Kapahi, Connor2025-10-202025-10-202025-10-202025-10-17https://hdl.handle.net/10012/22596In this thesis, several projects from biomedical optics measurements of the retina to precision gravimetric designs with neutron interferometers are presented, united by the common theme of applied quantum information techniques to develop next-generation precision metrological instruments. In particular, we introduce theoretical tools for analyzing neutron optical experiments and highlight parallels between neutron and light optics. These tools are applied to a new neutron prism design, demonstrating significantly higher transmission than traditional designs. Designs for devices applying these techniques, including a neutron Fresnel prism, spectrum analyzer, and spin collimator, are discussed. Potential advantages in neutron flux and spectrum resolution are quantified for these designs. The isometry between neutron spin and the polarization of light is exploited to validate the neutron spin collimator experimentally. Applications of structured states of light and experiments applying spin-orbit states to create patterns in the human visual system are described. Results demonstrate an increase in the perceived extent of these patterns, from 3° for Haidinger's Brush to 10° for a spin-orbit state. Work demonstrating a new method of generating a lattice of spin-orbit states in light is applied to neutron optics. Throughout the preceding experiments, methods of modeling neutron optics experiments with light and a semi-classical path-integral approximation have been developed. These methods are then applied to design an experiment that measures the gravitational constant using a neutron interferometer. A three-phase grating moiré interferometer (3-PGMI) design is first tested with infrared light. The deflection caused by a wafer sample is measured with the 3-PGMI and found to match direct measurements. The path-integral model is then applied to determine the uncertainty in the gravitational constant that can be achieved with a near-term measurement with a neutron 3-PGMI. An experiment to measure the gravitational constant is described, with an uncertainty budget, resulting in a measurement to 150 ppm. Potential corrections to previous experiments measuring the gravitational constant, due to lunar gravitational forces are quantified. Future applications of the tools and techniques described in this thesis are then discussed.enneutron opticsneutron interferometrystructured wavesgravitational constantentoptic phenomenonDoctoral Thesis