to include less symmetric elliptical discs or spherical caps.

Laser-cooled atomic ions have led to an unprecedented amount of control over the quantum states of matter. The Coulombic interaction allows for information to be transferred between neighboring ions, and this interaction can be used to entangle qubits for logic operations in quantum information processors. The same procedure for logic operations can be used for high resolution atomic spectroscopy, and is the basis for the most accurate atomic optical clocks to date. This thesis describes how laser-cooled atomic ions can impact physical chemistry through the development of molecular ion spectroscopy techniques and the simulation of magnetic systems by ion trap quantum computers. A new technique developed for spectroscopy, Sympathetic Heating Spectroscopy (SHS), takes advantage of the Coulombic interaction between two trapped ions: the control ion and a spectroscopy ion. SHS uses the back action of the interrogating laser to map spectroscopy ion information onto the Doppler shift of the control ion for measurement. SHS only requires Doppler cooling of the ions and fluorescence measurement and represents a simplification of quantum logic spectroscopy. This technique is demonstrated on two individual isotopes of calcium: Ca-40(+) for cooling and Ca-44(+) as the spectroscopy ion. Having demonstrated SHS with atomic ions, the next step was to extend the technique by loading and characterizing molecular ions. The identification of an unknown molecular ion is necessary and can be achieved by monitoring the change in motion of the two ion crystal, which is dependent on the molecular ion mass. The motion of two trapped ions is described by their normal modes, which can be accurately measured by performing resolved sideband spectroscopy of the S(1/2)-D(5/2) transition of calcium. The resolved sidebands can be used to identify unknown ions (atomic and molecular) by calculating the mass based on the observed value in axial normal mode frequencies. Again, the trapped molecular ion is sympathetically cooled via the Coulombic interaction between the Ca-40(+) and the unknown molecular ion. The sensitivity of SHS could be improved by implementing sympathetic sideband cooling and determining the heating by measuring single quanta of motion. The ultimate limit of control would be the development of an ion trap quantum computer. Many theoretical quantum computing researchers have made bold claims of the exponential improvement a quantum computer would have over a classical computer for the simulation of physical systems such as molecules. These claims are true in principle for ideal systems, but given non-ideal components it is necessary to consider the scaling due to error correction. An estimate of the resource requirements, the total number of physical qubits and computational time, required to compute the ground state energy of a 1-D quantum Transverse Ising Model (TIM) of N spin-1/2 particles, as a function of the system size and the numerical precision, is presented. This estimate is based on analyzing the impact of fault-tolerant quantum error correction in the context of the quantum logic array architecture. The results show that a significant amount of error correction is required to implement the TIM problem due to the exponential scaling of the computational time with the desired precision of the energy. Comparison of this result to the resource requirements for a fault-tolerant implementation of Shor's quantum factoring algorithm reveals that the required logical qubit reliability is similar for both the TIM problem and the factoring problem.

The present thesis is devoted to theoretical studies of resonant X-ray scattering and propagation of strong X-ray pulses. In the first part of the thesis the nuclear dynamics of different molecules is studied using resonant X-ray Raman and resonant Auger scattering techniques. We show that the shortening of the scattering duration by the detuning results in a purification of the Raman spectra from overtones and soft vibrational modes. The simulations are in a good agreement with measurements, performed at the MAX-II and the Swiss Light Source with vibrational resolution. We explain why the scattering to the ground state nicely displays the vibrational structure of liquid acetone in contrast to excited final state. Theory of resonant X-ray scattering by liquids is developed. We show that, contrary to aqueous acetone, the environmental broadening in pure liquid acetone is twice smaller than the broadening by soft vibrational modes significantly populated at room temperature. Similar to acetone, the "elastic" band of X-ray Raman spectra of molecular oxygen is strongly affected by the Thomson scattering. The Raman spectrum demonstrates spatial quantum beats caused by two interfering wave packets with different momenta as the oxygen atoms separate. It is found that the vibrational scattering anisotropy caused by the interference of the "inelastic" Thomson and resonant scattering channels in O2. A new spin selection rule is established in inelastic X-ray Raman spectra of O2. It is shown that the breakdown of the symmetry selection rule based on the parity of the core hole, as the core hole and excited electron swap parity. Multimode calculations explain the two thresholds of formation of the resonant Auger spectra of the ethene molecule by the double-edge structure of absorption spectrum caused by the out-of- and in-plane modes. We predict the rotational Doppler effect and related broadening of X-ray photoelectron and resonant Auger spectra, which has the same magnitude as its counterpart-the translational Doppler effect. The second part of the thesis explores the interaction of the medium with strong X-ray free-electron laser (XFEL) fields. We perform simulations of nonlinear propagation of femtosecond XFEL pulses in atomic vapors by solving coupled Maxwell's and density matrix equations. We show that self-seeded stimulated X-ray Raman scattering strongly influences the temporal and spectral structure of the XFEL pulse. The generation of Stokes and four-wave mixing fields starts from the seed field created during pulse propagation due to the formation of extensive ringing pattern with long spectral tail. We demonstrate a compression into the attosecond region and a slowdown of the XFEL pulse up to two orders of magnitude. In the course of pulse propagation, the Auger yield is strongly suppressed due to the competitive channel of stimulated emission. We predict a strong X-ray fluorescence from the two-core-hole states of Ne created in the course of the two-photon X-ray absorption. / QC 20110426

The possibility and feasibility is investigated of including in the modelling of nuclear cluster reactions a unified treatment of the effects both of the non-orthogonalities between transfer channels, and of the antisymmetrisation required by the Pauli Principle. The deuteron - nucleus interaction, the simplest cluster reaction, is considered in detail within the Coupled Channels framework. The Coupled Channels formalism was chosen because it accurately handles inelastic and transfer couplings of arbitary strengths. The fact that transfer channels are orthogonal to each other only asymptotically is taken into account by reallocating the wave function in the internal region, from the deuteron channels to the transfer channels, taking components from the deuteron channels in ways exactly analogous to the way the antisymmetrisation requirements remove blocked deuteron-core components. Thus a unified treatment of the two effects is facilitated. It is found further that when all possible transfer channels are included, along with all Pauli blockings from the core nucleons, then under certain conditions at low energies, the wave function in the deuteron channel is small and oscillatory in the internal region, leaving the deuteron as a cluster to have largely asymptotic significance. In this limit, the exact non-local potential governing the deuteron channel simplifies considerably in one approximation to be replaceable by just several orthogonality conditions, and these are easily modelled in solving the coupled equations for the radial wave functions. This simplified and unified model has the advantage, since the deuteron's internal wave form is significant only asymptotically, of allowing automatically for arbitary deuteron polarisation by the core (though not vice-versa). Furthermore, the asymptotic matching is not at a fixed radius as in R-matrix theory, but is a continuous process that depends on the binding energies of the actual proton & neutron bound states in the residual nucleus.