The 2008 measurement of the electron magnetic moment is the most precisely measured property of an elementary particle, with an astonishing precision of 0.28 parts per trillion. It makes possible the most precise determination of the fine structure constant and the most precise test of quantum electrodynamics and the Standard Model of particle physics. This thesis describes the installation of a new apparatus designed to have improved stability, more optimal control over the radiation field and inhibited spontaneous emission, and narrower resonance lines. / Physics

In this thesis I develop a formalism for analyzing quantum optics in photonic crystal slab cavities which may be coupled, lossy, and non-orthogonal. Using a tight-binding approximation I find classical coupled-cavity quasimodes which overlap in space and frequency. These classical modes are used to develop a multiphoton basis for quantum optics with non-orthogonal photon states. I develop creation and annihilation operators with a novel commutation relation as a consequence of the nonorthogonality of the quasimodes. With these operators the effective Hamiltonian, number operator, electric field operator and quadrature operators are obtained. The quantum jump technique is applied to handle the effects of loss. This technique is compared with the master equation, and conditions for the quantum jump technique being preferable are described. The quantum jump technique is implemented numerically, allowing for time-dependent linear and X(2) non-linear pumping. I use a combination of analytic results and characteristic functions to examine the evolution of coherent and squeezed states in a single lossy quasimode. The analysis is then extended to two nonorthogonal quasimodes. States are investigated using reduced characteristic functions. / Thesis (Master, Physics, Engineering Physics and Astronomy) -- Queen's University, 2013-09-27 12:00:10.281

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