Impact and Mitigation of Wavefront Distortions in Precision Interferometry

Wavefront distortions, arising from mismatches, degrade quantum noise mitigation strategies in precisionmetrological devices, such as LIGO. Direct mode decomposition quantifies wavefront distortions in termsof solutions to the paraxial wave equation. The first part of this thesis develops high dynamic rangemode decomposition, by using photodiode readout and developing novel alignment strategies. Limiting noise sources are suppressed and the noise performance is characterized in the 1 mHz to 10 kHz frequency range.

Higher order, Hermite-Gauss, spatial modes may be used in precision metrology to sidestep thermal noise.This thesis demonstrates the production of higher order, Hermite-Gauss spatial modes, but, also finds that these modes are more susceptible to mode mismatch losses than the fundamental mode.

Another form of precision metrology is atomic interferometry. Optical cavities reject wavefront distor-tions in the laser beams used to manipulate the atoms; however, they introduce an elongation of thebeam-splitter pulses. A numerical study finds that this elongation suppresses the atomic excitation prob-ability, when the transition is not exactly on resonance, reducing atomic flux. Long baseline, high finesseresonators are particularly affected.

The closing section of this thesis describes a tool used to validate numerical models used throughout thiswork.