archives@tulane.edu / The Feynman diagrams have become a highly valued tool for complex calculations and understanding the physics of elementary particles within the framework of quantum field theory. In this thesis, we present an overview on constructing and utilizing Feynman diagrams in quantum field theory along with an overview of quantum field theory itself. We begin with a review of prerequisite topics then progress to discussing symmetries using Lie groups, algebras, and representation theory. We then use the representations of the Lorentz group to derive the fields in a classical context then proceed with quantization to create the corresponding quantum fields while providing a thorough analysis of each quantum field. Path integrals are constructed for each quantum field by deriving their propagators then the formulas for scattering are derived in the context of quantum field theory. Quantum symmetries are briefly explored with the intention of quantizing classical results such as Noether's theorem. Then we construct interacting quantum field theories and introduce the Feynman diagrams and Feynman rules for different interaction theories and provide examples and applications of the Feynman diagrams. The physics behind the diagrams is carefully analyzed and interpreted. Finally, we conclude this thesis with a summary of what we have covered along with possible routes of study after mastering the contents of this thesis that will lead to current research topics. / 1 / Junhyup Sung

Nonclassical states of light are of increasing interest due to their applications in the emerging field of quantum information processing and communication. Squeezed light is such a state of the electromagnetic field in which the quantum noise properties are altered compared with those of coherent light. Squeezed light and squeezed vacuum states are potentially useful for quantum information protocols as well as optical measurements, where sensitivities can be limited by quantum noise. We experimentally study a source of squeezed vacuum resulting from the interaction of near-resonant light with both cold and hot Rb atoms via the nonlinear polarization self-rotation effect (PSR). We investigate the optimal conditions for noise reduction in the resulting squeezed states, reaching quadrature squeezing levels of up to 2.6 dB below shot noise, as well as observing noise reduction for a broad range of detection frequencies, from tens of kHz to several MHz. We use this source of squeezed vacuum at 795 nm to further study the noise properties of these states and how they are affected by resonant atomic interactions. This includes the use of a squeezed light probe to give a quantum enhancement to an optical magnetometer, as well as studying the propagation of squeezed vacuum in an atomic medium under conditions of electromagnetically induced transparency (EIT). We also investigate the propagation of pulses of quantum squeezed light through a dispersive atomic medium, where we examine the possibilities for quantum noise signals traveling at subluminal and superluminal velocities. The interaction of squeezed light with resonant atomic vapors finds various potential applications in both quantum measurements and continuous variable quantum memories.

In this dissertation, we use lattice quantum chromodynamics to explore the radiative transitions of πK to K, to calculate the radiative width of the resonant K*(892) which appears in the P-wave πK → γK transition amplitude. The matrix elements are extracted from three-point functions calculated in a finite-volume discretized lattice with a pion mass of 284 MeV. The finite-volume amplitudes, which are constrained over a large number of πK energy points and four-momentum transfers, are mapped to the infinite volume transition amplitude by using the Lellouch-Lüscher formalism. The radiative width is determined to be 35(8) keV by analytically continuing the amplitude into the complex energy plane and calculating the residue at the K* pole.

No description available.

Apesar de ser um experimento bem conhecido na literatura relacionada ao estudo da informação quântica, o Oscilador Paramétrico Ótico (OPO) operando acima do limiar não forneceu sempre os resultados esperados por sua teoria, pois apresentava excesso de ruído na fase de seus feixes, de origem desconhecida. Neste trabalho apresentamos de forma sistemática a teoria padrão do Oscilador Paramétrico Ótico no contexto quântico. Além disso, introduzimos um modelo ad-hoc para o excesso de ruído de fase do OPO que reproduz os resultados obtidos em nossos experimentos. Em nosso modelo, inserimos um ruído na fase de cada feixe do OPO proporcional a intensidade dos campos intracavidade. Este ruído apresenta correlações não perfeitas entre os feixes, como foi demonstrado experimentalmente. Apesar de desconhecidas a origem desse excesso de ruído, temos indicações de que ele é causado por centros expalhadores de luz no cristal do OPO devido a presença de fônons de origem térmica. / In spite of the fact that the Optical Parametric Oscillator (OPO) is one of the most known experiments related with quantum information research, its experimental results did not have a good agreement with the theory, in the above threshold regime, because of an unexpected excess noise in the phase quadrature on its beams. In this work we sistematicaly present the quantum theory of OPO. Moreover, we introduce an ad-hoc model for the excess noise in the phase quadrature in the OPO that reproduces our experimental data. In our model, the excess noise in the phase quadrature is proportional of the intensity of each OPO beam. This noise presents non-perfect correlations among the fields, as is experimentaly observed. Despite of the unknown origin of this excess noise, we have some indications that it is caused by scattering centers produced by fonons of thermal origin.

Beams of light can carry spin and orbital angular momentum. Spin angular momentum describes how the direction of the electric field rotates about the propagation axis, while orbital angular momentum describes the rotation of the field amplitude pattern. These concepts are well understood for monochromatic beams, but previous theoretical studies have constructed polychromatic superpositions where the connection between angular momentum and rotation of the electric field becomes much less clear. These states are superpositions of two states of light carrying opposite signs of angular momentum and slightly detuned frequencies. They rotate at the typically small detuning frequency and thus we call them slowly rotating modes of light. Strangely, some of these modes appear to rotate in the direction opposing the sign of their angular momentum, while others exhibit overall rotation with no angular momentum at all! These findings have been the subject of some controversy, and in 2012, Susanna Todaro (HMC ’12) and I began work on trying to shed light on this “angular momentum paradox." In this thesis, I extend previous work in theory, simulation, and experiment. Via theory and modeling in Mathematica, I present a possible intuitive explanation for the angular momentum paradox. I also present experimental realization of slowly rotating spin superpositions, and outline the steps necessary to generate slowly rotating orbital angular momentum superpositions.

The current thesis is based on the research of the psychoanalytical concepts of agency, subject and structure while it correlates the same notions with the clinical observations of patients with personality disorder in crisis [patient group]. It also proposes an answer to the problem of agency and structure, incorporating structuration theory and recursivity. This is done by the construction and outline of a new framework, which is designated as the scaffolding model. The analysis of the analytical observations demonstrated that patients present in the clinical arena with dual narratives that include two accounts, which have been identified as the problem and the solution formed scenarios. This twofold situation is guided by a dyadic functioning process, which is a functional pattern that not only regulates language but it also maintains an integrated function in the brain and in the mind of the subject. It constitutes a new structure, which associates the brain-mind and language [+senses], forming a “self-organization system”. Agency, here, is the power or vacuum that allows symbolic action. This research offers a new tool in the treatment of members of the patient group or in the treatment of subjects who present ambivalently or in conflict. This new approach designated as dual narratives facilitate a different perspective than the ones already established, such as cognitive analytical therapy, which give answers to the same clinical situations. Dual narratives work at two levels. This is done by preventing risks and by looking into the causes of the ambivalence of the subject, using Lacanian concepts, such as the notion of the signifier, and exploring the subjective position.

Apesar de ser um experimento bem conhecido na literatura relacionada ao estudo da informação quântica, o Oscilador Paramétrico Ótico (OPO) operando acima do limiar não forneceu sempre os resultados esperados por sua teoria, pois apresentava excesso de ruído na fase de seus feixes, de origem desconhecida. Neste trabalho apresentamos de forma sistemática a teoria padrão do Oscilador Paramétrico Ótico no contexto quântico. Além disso, introduzimos um modelo ad-hoc para o excesso de ruído de fase do OPO que reproduz os resultados obtidos em nossos experimentos. Em nosso modelo, inserimos um ruído na fase de cada feixe do OPO proporcional a intensidade dos campos intracavidade. Este ruído apresenta correlações não perfeitas entre os feixes, como foi demonstrado experimentalmente. Apesar de desconhecidas a origem desse excesso de ruído, temos indicações de que ele é causado por centros expalhadores de luz no cristal do OPO devido a presença de fônons de origem térmica. / In spite of the fact that the Optical Parametric Oscillator (OPO) is one of the most known experiments related with quantum information research, its experimental results did not have a good agreement with the theory, in the above threshold regime, because of an unexpected excess noise in the phase quadrature on its beams. In this work we sistematicaly present the quantum theory of OPO. Moreover, we introduce an ad-hoc model for the excess noise in the phase quadrature in the OPO that reproduces our experimental data. In our model, the excess noise in the phase quadrature is proportional of the intensity of each OPO beam. This noise presents non-perfect correlations among the fields, as is experimentaly observed. Despite of the unknown origin of this excess noise, we have some indications that it is caused by scattering centers produced by fonons of thermal origin.

Numerical solutions of quantum mechanical problems have witnessed tremendous advances over the past years. In this thesis, we develop an iterative approach to problems of double-well potentials and their variants with parity-time-reversal symmetry- breaking perturbations. We show that the method provides an efficient scheme for obtaining accurate energies and wave functions. We discuss in this thesis potential applications to a variety of related topics such as phase transitions, symmetry breaking, and external field-induced effects.

The major challenges in trapped-ion quantum computation are to scale up few-ion experiments to many qubits and to improve control techniques so that quantum logic gates can be carried out with higher fidelities. This thesis re- ports experimental progress in both of these areas. In the early part of the the- sis we describe the fabrication of a surface-electrode ion trap, the development of the apparatus and techniques required to operate it and the successful trap- ping of ⁴⁰Ca⁺ ions. Notably we developed methods to control the orientation of the principal axes and to minimise ion micromotion. We propose a repumping scheme that simplifies heating rate measurements for ions with low-lying D levels, and use it to characterise the electric field noise in the trap. Surface-electrode traps are important because they offer a route to dense integration of electronic and optical control elements using existing microfabrication technology. We explore this scaling route by testing a series of three traps that were microfabricated at Sandia National Laboratories. Investigations of micromotion and charging of the surface by laser beams were carried out and improvements to future traps are suggested. Using one of these traps we also investigated anomalous electrical noise from the electrode surfaces and discovered that it can be reduced by cleaning with a pulsed laser. A factor of two de- crease was observed; this represents the first in situ removal of this noise source, an important step towards higher gate fidelities. In the second half of the thesis we describe the design and construction of an experiment for the purpose of replacing laser-driven multi-qubit quantum logic gates with microwave-driven ones. We investigate magnetic-field-independent hyperfine qubits in ⁴⁰Ca⁺ as suitable qubits for this scheme. We make a design study of how best to integrate an ion trap with the microwave conductors required to implement the gate and propose a novel integrated resonant structure. The trap was fabricated and ions were successfully loaded. Single-qubit experiments show that the microwave fields above the trap are in excellent agreement with software simulations. There are good prospects for demonstrating a multi-qubit gate in the near future. We conclude by discussing the possibilities for larger-scale quantum computation by combining microfabricated traps and microwave control.