In this work, we present state-of-the-art numerical methods and their applications for computing a particular class of observables using lattice quantum chromodynamics (Lattice QCD), a discretized version of the fundamental theory of quarks and gluons. These observables require calculating so called "disconnected diagrams" and are important for understanding many aspects of hadron structure, such as the strange content of the proton. We begin by introducing the reader to the key concepts of Lattice QCD and rigorously define the meaning of disconnected diagrams through an example of the Wick contractions of the nucleon. Subsequently, the calculation of observables requiring disconnected diagrams is posed as the computationally challenging problem of finding the trace of the inverse of an incredibly large, sparse matrix. This is followed by a brief primer of numerical sparse matrix techniques that overviews broadly used methods in Lattice QCD and builds the background for the novel algorithm presented in this work. We then introduce singular value deflation as a method to improve convergence of trace estimation and analyze its effects on matrices from a variety of fields, including chemical transport modeling, magnetohydrodynamics, and QCD. Finally, we apply this method to compute observables such as the strange axial charge of the proton and strange sigma terms in light nuclei. The work in this thesis is innovative for four reasons. First, we analyze the effects of deflation with a model that makes qualitative predictions about its effectiveness, taking only the singular value spectrum as input, and compare deflated variance with different types of trace estimator noise. Second, the synergy between probing methods and deflation is investigated both experimentally and theoretically. Third, we use the synergistic combination of deflation and a graph coloring algorithm known as hierarchical probing to conduct a lattice calculation of light disconnected matrix elements of the nucleon at two different values of the lattice spacing. Finally, we employ these algorithms to do a high-precision study of strange sigma terms in light nuclei; to our knowledge this is the first calculation of its kind from Lattice QCD.

This thesis presents progress in developing a trapped atom interferometer on a chip, based on AC Zeeman potentials. An atom interferometer is a high-precision measuring tool that can detect various types of forces and potentials. The trapped atom interferometer introduced in this thesis targets the shortcomings of traditional ballistic atom interferometers, which are typically meter-scale in height. Notably, a trapped atom interferometer has a localized atomic sample, a potentially longer interferometric phase accumulation time, and the prospect of being the basis for a more compact instrument. This thesis presents multiple projects in the development of a trapped atom interferometer based on the AC Zeeman potentials and traps: 1) production of ultracold potassium on a chip, 2) the theory of potential roughness in chip traps, 3) microwave chip trap design, and 4) a trapped atom interferometer with rubidium atoms, based on a laser dipole trap and an AC Zeeman force. (1) Potassium is a good candidate for the atom interferometer due to its bosonic and fermionic isotopes, multiple "magic" magnetic fields, and the convenience of RF and microwave trapping. The laser cooling and trapping system were upgraded to improve the temperature and population of potassium atoms in the chip trap. On-chip cooling resulted in a significant inelastic loss, which prevented the production of a potassium Bose-Einstein condensate. (2) Numerical simulations of chip wire defects predict that the AC Zeeman trapping potential should be substantially smoother than its DC Zeeman counterpart: the suppression of the roughness is due to magnetic polarization selection rules and the AC skin effect. (3) Furthermore, the thesis presents a number of studies on the straight and curved microstrip transmission lines that form the building blocks of the microwave atom chip for the AC Zeeman trap. (4) Finally, we constructed a rubidium-based Ramsey interferometer that can be converted to an atom interferometer by applying a spin-dependent AC Zeeman force: the interferometer was used to measure DC and AC Zeeman energy shifts and fringes were observed with an AC Zeeman force.

This thesis presents the first experimental demonstration of a two-wire AC Zeeman trap on an atom chip. The AC Zeeman energy is a resonant, bipolar, state-dependent atomic energy shift produced by alternating magnetic fields with frequencies near hyperfine transitions. We demonstrate that high gradients in this energy, as near an atom chip, can produce a spin-state selective force greater than gravity for ultracold rubidium atoms. Our novel trap is generated by a local minimum in AC Zeeman energy. Using less than one watt of power, we demonstrate trap frequency on the order of a few hundred Hz, trap depth about 5 μK, and quarter-second lifetimes. Motivated by trapped atom interferometry, this proof of principle AC Zeeman trap can also augment atom and ion experiments as a dynamic spin-dependent potential. Different parameters in the current arrangement can produce regions of linear gradient, flat saddle points, square- and donut-shaped traps, offering a new set of tools for atom chip experiments. This thesis also presents the relevant dressed atomic theory, four AC Zeeman trap designs, Rabi frequency measurements, numerical trap simulations, and the AC skin effect in wide rectangular wires.

This thesis presents the design, fabrication and testing of novel grating based Optical Fibre Sensor (OFS) systems being interrogated using “off the shelf” interrogation systems, with the eventual development of marketable commercial systems at the forefront of the research. Both in the industrial weighing and aerospace industries, there has been a drive to investigate the feasibility of using optical fibre sensors being deployed where traditionally their electrical or mechanical counterparts would traditionally have been. Already, in the industrial weighing industry, commercial operators are deploying OFS-based Weigh-In-Motion (WIM) systems. Likewise, in the aerospace industry, OFS have been deployed to monitor such parameters as load history, impact detection, structural damage, overload detection, centre of gravity and the determination of blade shape. Based on the intrinsic properties of fibre Bragg gratings (FBGs) and Long Period Fibre Gratings (LPFGs), a number of novel OFS-based systems have been realised. Experimental work has shown that in the case of static industrial weighing, FBGs can be integrated with current commercial products and used to detect applied loads. The work has also shown that embedding FBGs in e-glass, to form a sensing patch, can result in said patches being bonded to rail track, forming the basis of an FBG-based WIM system. The results obtained have been sufficiently encouraging to the industrial partner that this work will be progressed beyond the scope of the work presented in this thesis. Likewise, and to the best of the author’s knowledge, a novel Bragg grating based systems for aircraft fuel parameter sensing has been presented. FBG-based pressure sensors have been shown to demonstrate good sensitivity, linearity and repeatability, whilst LPFG-based systems have demonstrated a far greater sensitivity when compared to FBGs, as well the advantage of being potentially able to detect causes of fuel adulteration based on their sensitivity to refractive index (RI). In the case of the LPFG-based system, considerable work remains to be done on the mechanical strengthening to improve its survivability in a live aircraft fuel tank environment. The FBG system has already been developed to an aerospace compliant prototype and is due to be tested at the fuel testing facility based at Airbus, Filton, UK. It is envisaged by the author that in both application areas, continued research in this area will lead to the eventual development of marketable commercial products.

Knowledge of the electric and magnetic elastic form factors of the nucleon is essential for an understanding of nucleon structure. of the form factors, the electric form factor of the neutron has been measured over the smallest range in Q2 and with the lowest precision. Jefferson Lab experiment 02-013 used a novel new polarized 3He target to nearly double the range of momentum transfer in which the neutron form factor has been studied and to measure it with much higher precision. Polarized electrons were scattered off this target, and both the scattered electron and neutron were detected. GEn was measured to be 0.0242 +/- 0.0020(stat) +/- 0.0061(sys) and 0.0247 +/- 0.0029(stat) +/- 0.0031(sys) at Q2 = 1.7 and 2.5 GeV2, respectively.

Solid state deuteron NMR experiments, especially magic angle spinning (MAS) and off-magic angle spinning (OMAS), are developed to explore dynamical systems. A theoretical discussion of interactions relevant for spin-1 nuclei is presented. Practical aspects of MAS/OMAS experiments are described an detail. The dominant quadrupolar coupling interaction in deuteron NMR has been simulated and the effects of multiple-frame molecular motions on MAS/OMAS spectra are taken into account in this calculation. Effects of chemical shift anisotropy are also simulated, and shown to be small under conditions of rapid sample spinning.;Two numerical methods, direct integration and an efficient simulation routine based on Floquet thoery, are discussed. Improvements in computational efficiency of the Floquet method in computing solid stae deuteron MAS/OMAS spectrum makes the quantitative analysis of molecular motion possible: complex multiple frame molecular motions, deuteron quadrupolar interactions and chemical shift anisotropy are now included in a single simulation routine and the effects of the multiple-frame molecular motions can be analyzed by comparing the line shapes of simulations with those of experiments.;The enhanced motional sensitivity of deuteron NMR MAS/OMAS makes it possible to detect temperature-dependent motion rates of urea molecules in octanoic acid/urea inclusion compounds. Temperature-dependent deuteron OMAS line shapes have been recorded and fitted through least-square procedures, to provide rates of rotation about both CN and CO bonds. Activation energies have been calculated for these motions. The power and utility of OMAS is demonstrated by this investigation.;The phenyl ring motions in appropriately labeled L-phenylalanine and N-acetyl-L-phenylalanine methyl ester/cyclodextrin inclusion compound have also been studied through high field deuteron MAS experiments. Phenylalanine MAS spectra with ultra-fast ring-flip motion have been simulated and the range of phenyl ring flip rates is obtained by comparing the simulated and experimental spectra. In the studies of phenylalanine/cyclodextrin inclusion compound, an approach to a physically reasonable diffusion model has also been made by increasing the number of jump sites per unit solid angle included in the calculation. These simulations involve repeated diagonalization of very large matrices and demonstrate the capability of the approach to handle complex dynamical systems.

In recent years, a great deal of progress has been made in understanding the ionization processes that result from the interaction of an intense laser pulse with multielectron atoms. However, due to experimental limitations, the effect of the laser field's spatial dependence on strong-field processes has rarely been investigated. Presented in this work is a theoretical analysis of this spatial dependence including a proposal for an experimentally observable result of the phenomenon. We begin by outlining the elements of the laser field that will vary as a function of position and show their effects on simple free electron trajectories. We then develop a classical, three-dimensional simulation of the entire process of double ionization of helium in an intense laser field using realistic, non-paraxial focal conditions. The existence of an out-of-phase electric field component in the laser propagation direction is determined, which produces an effective longitudinal ellipticity, resulting in a reduction in the double ion yields as a function of position in the laser focus. It is found that under conditions of tight focusing, the effective focal volume for non-sequential double ionization is significantly reduced.

The recent prospect of efficient, reliable, and secure quantum communication relies on the ability to coherently and reversibly map nonclassical states of light onto long-lived atomic states. A promising technique that accomplishes this employs Electromagnetically Induced Transparency (EIT), in which a strong classical control field modifies the optical properties of a weak signal field in such a way that a previously opaque medium becomes transparent to the signal field. The accompanying steep dispersion in the index of refraction allows for pulses of light to be decelerated, then stored as an atomic excitation, and later retrieved as a photonic mode. This dissertation presents the results of investigations into methods for optimizing the memory efficiency of this process in an ensemble of hot Rb atoms. We have experimentally demonstrated the effectiveness of two protocols for yielding the best memory efficiency possible at a given atomic density. Improving memory efficiency requires operation at higher optical depths, where undesired effects such as four-wave mixing (FWM) become enhanced and can spontaneously produce a new optical mode (Stokes field). We present the results of experimental and theoretical investigations of the FWM-EIT interaction under continuous-wave (cw), slow light, and stored light conditions. In particular, we provide evidence that indicates that while a Stokes field is generated upon retrieval of the signal field, any information originally encoded in a seeded Stokes field is not independently preserved during the storage process. We present a simple model that describes the propagation dynamics and provides an intuitive description of the EIT-FWM process.

At the Thomas Jefferson National Accelerator Facility, glass target cells containing a high density of highly polarized 3He nuclei are used in electron scattering experiments studying the substructure of the neutron. In addition to 3He, these cells contain a small amount of rubidium (Rb), potassium (K), and nitrogen (N2), which facilitate the polarization process. The work presented here represents studies of the interactions between the alkali vapor and 3He nuclei when both are polarized and unpolarized.;Our investigations into the mechanisms responsible for the relaxation of the 3He polarization have measured unusually large polarization losses. In addition, most cells studied exhibited polarization lifetimes much shorter than those typically observed in cells used for scattering experiments. These results suggest there are relaxation mechanisms that depend on whether the cell contains polarized or unpolarized alkali vapor, solid alkali, or no alkali. Previous cell studies have assumed these relaxation mechanisms are independent of the presence of alkali in any form. Modication of the polarization rate equations to include these new relaxation mechanisms are given. Further studies are needed to fully understand the origin of these additional relaxation mechanisms.;Studies of the interactions between 3He and alkali vapor, when both are unpolarized, were motivated by the need to determine the number density of 3He inside sealed cells. The system we have implemented to measure the number density examines the broadening of the absorption profiles of the D1 and D2 lines of Rb and K due to collisions with 3He and N2. However, in order to relate this broadening to the gas density, the value of the velocity-averaged collisional cross-section (broadening coefficient) for the interacting pair of atoms must be known. While the value of the coefficient has been measured for Rb, no data have been published for K interacting with 3He at the high number densities required for scattering experiments. Furthermore, pressure broadening theory predicts a temperature dependence for the coefficients, but very little experimental data has been published. In addition to broadening, a shift in the central frequency is also predicted and has been experimentally verified. We have measured both the broadening and shift of the D1 and D2 lines of Rb and K in the presence of 3He and N2 over a range of number densities and temperatures.

This experiment measured the time distribution of muonic hydrogen atoms which were formed when negative muons were brought to rest in H{dollar}\sb2{dollar} gas, containing Au target foils, at five pressures (750 mbar, 375 mbar, 188 mbar, 94 mbar and 47 mbar at 4.6 mm foil spacing). A Monte Carlo method is applied for deducing the initial velocity distribution, and preliminary results are obtained. The initial velocity distribution of {dollar}\mu{dollar}H atoms is reasonably well described as a 'Maxwellian' velocity distribution with a mean energy E = 3.4 eV. The corresponding muon mean capture energy is obtained: E{dollar}\sb{lcub}\rm c{rcub}{dollar} {dollar}\approx{dollar} 34 eV for {dollar}\mu{dollar}H atom and E{dollar}\sb{lcub}\rm c{rcub}{dollar} {dollar}\approx{dollar} 68 eV for {dollar}\mu{dollar}H{dollar}\sb2{dollar} molecules. We also find the negative muon capture energy distribution is exponential.;In addition, a significant improvement of the negative muon mean life {dollar}\tau{dollar} in Au is abtained in this experiment.: {dollar}\tau\sb{lcub}\rm Au{rcub}{dollar} = 69.716 {dollar}\pm{dollar} 0.144 ns. The "full decay curve fitting method" which we use in this experiment has an advantage over the previous method in three aspects: (1) We have measured the mean life and determined the time resolution {dollar}\sigma{dollar}(E) of a detector at a particular energy level; (2) We have determined the effective zero time of the decay curve; (3) We have provided a possible way to measure the mean life {dollar}\tau{dollar} when {dollar}\tau{dollar} is less than the time resolution {dollar}\sigma{dollar}(E) of the detector ({dollar}\tau{dollar} {dollar}<{dollar} {dollar}\sigma{dollar}(E)).