<p> Quantum Monte Carlo techniques stochastically evaluate integrals to solve the many-body Schr&ouml;dinger equation. QMC algorithms scale favorably in the number of particles simulated and enjoy applicability to a wide range of quantum systems. Advances in the core algorithms of the method and their implementations paired with the steady development of computational assets have carried the applicability of QMC beyond analytically treatable systems, such as the Homogeneous Electron Gas, and have extended QMC&rsquo;s domain to treat atoms, molecules, and solids containing as many as several hundred electrons.</p><p> FN-DMC projects out the ground state of a wave function subject to constraints imposed by our ansatz to the problem. The constraints imposed by the fixed-node Approximation are poorly understood. One key step in developing any scientific theory or method is to qualify where the theory is inaccurate and to quantify how erroneous it is under these circumstances.</p><p> I investigate the fixed-node errors as they evolve over changing charge density, system size, and effective core potentials. I begin by studying a simple system for which the nodes of the trial wave function can be solved almost exactly. By comparing two trial wave functions, a single determinant wave function flawed in a known way and a nearly exact wave function, I show that the fixed-node error increases when the charge density is increased. Next, I investigate a sequence of Lithium systems increasing in size from a single atom, to small molecules, up to the bulk metal form. Over these systems, FN-DMC calculations consistently recover 95% or more of the correlation energy of the system. Given this accuracy, I make a prediction for the binding energy of Li₄ molecule. Last, I turn to analyzing the fixed-node error in first and second row atoms and their molecules. With the appropriate pseudo-potentials, these systems are iso-electronic, show similar geometries and states. One would expect with identical number of particles involved in the calculation, errors in the respective total energies of the two iso-electronic species would be quite similar. I observe, instead, that the first row atoms and their molecules have errors larger by twice or more in size. I identify a cause for this difference in iso-electronic species. The fixed-node errors in all of these cases are calculated by careful comparison to experimental results, showing that FN-DMC to be a robust tool for understanding quantum systems and also a method for new investigations into the nature of many-body effects.</p>

<p> The Baranger model is used to compute collisional broadening and shift of the D1 and D2 spectral lines of M + Ng, where M = K, Rb, Cs and Ng = He, Ne, Ar, using scattering phase shift differences which are calculated from scattering matrix elements. Scattering matrix elements are calculated using the Channel Packet Method where the collisions are treated non-adiabatically and include spin-orbit and Coriolis couplings. Non-adiabatic wavepacket dynamics are determined using the split-operator method together with a unitary transformation between adiabatic and diabatic representations. Scattering phase shift differences are thermally weighted and integrated over energies ranging from E = 0 Hartree up to E = 0.0075 Hartree and averaged over values of total angular momentum that range from J = 0.5 up to J = 400.5. Phase shifts are extrapolated linearly to provide an approximate extension of the energy regime up to E = 0.012 Hartree. Broadening and shift coefficients are obtained for temperatures ranging from T = 100 K up to T = 800 K and compared with experiment. Predictions from this research find application in laser physics and specifically with improvement of total power output of Optically Pumped Alkali Laser systems.</p>

<p> The set of parameters used in the Goldstone-boson-exchange (GBE) model of quark-quark interactions by a group from the University of Graz to calculate baryon energy spectra is not optimal. A systematic approach to optimize these free parameters for a greater collection of baryons than previously treated is presented here. The baryons considered possess a physical symmetry where their constituent quarks are either made of all identical quarks or just two identical quarks. In order to calculate the various energy states of these baryons, the Faddeev method is used under the premise that three-quark interactions are modeled by an infinitely rising confinement potential. The new parameters and resulting energy calculations obtained yield better agreement with experimental data than previously achieved. In addition to providing a stronger case for the GBE model, these newfound parameters have the potential to give further insight into how quarks interact and pave the way for more advanced work in the field of three-quark problems.</p>

<p> Rare-earth-doped fiber lasers and amplifiers are relatively easy to efficiently produce a stable and high quality laser beam in a compact, robust, and alignment-free configuration. Recently, high power fiber laser systems have facilitated wide spread applications in academics, industries, and militaries in replacement of bulk solid-state laser systems. The master oscillator power amplifier (MOPA) composed of a highly-controlled seed, high-gain preamplifiers, and high-efficiency power amplifiers are typically utilized to scale up the pulse energy, peak power, or average power. Furthermore, a direct-current-modulated nanosecond diode laser in single transverse mode can simply provide a compact and highly-controlled seed to result in the flexible output parameters, such as repetition rate, pulse duration, and even temporal pulse shape. However, when scaling up the peak power for high intensity applications, such a versatile diode-seeded nanosecond MOPA laser system using rare-earth-doped fibers is unable to completely save its own advantages compared to bulk laser systems. Without a strong seeding among the amplifiers, the guided amplified spontaneous amplification is easy to become dominant during the amplification, leading to the harmful self-lasing or pulsing effects, and the difficulty of the quantitative numerical comparison. In this dissertation, we study a high-efficiency and intense nanosecond ytterbium fiber MOPA system with good beam quality and stability for high intensity applications. The all-PM-fiber structure is achieved with the output extinction ratio of >12 dB by optimizing the interconnection of high power optical fibers.</p><p> The diode-seeded MOPA configuration without parasitic stimulated amplification (PAS) is implemented using the double-pass scheme to extract energy efficiently for scaling peak power. The broadband PAS was studied experimentally, which matches well with our numerical simulation. The 1064-nm nanosecond seed was a direct-current-modulated Fabry-P&eacute;rot diode laser associated with a weak and pulsed noise spanning from 1045 to 1063 nm. Even though the contribution of input noise pulse is only &lt;5%, it becomes a significant transient spike during amplification. The blue-shifted pulsed noise may be caused by band filling effect for quantum-well seed laser driven by high peak current. The study helps the development of adaptive pulse shaping for scaling peak power or energy at high efficiency. On the other hand, the broadband spike with a 3-dB bandwidth of 8.8 nm can support pulses to seed the amplifier for sub-nanosecond giant pulse generation.</p><p> Because of the very weak seed laser, the design of high-gain preamplifier becomes critical. The utilization of single-mode core-pumped fiber preamplifier can not only improve the mode contrast without fiber coiling effect but also significantly suppress the fiber nonlinearity. The double-pass scheme was therefore studied both numerically and experimentally to improve energy extraction efficiency for the lack of attainable seed and core-pumped power. As a result, a record-high peak power of > 30 kW and energy of > 0.23 mJ was successfully achieved to the best of our knowledge from the output of clad-pumped power amplifier with a beam quality of M² &sim;1.1 in a diode-seeded 15-&micro;m-core fiber MOPA system. After the power amplifier, the MOPA conversion efficiency can be dramatically improved to >56% for an energy gain of >63 dB at a moderate repetition rate of 20 kHz with a beam quality of M² &lt;1.5. The output energy of >1.1 mJ with a pulse duration of &sim;6.1 ns can result in a peak power up to >116 kW which is limited by fiber fuse in long-term operation. Such a condition able to generate the on-target laser intensity of > 60 GW/cm² for applications is qualified to preliminarily create a laser-plasma light source. Moreover, the related simulation results also reveal the double-passed power amplifier can further simplify MOPA.</p><p> Such an intense clad-pumped power amplifier can further become a nonlinear fiber amplifier in all-normal dispersion instead of a nonlinear passive fiber. The combination of laser amplification and nonlinear conversion together can therefore overcome the significant pump depletion during the propagation along the passive fiber for power scaling. As a result, an intense spectrum spanning from 980 to 1600 nm as a high-power nanosecond supercontinuum source can be successfully generated with a conversion efficiency of >65% and a record-high peak power of >116 kW to the best of our knowledge. Because of MOPA structure, the influence of input parameters of nonlinear fiber amplifier on supercontinuum parameters can also be studied. The onset and interplay of fiber nonlinearities can be revealed stage by stage. Such an unique and linearly-polarized light source composed of an intense pump and broad sideband seed is beneficial for efficiently driving the broadband tunable optical parametric amplification free from the bulkiness and timing jitter.</p><p> Keywords: High power fiber laser and amplifier, ytterbium fiber, master oscillator power amplification, parasitic stimulated amplification, multi-pass fiber amplification, peak power/pulse energy scaling, fiber nonlinear optics, supercontinuum generation.</p>

<p> Laser cooling and trapping are central to modern atomic physics. It has been roughly three decades since laser cooling techniques produced ultracold atoms, leading to rapid advances in a vast array of fields and a number of Nobel prizes. Prior to the work presented in this thesis, laser cooling had not yet been extended to molecules because of their complex internal structure. However, this complexity makes molecules potentially useful for a wide range of applications. The first direct laser cooling of a molecule and further results we present here provide a new route to ultracold temperatures for molecules. In particular, these methods bridge the gap between ultracold temperatures and the approximately 1 kelvin temperatures attainable with directly cooled molecules (e.g. with cryogenic buffer gas cooling or decelerated supersonic beams). Using the carefully chosen molecule strontium monofluoride (SrF), decays to unwanted vibrational states are suppressed. Driving a transition with rotational quantum number <i>R</i>=1 to an excited state with <i> R'</i>=0 eliminates decays to unwanted rotational states. The dark ground-state Zeeman sublevels present in this specific scheme are remixed via a static magnetic field. Using three lasers for this scheme, a given molecule should undergo an average of approximately 100,000 photon absorption/emission cycles before being lost via unwanted decays. This number of cycles should be sufficient to load a magneto-optical trap (MOT) of molecules. In this thesis, we demonstrate transverse cooling of an SrF beam, in both Doppler and a Sisyphus-type cooling regimes. We also realize longitudinal slowing of an SrF beam. Finally, we detail current progress towards trapping SrF in a MOT. Ultimately, this technique should enable the production of large samples of molecules at ultracold temperatures for molecules chemically distinct from competing methods.</p>

<p> Superconducting qubits and resonators with quality factors exceeding 10⁷ are of great interest for quantum information processing applications. The improvement of present devices necessarily involves the consideration of participation ratios, which budget the influence of each physical component in the total energy decay rate. Experiments on compact resonators in which participation ratios were varied has demonstrated the validity of this method, yielding a two-fold improvement in quality factor. Similar experiments on compact transmon qubit devices led to a three-fold improvement over previous transmons, validating the method of participation ratios for qubits as well. Through the use of a 3D cavity, a further minimization of the participation of surface components combined with the removal of unnecessary components, produced an additional ten-fold increase in coherence times. Finally, the fluxonium qubit was redesigned in a similar minimalist environment with an improved superinductance, thus combining the advantages of the 3D architecture with the natural insensitivity to dissipation of the fluxonium, resulting in <i>another</i> tenfold increase in relaxation times. This large increase in relaxation and coherence times enables experiments that were previously impossible, thus preparing the field of quantum information to advance on other fronts.</p>

<p> After an introduction to the variational principle of three body systems via the Helium atom, we present general analytical formulas for the radial parts of integrals that occur when three body systems are described using wave functions that consist of powers and exponentials in all three interparticle Hylleraas coordinates [Hylleraas1929]. This work is an extension of integrals given by Harris, Frolov and Smith, Jr. [Harris2004]. Specifically included are radial integrals encountered in calculations involving the dipole moment matrix element in Hylleraas coordinates that contain a function <i>f(kr </i>₁) (such as a spherical Bessel function) in addition to a plane wave, a hydrogenic orbital and exponentials in all three interparticle coordinates.</p>

<p> Large vacuum fluctuations of a quantum stress tensor can be described by the asymptotic behavior of its probability distribution. Here we focus on stress tensor operators which have been averaged with a sampling function in time. The Minkowski vacuum state is not an eigenstate of the time-averaged operator, but can be expanded in terms of its eigenstates. We calculate the probability distribution and the cumulative probability distribution for obtaining a given value in a measurement of the time-averaged operator taken in the vacuum state. In these calculations, we use the normal ordered square of the time derivative of a massless scalar field in Minkowski spacetime as an example of a stress tensor operator. We analyze the rate of decrease of the tail of the probability distribution for different temporal sampling functions, such as compactly supported functions and the Lorentzian function. We find that the tails decrease relatively slowly, as exponentials of fractional powers, in agreement with previous work using the moments of the distribution. Our results lead additional support to the conclusion that large vacuum stress tensor fluctuations are more probable than large thermal fluctuations, and may have observable effects.</p><p>

<p> As the LHC enters its second run at 13 TeV, new parameter space will become available that will allow for a more extensive search for supersymmetric partners. This thesis explores limits on a baryon number violating R-parity-violating (RPV) extension of the s-channel production of top squarks, examining the experimental signature for the R-parity conserving decay of the top squark into the lightest neutralino and a hadronically decaying top quark. Using Monte Carlo simulations I calculate upper bounds for the RPV coupling parameters &lambda;'' for a range of top squark and neutralino masses that would allow for its existence. </p><p>

In this dissertation the parity violating neutron deuteron scattering amplitudes are calculated using pionless effective field theory to leading order. The five low energy parity violating constants present in pionless effective field theory are estimated by matching onto the ``best" values for the parameters of the model by Desplanques, Donoghue, and Holstein (DDH). Using these estimates and the calculated amplitudes, predictions for the spin rotation of a neutron through a deuteron target are given with a value of 1.8 × 10-8 rad cm-1. Also given are the longitudinal analyzing power in neutron deuteron scattering with a polarized neutron yielding 2.2 × 10-8, and a polarized deuteron giving 4.0 × 10-8. These observables are discussed in the broader context of hadronic parity violation and as possible future experiments to determine the values of the five low energy parity violating constant present in pionless effective theory.